ACC501 — Final Term Summary (Lectures 23–45)

📘 Lecture 23 — ZERO GROWTH STOCKS

📖 Overview: This lecture covers three main types of stock valuation models based on dividend patterns: zero growth stocks, constant growth stocks, and non-constant growth stocks. Understanding these models is essential for determining the fair value of common shares in different dividend scenarios.

🗂️ Topics Covered

The lecture covers zero growth stocks valued as perpetuities, constant growth stocks using the dividend growth model, the relationship between stock price growth and dividend growth, and non-constant growth stocks where dividends change over time before settling into steady growth. It includes multiple numerical examples demonstrating each valuation approach.

📝 Lecture Summary

ZERO GROWTH STOCKS

A share of common stock in a company with a constant dividend is termed as zero growth type of stocks. This implies that D₁ = D₂ = D₃ = D = constant. Since the dividend is always the same, the stock can be viewed as an ordinary perpetuity with a cash flow equal to D every period.

The per share value is P₀ = D/R, where R is the required rate of return.

🔑 Definition — Zero Growth Stock: A common stock where dividends remain constant over time, never growing.

📐 Formula: P₀ = D/R → The stock price equals the constant dividend divided by the required rate of return.

📌 Example: CVP corporation has a policy of paying a $10 per share dividend every year indefinitely. If the required rate of return is 20%, the value of a share is $10/0.20 = $50 per share.

Constant Growth Stocks

Stocks where dividends grow at a steady rate are termed as having a growth rate g. If we let D₀ be the dividend just paid, then the next dividend D₁ is D₁ = D₀ × (1 + g). The dividend in two periods is D₂ = D₁ × (1 + g) = D₀ × (1 + g)². Generalizing: Dₜ = D₀ × (1 + g)ᵗ.

An asset with cash flows that grow at a constant rate forever is called a growing perpetuity. The reason for constant growth of dividend lies in the fact that companies have this aspect as an explicit goal.

As long as the growth rate g is less than the discount rate R, the present value of cash flows can be written as P₀ = D₀(1 + g)/(R - g) = D₁/(R - g). This is commonly known as the dividend growth model.

🔑 Definition — Constant Growth Stock: A stock where dividends grow at a constant rate g every period.

📐 Formula: P₀ = D₁/(R - g) = D₀(1 + g)/(R - g) → The stock price equals next year's dividend divided by the difference between the required return and the growth rate.

📌 Example: Suppose D₀ is $2.30, R is 13% and g is 5%. The price per share is P₀ = $2.30 × 1.05/(0.13 - 0.05) = $2.415/0.08 = $30.19.

The price of the stock at any time t is Pₜ = Dₜ(1 + g)/(R - g) = Dₜ₊₁/(R - g). The dividend growth model makes the implicit assumption that the stock price will grow at the same constant rate as the dividend. P₄ = P₀ × (1 + g)⁴.

If the growth rate g is bigger than discount rate R, then the present value of dividends keeps getting bigger and bigger, so the stock price is infinitely large. The same is true if growth rate and discount rate are equal.

📐 Formula for any growing perpetuity: PV = C₁/(R - g) = C₀(1 + g)/(R - g)

📌 Example — GG Company: The next dividend is $4 per share, investors require 16% return, and dividends grow by 6% every year. The price today is P₀ = $4/(0.16 - 0.06) = $40. The dividend in 4 years is D₄ = $4 × 1.06³ = $4.764. The price in 4 years is P₄ = $4.764 × 1.06/(0.16 - 0.06) = $5.05/0.10 = $50.50. Verify: P₄ = $40 × 1.06⁴ = $50.50. 💡 Why this matters: This shows that stock price grows at the same rate as dividends in the constant growth model.

Non-Constant Growth Stocks

Consider a company currently not paying any dividends. You predict in 5 years the company will pay a dividend for the first time, say $0.50, growing at 10% per year indefinitely. The required rate is 20%.

First calculate what it will be worth once dividends are paid, then calculate the present value of that future price to get today's price. The 1st dividend will be paid in 5 years. The price in 4 years will be P₄ = D₅/(R - g) = $0.50/(0.20 - 0.10) = $5. Current value by discounting back four years at 20%: P₀ = $5/1.20⁴ = $5/2.0736 = $2.41.

For non-constant growth with dividends in intermediate years: Consider dividend forecasts: Year 1 = $1.00, Year 2 = $2.00, Year 3 = $2.50. After year 3, dividend grows at constant 5% per year. Required return is 10%.

First compute the present value of the stock price three years down the road, then add the present value of dividends paid between now and then. The price in 3 years is P₃ = D₃(1 + g)/(R - g) = $2.50 × 1.05/(0.10 - 0.05) = $52.50.

Total value: P₀ = D₁/(1+R)¹ + D₂/(1+R)² + D₃/(1+R)³ + P₃/(1+R)³ = $1/1.10 + $2/1.10² + $2.50/1.10³ + $52.50/1.10³ = $0.91 + $1.65 + $1.88 + $39.44 = $43.88.

🔑 Definition — Non-Constant Growth Stock: A stock where dividends grow at different rates over different time periods before eventually settling into constant growth.

⭐ Key Takeaways

The three stock valuation models depend entirely on the dividend pattern: zero growth uses the perpetuity formula P₀ = D/R, constant growth uses the dividend growth model P₀ = D₁/(R-g) where stock price grows at the same rate g as dividends, and non-constant growth requires discounting each dividend separately plus the terminal price. The growth rate must always be less than the required return for finite stock prices. For non-constant growth, always compute the future stock price when dividends become constant, then discount everything back to present.

🧠 Quick Revision Questions

1. What is the formula for a zero growth stock and why does it work?
2. Under what condition does the constant growth model give an infinite stock price?
3. In the GG Company example, why is P₄ exactly equal to P₀ × (1+g)⁴?
4. For a non-constant growth stock that pays its first dividend in 5 years, why do we compute the stock price in year 4 (not year 5)?
5. In the last example with dividends of $1, $2, and $2.50, what is D₄ and how is it used?

📘 Lecture 24 — NON-CONSTANT GROWTH STOCKS

📖 Overview: This lecture examines stock valuation when growth rates are not constant, using a case study of supernormal growth. It also explores the components of required return and provides a detailed overview of common and preferred stock features, including shareholder rights, dividend policies, and the structure of stock markets.

🗂️ Topics Covered

This lecture covers non-constant growth stock valuation using the CR Inc. supernormal growth case, calculation of dividends during supernormal and stable growth periods, and determination of stock price using present value of future dividends. It then explains the components of required return (dividend yield and capital gains yield) and provides a summary of stock valuation methods. Finally, it discusses common stock features including shareholder rights, cumulative vs. straight voting, proxy voting, classes of stock, dividends, and preferred stock features, along with an overview of primary and secondary stock markets.

📝 Lecture Summary

Non-Constant Growth Stocks

Companies may experience periods of supernormal growth where growth rates are unsustainably high for a limited time. To value such stocks, we must calculate dividends during the supernormal growth period and then find the stock price when growth stabilizes. The price at the end of the supernormal period is calculated using the constant growth model for the long-run growth rate.

CR Inc.: A Case of Supernormal Growth

• Company growing at 30% per year for 3 more years, then drops to 10% indefinitely.
• Total dividends just paid: $5 million; required return: 20%.
• Year 1 Dividend: $5.00 × 1.3 = $6.500 million
• Year 2 Dividend: $6.50 × 1.3 = $8.450 million
• Year 3 Dividend: $8.45 × 1.3 = $10.985 million

The price at time 3 (P₃) is calculated using the long-run growth rate (g = 10%): P₃ = D₃ × (1 + g) / (R - g) P₃ = $10.985 × 1.10 / (0.20 – 0.10) = $120.835 million

To determine the value today (P₀), we need the present value of all dividends plus the present value of P₃: P₀ = D₁/(1+R)¹ + D₂/(1+R)² + D₃/(1+R)³ + P₃/(1+R)³ P₀ = $6.50/1.10¹ + $8.45/1.10² + $10.985/1.10³ + $120.835/1.10³ P₀ = $5.42 + $5.87 + $6.36 + $69.93 = $87.58 million

📐 Per share value: $87.58 million / 20 million shares = $4.38 per share

Components of Required Return

From the dividend growth model P₀ = D₁/(R - g), rearranging to solve for R gives: R = D₁/P₀ + g

This tells us total return (R) has two components:

• Dividend Yield (D₁/P₀): Expected cash dividend divided by current price, similar to current yield on a bond
• Capital Gains Yield (g): The rate at which stock price grows

📌 Example: Stock selling for $20/share, next dividend $1, growth rate 10%. R = $1/20 + 10% = 5% + 10% = 15% Verify: P₁ = $1 × 1.10 / (0.15 – 0.10) = $1.10/0.05 = $22 Stock price grew by 10% ($20 to $22); dividend yield = $1/$20 = 5%; capital gains yield = $2/$20 = 10%; total return = 15%.

💡 Why this matters: This decomposition helps investors understand expected sources of return and compare stocks with different growth characteristics.

Summary of Stock Valuation

• General Case: P₀ = present value of all future dividends D₁, D₂, D₃..., discounted at required return R
• Constant Growth: If dividend grows at steady rate g, P₀ = D₁/(R - g) — the dividend growth model
• Zero Growth: If dividend is constant (g=0), P₀ = D/R
• Non-constant Growth: Requires calculating dividends period-by-period during supernormal growth, then using constant growth model for stable period
• Required return: R = D₁/P₀ (dividend yield) + g (capital gains yield)

Common Stock Features

Common stocks have no special preference either in paying dividends or in bankruptcy.

Shareholder Rights: Shareholders control the organization by electing directors who hire management.

Cumulative Voting: Permits minority participation. Total votes = number of shares × number of directors to be elected. Votes can be distributed however the shareholder wishes.

• A formula: [1/(N+1)% of stocks + 1] shares guarantees a seat, where N = number of directors to be elected.
• 📌 Example: Sami (20 shares) and Junaid (80 shares) electing 4 directors. Sami casts 20×4=80 votes for himself; Junaid casts 80×4=320 votes but cannot give all 4 candidates more than 80 votes each. Sami is guaranteed a seat.

Straight Voting: Directors elected one at a time. Majority shareholder (50%+1 shares) wins all seats — "all or nothing."

Staggering: Only a fraction of directors are up for election at one time. Makes it harder for minority to elect a director under cumulative voting and makes takeover attempts less likely.

Proxy Voting: A proxy is a grant of authority to someone else to vote the shareholder's shares. Management seeks proxies; dissatisfied shareholders may start a proxy fight to replace management.

Classes of Stocks: Some firms have multiple classes with unequal voting rights, primarily to raise equity while maintaining control.

Other Rights: Right to share proportionately in dividends; right to share in assets after liquidation; right to vote on major matters (e.g., mergers); preemptive right — right to share proportionately in any new stock sold before it's offered to the public.

Dividends: Return on capital paid to shareholders at the discretion of the board of directors.

• Not a liability unless declared
• Not a business expense (not tax deductible)
• Dividends received by individuals are ordinary income (fully taxable); corporations can exclude a percentage of dividends received from other corporations

Preferred Stock Features

Preferred stock has dividend priority over common stock, normally with fixed dividend rate, sometimes without voting rights. Preference means preferred shareholders must receive dividends before common shareholders.

Stated Value: Preferred shares have stated liquidating value; dividends are described in dollars per share.

Accumulation of Dividends: Most preferred dividends are cumulative — if not paid in a year, they are carried forward as arrearage. Unpaid preferred dividends are not debts; directors can defer indefinitely, but common stockholders must also forego dividends.

Is Preferred Stock Debt? Preferred shareholders receive stated dividends and stated value; hold credit ratings like bonds; sometimes convertible into common stock and callable.

The Stock Market

• Primary Market: Where new securities are originally sold to investors (companies raise money)
• Secondary Market: Where previously issued securities are traded among investors

Dealer: Buys and sells securities from maintained inventory. Bid price = price dealer pays; ask price = price dealer sells; difference = spread.

Broker: Arranges transactions among investors without buying/selling for own account; facilitates trades.

⭐ Key Takeaways

The most critical concepts from this lecture are: (1) For non-constant growth stocks, you must calculate dividends during the supernormal period, find the terminal price using the constant growth model, then discount everything back to present value; (2) Required return R = Dividend Yield (D₁/P₀) + Capital Gains Yield (g), where g is both the dividend growth rate and the stock price appreciation rate; (3) Cumulative voting protects minority shareholders, with [1/(N+1)% + 1 share] guaranteeing a board seat, while straight voting allows majority control; (4) Preferred stock has dividend priority over common stock, accumulated dividends may be carried forward as arrearage, and payment is at the board's discretion; (5) The primary market involves new securities issuance to raise capital, while the secondary market involves trading existing securities between investors through dealers (who maintain inventory) or brokers (who match buyers and sellers).

🧠 Quick Revision Questions

1. In the CR Inc. example, what is the terminal stock price (P₃) and how is it calculated using the long-run growth rate?
2. What are the two components of required return R according to the dividend growth model, and what does each represent?
3. Under cumulative voting, what percentage of shares plus one share guarantees a board seat when N directors are to be elected?
4. What is the difference between cumulative voting and straight voting in terms of minority shareholder representation?
5. What distinguishes a dealer from a broker in the stock market, and what are the bid price, ask price, and spread?

📘 Lecture 25 — Preferred Stock Features

📖 Overview: This lecture introduces the features of preferred stock, including dividend priority, cumulative dividends, and the distinction between debt and equity. It then explains the structure of stock markets (primary vs. secondary) and the roles of dealers and brokers. Finally, it introduces capital budgeting and the concept of Net Present Value (NPV) for evaluating investment decisions.

🗂️ Topics Covered

The lecture covers preferred stock features like stated value and cumulative dividends, and debates whether preferred stock is debt or equity. It then distinguishes between primary and secondary stock markets, defining dealers and brokers. The main topic shifts to capital budgeting, focusing on estimating Net Present Value (NPV) and its rule for accepting or rejecting projects.

📝 Lecture Summary

Preferred Stock Features

Preferred stock has dividend priority over common stock, normally with a fixed dividend rate, sometimes without voting rights. "Preference" means preferred shareholders must receive a dividend before common shareholders are entitled to anything. Preferred shares have a stated liquidating value, and the cash dividend is described in dollars per share. A preferred dividend is not like bond interest; directors may decide not to pay it irrespective of net income. Dividends on preferred stock may be cumulative or non-cumulative; most are cumulative. If preferred stocks are cumulative and not paid in a particular year, they are carried forward as an arrearage. Unpaid preferred dividends are not debts of the firm. Directors can defer the preferred dividend indefinitely, but common stockholders must also forego dividends. Sometimes delayed payments are compensated by voting rights.

🔑 Definition — Cumulative Preferred Stock: A type of preferred stock where unpaid dividends accumulate and must be paid before any dividends can be paid to common stockholders.

Is Preferred Stock Debt or Equity?

Preferred shareholders are only entitled to receive a stated dividend and the stated value of their shares. Preferred stocks hold credit ratings much like bonds. They are sometimes convertible into common stock and are often callable.

The Stock Market

Shares of stock are bought and sold at stock exchanges. The stock market consists of the primary market (where new securities are originally sold to investors; companies sell securities to raise money) and the secondary market (where previously issued securities are traded among investors).

🔑 Definition — Dealer: An agent who buys and sells securities from a maintained inventory, standing ready to buy from investors wishing to sell and sell to investors wishing to buy. The price the dealer wishes to pay is the bid price; the price they sell for is the ask price. The difference is the spread.

🔑 Definition — Broker: An agent who arranges security transactions among investors, matching buyers with sellers, without buying or selling for their own accounts.

Capital Budgeting

Capital budgeting asks: "What long-term investment should the firm take on?" An investment is worth undertaking if it creates value, characterized by its worth in the marketplace being more than its cost. For example, buying a run-down house for $25,000, spending $25,000 on repairs (total $50,000), and then finding it is worth $60,000. The market value ($60,000) exceeds the cost ($50,000) by $10,000, creating $10,000 in value. A manager must identify the feasibility of investing $50,000 ahead of time — determining whether a proposed project will be worth more than it costs. The difference between an investment's market value and its cost is called the Net Present Value (NPV) . NPV measures how much value is created or added today by undertaking an investment. Capital budgeting is a search for investments with positive NPVs. Investment decisions are simplified when a market exists for similar assets; otherwise, we must estimate value using indirect market information.

💡 Why this matters: NPV is the core tool for determining if a project increases shareholder value.

Estimating Net Present Value

To estimate the value of a new business (e.g., fertilizer), we:

1. Estimate future cash flows.
2. Apply discounted cash flow (DCF) to estimate the present value of cash flows.
3. Estimate the difference between the present value of future cash flows and the cost of investment.

Example:

• Cash revenues: $20,000 per year
• Cash costs (including taxes): $14,000 per year
• Business life: 8 years
• Salvage value in 8 years: $2,000
• Project cost to launch: $30,000
• Discount rate: 15%
• Shares outstanding: 1,000

📐 Formula: Present Value (PV) = PV of annuity + PV of lump sum PV = $6,000 x (1 – 1/1.15⁸) / 0.15 + $2,000 / 1.15⁸ PV = $6,000 x 4.4873 + $2,000 / 3.0590 PV = $26,924 + $654 = $27,578

📐 Formula: Net Present Value (NPV) = Present Value of future cash flows – Initial Cost NPV = -$30,000 + $27,578 = -$2,422

📌 Example: Since NPV is negative (-$2,422), this is not a good investment. It would decrease the total value of stock by $2,422. With 1,000 shares outstanding, the impact is a loss of $2,422 / 1,000 = -$2.422 per share. If NPV were positive, the effect would be favorable.

This leads to the Net Present Value Rule: “An investment should be accepted if the net present value is positive and rejected if it is negative.” If NPV is zero, we are indifferent. The task of coming up with cash flows and the discount rate is more important than the discounting process itself.

⭐ Key Takeaways

Preferred stock has dividend priority over common stock, often with a cumulative feature where unpaid dividends accumulate as arrearage. The stock market consists of primary and secondary markets, with dealers buying/selling from inventory (earning the bid-ask spread) and brokers matching buyers and sellers. Capital budgeting uses NPV analysis: a project is accepted if its present value of future cash flows exceeds its initial cost (positive NPV), increasing shareholder value. The discounted cash flow (DCF) method is used to estimate the present value of future cash flows, and the NPV rule is the fundamental decision criterion for investments.

🧠 Quick Revision Questions

1. What does "cumulative" mean when referring to preferred stock dividends?
2. What is the difference between a dealer and a broker in the stock market?
3. A project costs $100,000 and is expected to generate a present value of future cash flows of $95,000. Should the project be accepted according to the NPV rule?
4. In the NPV calculation example, why was the investment considered "not good"?
5. What is the primary goal for a firm when using Net Present Value in capital budgeting?

📘 Lecture 26 — Using NPV

📖 Overview: This lecture explores the Net Present Value (NPV) rule for investment decisions and introduces the Payback Period as an alternative capital budgeting method. It demonstrates how NPV guides value-maximizing choices while critically examining the payback rule's strengths and weaknesses.

🗂️ Topics Covered

The lecture begins with the NPV rule and a practical example of launching a new product with projected cash flows over five years. It then introduces the Payback Period rule, showing how to calculate it using various examples, including a project with multiple payback periods. Finally, it compares the two methods, highlighting the payback rule's shortcomings like ignoring time value of money and its advantages like simplicity and liquidity focus.

📝 Lecture Summary

USING NPV

Given that the goal of financial management is to increase share value, the net present value rule states: "An investment should be accepted if the net present value is positive and rejected if it is negative." In the unlikely event that NPV is zero, we would be indifferent between taking and not taking the investment. Two important comments are made: first, the task of coming up with cash flows and the discount rate is much more important than the process of discounting itself. Second, the process of discounting cash flows only gives an estimated figure of NPV; the true NPV can be found by putting the investment for sale and seeing what we got for it.

💡 Why this matters: The NPV rule directly links investment decisions to the goal of maximizing shareholder wealth.

Suppose we are asked to decide whether or not to launch a new product. Based on projected costs and sales, we expect cash flows over a 5-year life to be $2,000 in the first two years, $4,000 in the next two, and $5,000 in the last year. It would cost about $10,000 to begin production. Given a 10% discount rate, we calculate the total value of the product by discounting its cash flow to present: PV = $2,000/1.1 + 2,000/1.1² + 4,000/1.1³ + 4,000/1.1⁴ + 5,000/1.1⁵ = $1,818 + 1,653 + 3,005 + 2,732 + 3,105 = $12,313 The present value of expected cash flows is $12,313, but the cost is $10,000, so the NPV is $12,313 – 10,000 = $2,313. Based on the NPV rule, we should take on the project.

🔑 Definition — Net Present Value (NPV) Rule: An investment should be accepted if the net present value is positive and rejected if it is negative.

The Payback Rule

The payback period is the amount of time required for an investment to generate cash flows sufficient to recover its initial cost. The rule is: "An investment is acceptable if its calculated payback period is less than some specified number of years."

🔑 Definition — Payback Period: The amount of time required for an investment to generate cash flows sufficient to recover its initial cost.

Suppose the initial investment is $60,000, and the cash flows are $20,000 in the first year and $90,000 in the second. The cash flows over the first two years are $110,000, so the project pays back sometime in the second year. After the first year, the project has paid back $20,000, leaving $40,000 to be recovered. This $40,000 is $40,000/90,000 = 4/9 of the second year's cash flows. Spreading this ratio over 365 days: 4/9 x 365 ≈ 162 days, meaning the payback period is just over 1 year and 5 months.

📌 Example: The projected cash flows from a proposed investment are: Year 1: $100, Year 2: $200, Year 3: $500. The project costs $500. After the first 2 years, cash flows total $300. After the 3rd year, the total cash flow is $800, so the project pays back between the end of year 2 and end of year 3. Out of $500 cash flows for the 3rd year, we need to cover $200, so we wait $200/500 = 0.40 years. The payback period is 2.4 years or about two years and five months.

Considering Projects A through E:

• Project A: Payback period is 2.6 years
• Project B: Never pays back
• Project C: Payback period is 4 years
• Project D: Has two payback periods (2 and 4 years, both correct)
• Project E: Unrealistic but pays back in 6 months, illustrating that a rapid payback does not guarantee a good investment

Compared to NPV, the payback period rule has several shortcomings: time value of money is ignored, it fails to consider risk differences, and it doesn't provide an objective basis for a particular cutoff period. The primary shortcomings are: by ignoring time value, we may be led to take investments worth less than they cost; by ignoring cash flows beyond cutoff, we may reject profitable long-term investments. Generally, it tends to bias us towards shorter-term investments.

However, the qualities of the payback period rule include: simple and easy to calculate, useful for large numbers of small investment decisions by corporations; its bias towards short-term projects emphasizes liquidity, i.e., quickly freeing up cash for other uses; and it adjusts for more uncertain cash flows expected later in a project's life (though by ignoring them altogether).

📌 Example: Consider Long-term vs. Short-term investments:

• Short: Year 0: -$250, Year 1: $100, Year 2: $200 (payback = 1 + $150/200 = 1.75 years)
• Long: Year 0: -$250, Year 1: $100, Year 2: $100, Year 3: $100, Year 4: $100 (payback = 2 + $50/100 = 2.5 years) With a cutoff of two years, Short is accepted and Long is not. However, requiring a 15% return: NPV (Short) = -$250 + 100/1.15 + 200/1.15² = -$11.81 NPV (Long) = -$250 + 100 x (1 – 1/1.15⁴)/.15 = $35.5 The NPV of the shorter-term investment is negative, diminishing shareholder equity, while the longer-term investment increases share value.

Summary

The payback period is a break-even measure in an accounting sense but not in an economic sense. It does not focus on the right issue of the impact of an investment on the value of stock. Its simplicity is helpful for decisions on minor investments.

Advantages: Easy to understand, adjusts for uncertainty of later cash flows, biased towards liquidity. Disadvantages: Ignores the time value of money, requires an arbitrary cutoff point, ignores cash flows beyond the cutoff date, biased against long-term projects such as research and development and new projects.

⭐ Key Takeaways

The NPV rule is the theoretically correct method for investment decisions because it directly measures the increase in shareholder value, accepting projects only when NPV is positive. The payback period, while simple and useful for emphasizing liquidity, has serious flaws: it ignores the time value of money, requires an arbitrary cutoff, and disregards cash flows after the payback point, potentially leading to value-destroying decisions by favoring short-term projects over profitable long-term ones.

🧠 Quick Revision Questions

1. According to the NPV rule, when should an investment be accepted?
2. What is the payback period for a project costing $500 with cash flows of $100 in year 1, $200 in year 2, and $500 in year 3?
3. Why might the payback rule lead to a decision that reduces shareholder value?
4. What are the two primary shortcomings of the payback period rule?
5. Give one advantage and one disadvantage of using the payback period rule.

📘 Lecture 27 — Average Accounting Return

📖 Overview: This lecture introduces two capital budgeting techniques: Average Accounting Return (AAR) and Internal Rate of Return (IRR). It explains how AAR uses accounting profits rather than cash flows, while IRR focuses on the discount rate that makes NPV zero, and highlights the strengths and weaknesses of both methods.

🗂️ Topics Covered

First, Average Accounting Return is defined and illustrated through a store investment example with a 5-year life, showing how average net income and average book value are calculated. Then, Internal Rate of Return is introduced as the discount rate that makes NPV zero, with trial-and-error calculation methods. Finally, Problems with IRR are examined, including non-conventional cash flows causing multiple rates of return and issues with mutually exclusive investments where NPV should be used instead of IRR for ranking decisions.

📝 Lecture Summary

Average Accounting Return

It is defined as some measure of average accounting profit divided by some measure of average accounting value. Specifically, it uses average net income and average book value.

A store investment example is provided:

• Required investment in improvements: $500,000
• Store has a 5-year life; investment is 100% depreciated over 5 years: $500,000 / 5 = $100,000 per year
• Tax rate is 25%

The projected financials are:

• Average net income is: [$100,000 + 150,000 + 50,000 + 0 + (-50,000)] / 5 = $50,000
• Average book value = ($500,000 + 0) / 2 = $250,000

📐 Formula: AAR = Average net income / Average book value = $50,000 / $250,000 = 0.20 or 20%

The AAR rule states: “A project is acceptable if its average accounting return exceeds a target average accounting return.”

Drawbacks of AAR:

• It is not a rate of return in any meaningful economic sense, as it ignores the time value of money.
• It lacks an objective or target AAR to be compared with.
• It focuses on net income and book value rather than cash flow and market value.

Advantages:

• Easy to calculate.
• Needed information will usually be available.

Internal Rate of Return

With IRR, we try to find a single rate of return that summarizes the merits of a project. This rate is an “internal” rate because it only depends on the cash flows of a particular investment, not on rates offered elsewhere.

Consider a project that costs $100 today and pays $110 in one year. It pays a return of 10%, which is the internal rate of return.

The IRR Rule states: “Based on IRR rule an investment is acceptable if the IRR exceeds the required return. It should be rejected otherwise.”

For this example, the NPV at discount rate R is: NPV = -$100 + 110/(1 + R). To find the break-even discount rate, we set NPV equal to zero and solve for R:

• NPV = 0 = -$100 + 110/(1 + R)
• $100 = $110/(1 + R)
• 1 + R = $110/100 = 1.10
• R = 10%

Thus, “the IRR on an investment is the required return that results in a zero NPV when it is used as the discount rate.”

For a more complicated investment with cash flows of $60 per year for two years and a cost of $100, we find IRR by equating NPV to zero: NPV = 0 = -$100 + 60/(1 + IRR) + 60/(1 + IRR)²

The IRR is found by trial and error:

• At 0%: NPV = $20.00
• At 10%: NPV = $4.13
• At 15%: NPV = -$2.46

The IRR is about 13.1%. If the required return is less than 13.1%, we would take this investment; otherwise, reject it.

Another example: A project costs $435.44 with cash flows of $100 in year 1, $200 in year 2, and $300 in year 3.

• At 0%: NPV = $164.56
• At 10%: NPV = $46.15
• At 15%: NPV = $0.00
• At 20%: NPV = -$39.61

The IRR is 15%. At 18% required return, we should not take this investment because the IRR (15%) is less than the required return (18%).

IRR and NPV rules always lead to identical decisions as long as:

• Project’s cash flows are conventional (first cash flow is negative and rest are positive).
• Projects are independent (decision to accept or reject one project does not affect others).

💡 Why this matters: The NPV profile graph shows that when NPV > 0, the discount rate is less than the IRR, and when NPV < 0, the discount rate is greater than the IRR, confirming that IRR is the break-even point.

Problems with IRR

Problems with IRR arise when cash flows are non-conventional or when comparing two or more investments.

Non-conventional Cash Flows: A mining project requires a $60 investment. Cash flows in year 1 are $155, but in year 2, $100 must be spent to restore the terrain, making both year 0 and year 2 negative.

• At 0%: NPV = -$5.00
• At 10%: NPV = -$1.74
• At 20%: NPV = -$0.28
• At 30%: NPV = $0.06
• At 40%: NPV = -$0.31

This creates a multiple rates of return problem, with IRRs of 25% and 33⅓%. The NPV is positive only if the required return is between 25% and 33⅓%. The IRR rule breaks down completely here, while NPV works just fine.

💡 Moral of the Story: When cash flows are not conventional, the obvious question “What is the rate of return?” may not be answered, although NPV works just fine.

Mutually Exclusive Investments: If two investments are mutually exclusive, taking one means you cannot take the other. The question is: “which investment is best?” The answer is the one with the largest NPV.

Example of mutually exclusive investments:

• IRR for A is 24%
• IRR for B is 21%

NPV at different discount rates:

The crossover point is at approximately 11.1%.

• At discount rates less than 11.1%, NPV for B is higher, so B is better even though A has a higher IRR.
• At discount rates greater than 11.1%, NPV for A is higher, so A is better.

Moral of the Story: Whenever we have mutually exclusive investments, we should not rank them based on their returns. IRR can be misleading in determining the best investment. Instead, we should look at their relative NPVs to avoid the possibility of choosing incorrectly.

Qualities of IRR:

• Most widely used capital budgeting method.
• Easily communicated and understood.
• We can estimate IRR even if we don’t know the discount rate.

⭐ Key Takeaways

The lecture contrasts AAR and IRR as capital budgeting tools. AAR is simple but flawed because it uses accounting profits and ignores the time value of money. IRR is more widely used as it focuses on cash flows and the discount rate that makes NPV zero; however, IRR can be misleading with non-conventional cash flows (causing multiple rates of return) and when comparing mutually exclusive investments where NPV should be the deciding factor. The fundamental takeaway is that for mutually exclusive projects, always use NPV for ranking decisions, not IRR.

🧠 Quick Revision Questions

1. What is the formula for Average Accounting Return (AAR), and what are its main drawbacks?
2. How is the Internal Rate of Return (IRR) defined in relation to Net Present Value (NPV)?
3. Under what conditions do the IRR and NPV rules always lead to identical decisions?
4. What problem arises when calculating IRR for a project with non-conventional cash flows?
5. When comparing two mutually exclusive investments, why might the one with a lower IRR be the better choice?

📘 Lecture 28 — PROFITABILITY INDEX

📖 Overview: This lecture introduces the Profitability Index (PI) as a capital budgeting tool that measures value created per dollar invested. It also discusses why firms use multiple evaluation criteria in practice and provides a historical comparison of capital budgeting techniques used by CFOs.

🗂️ Topics Covered

The lecture covers the definition and calculation of Profitability Index, its advantages and disadvantages, ranking problems with mutually exclusive investments, capital budgeting practice under uncertainty, historical trends in usage of various capital budgeting techniques (Payback, AAR, IRR, NPV), and a summary of all investment criteria including discounted cash flow methods and accounting criteria.

📝 Lecture Summary

PROFITABILITY INDEX

The Profitability Index (PI), also called the benefit-cost ratio, is defined as the present value of the future cash flows divided by the initial investment. If a project costs $200 and the present value of its future cash flows is $220, then PI = $220 / 200 = 1.10. The NPV for this investment is $20, making it desirable. For a positive NPV investment, PI will be greater than 1.00, and less than 1.00 for a negative NPV investment.

The PI of 1.10 tells us that per dollar invested, $1.10 in value or $0.10 in NPV results. Thus, PI measures value created per dollar invested. It is often proposed as a measure of performance for government or other non-profit investments. When capital is scarce, it is a sensible approach to allocate it to those projects with the highest PI.

🔑 Definition — Profitability Index (PI): The present value of future cash flows divided by the initial investment. 📐 Formula: PI = PV of Future Cash Flows / Initial Investment → measures value created per dollar invested. 📌 Example: An investment costs $5 and has a $10 PV (NPV = $5, PI = 2). Another investment costs $100 and has a $150 PV (NPV = $50, PI = 1.50). If these are mutually exclusive, the second is preferred despite a lower PI, because it creates more total value.

Ranking Problem: The Profitability Index can lead to incorrect decisions when comparing mutually exclusive investments, similar to the ranking problem with IRR. While PI shows value per dollar, a lower PI project may create more total NPV.

Advantages of PI:

• Closely related to NPV, generally leading to identical decisions
• Easy to understand and communicate
• May be useful when available investment funds are limited

Disadvantages of PI:

• May lead to incorrect decisions in comparisons of mutually exclusive investments

Capital Budgeting Practice

Firms use alternative procedures even though NPV seems to tell us directly what we want to know because we operate under considerable uncertainty. We can only estimate the NPV, and the true NPV might be quite different. Since the true NPV is unknown, the financial manager seeks clues to assess the reliability of the estimated NPV. For this purpose, firms often use multiple criteria for evaluating a proposal.

If an investment has a positive NPV, a short payback, and a very high AAR, all indicators give a green signal — payback and AAR are consistent with the conclusion that NPV is positive. If there is a positive estimated NPV, a long payback, and a low AAR, this could be a good investment, but we should be much more careful since we are getting conflicting signals. If the estimated NPV is based on projections in which we have little confidence, then further analysis is probably in order.

💡 Why this matters: Multiple criteria help managers assess the reliability of NPV estimates and avoid making decisions based on unreliable projections.

A Historical Comparison of Primary Use of Various Capital Budgeting Techniques (1959-1981):

• Payback period declined from 34% (1959) to 5.0% (1981)
• Average Accounting Return declined from 34% (1959) to 10.7% (1981)
• Internal Rate of Return increased from 19% (1959) to 65.3% (1981)
• NPV started from 0% (1959) and grew to 16.5% (1981)
• IRR or NPV combined grew from 19% (1959) to 81.8% (1981)

Percentage of CFOs Who Always Use a Given Technique in 2000:

Summary of Investment Criteria

1. Discounted Cash Flow Criteria: Net Present Value (NPV)

• The NPV of an investment is the difference between its market value and its cost.
• The NPV rule is to take a project if its NPV is positive.
• It is estimated by calculating the present value of the future cash flows and then subtracting the cost.

2. Discounted Cash Flow Criteria: Internal Rate of Return (IRR)

• IRR is the discount rate that makes the estimated NPV of an investment equal to zero.
• IRR rule is to take a project when its IRR exceeds the required return.
• It leads to the same decision as NPV for conventional, independent projects.
• For mutually exclusive and non-conventional projects, IRR may be misleading.

3. Discounted Cash Flow Criteria: Profitability Index (PI)

• PI is the ratio of present value to cost. It measures the present value of an investment per dollar invested.
• PI rule is to take an investment if the index exceeds 1.
• It is sometimes used to rank projects when a firm has more positive NPV investments than it can currently finance.

4. Accounting Criteria: Average Accounting Return (AAR)

• AAR is a measure of accounting profit relative to book value.
• AAR rule is to take an investment if its AAR exceeds a benchmark AAR.

5. Payback Criteria: Payback Period

• It is the length of time until the sum of an investment's cash flows equals its costs.
• Payback period rule is to take a project if its payback is less than some cutoff.
• It ignores risk, time value of money, and cash flows beyond the cutoff point.

⭐ Key Takeaways

The Profitability Index measures value created per dollar invested and is useful when capital is scarce, but it may lead to incorrect decisions for mutually exclusive investments, similar to the IRR ranking problem. Firms use multiple capital budgeting criteria simultaneously because NPV estimates are uncertain, and conflicting signals from different methods indicate the need for further analysis. Historical data shows a clear shift away from Payback and AAR toward discounted cash flow methods (IRR and NPV), with IRR and NPV being used by over 75% of CFOs by 2000, while PI remains the least used technique at only 12%.

🧠 Quick Revision Questions

1. If a project costs $500 and the present value of its future cash flows is $600, what is its Profitability Index and what does it tell us?
2. Why might a project with a lower PI be preferred over a project with a higher PI when they are mutually exclusive?
3. What does it mean when a positive NPV project has a long payback period and a low AAR, and what should the financial manager do?
4. Which capital budgeting technique had the highest percentage of "always use" by CFOs in 2000, and what was that percentage for large firms?
5. List two advantages and one disadvantage of using the Profitability Index for capital budgeting decisions.

📘 Lecture 29 — MAKING CAPITAL INVESTMENT DECISIONS

📖 Overview: This lecture introduces the process of evaluating proposed investments by focusing on relevant cash flows and discounted cash flow analysis. It covers the stand-alone principle, common pitfalls like sunk costs and opportunity costs, and demonstrates how to build pro forma financial statements to compute key capital budgeting metrics such as NPV and IRR.

🗂️ Topics Covered

The lecture explains the concept of incremental cash flows and the stand-alone principle as the foundation for project evaluation. It then examines common mistakes in identifying relevant cash flows, including sunk costs, opportunity costs, side effects, net working capital, and financing costs. Finally, it walks through constructing pro forma financial statements and using them to calculate operating cash flow, project cash flow, NPV, IRR, payback period, and average accounting return (AAR) for a sample project.

📝 Lecture Summary

Project Cash Flows

To evaluate a proposed investment, we must consider the changes in the firm’s cash flows and decide whether they add value to the firm. The first step is to decide which cash flows are relevant and which are not.

Relevant Cash Flows

A relevant cash flow for a project is a change in the firm’s overall future cash flow that comes about as a direct consequence of the decision to take the investment. Since these relevant cash flows are defined in terms of changes in, or increments to, the firm’s existing cash flow, they are called the incremental cash flows associated with the project.

🔑 Definition — Incremental Cash Flows: Any and all changes in the firm’s future cash flows that are a direct consequence of taking the project.

The Stand-Alone Principle

The stand-alone principle is the assumption that evaluation of a project may be based on the project’s incremental cash flows. This means analyzing the project as a "minifirm" with its own future revenues and costs, its own assets, and its own cash flows.

Common Pitfalls in Identifying Incremental Cash Flows

Although it seems easy to decide whether a cash flow is incremental, there are situations where mistakes are easy to make. The key categories to watch for are:

• Sunk Costs
• Opportunity Costs
• Side Effects
• Net Working Capital
• Financing Costs
• Other Issues

Sunk Costs

A sunk cost is a cost that has already been incurred and cannot be recouped, and therefore should not be considered in an investment decision. An example is a consultant’s fee paid for evaluating the option of launching a new product. This cost is irrelevant to the future decision.

Opportunity Costs

An opportunity cost is the most valuable alternative that is given up if a particular investment is undertaken. For example, if a piece of land bought years ago could be sold at current market rates but instead is used to build a school, the opportunity cost charged to the school project should be the land's current market price, not its original purchase price.

Side Effects

A project can have side or spillover effects, both good and bad. For example, sales of a new car by a certain company might come at the expense of the sales of the company's other cars. This phenomenon is called erosion, piracy, or cannibalism. Cash flows from the new product line should be adjusted downward to reflect lost profits on other lines.

Net Working Capital

Normally, a project requires investments in net working capital (NWC) in addition to long-term assets. This includes cash in hand, inventories, and accounts receivables, as well as accounts payables; the balance being the net working capital. As the project winds down, net working capital gets freed up. Investment in NWC resembles a loan, as the firm provides NWC at the beginning and recovers it towards the end.

🔑 Definition — Net Working Capital (NWC): Current assets minus current liabilities, representing the short-term investment required to support a project's operations.

Financing Costs

We do not include interest paid or any other financing costs like dividends or principal paid while analyzing a proposed investment. We are only interested in the cash flow generated by the assets of the project. The mixture of debt and equity a firm chooses to use in financing a project is a managerial variable and does not form part of the project evaluation process.

Other Issues

We are only concerned with measuring cash flows when they actually occur, rather than when they occur in an accounting sense. Also, we are interested in after-tax cash flows, as incremental cash flows means after-tax incremental cash flows.

Pro Forma Financial Statements

Pro forma financial statements project future years’ operations in a summarized format. To prepare these statements, we need estimates of quantities like unit sales, selling price per unit, variable cost per unit, and total fixed cost.

Suppose we want to prepare a set of pro forma financial statements for a project for ND Enterprises. The background information is:

1. Sales of 10,000 units/year @ $5/unit.
2. Variable cost/unit is $3. Fixed costs are $5,000/year. Project has no salvage value. Project life is 3 years.
3. Project cost is $21,000. Depreciation is $7,000/year.
4. Investment in net working capital is $10,000.
5. The firm’s required return is 20%. The tax rate is 34%.

Projected Income Statements

Projected Balance Sheets

Project Cash Flows

We know that:

Project Cash Flow = Project operating cash flow – Project change in net working capital – Project capital spending

We also know that:

Operating Cash Flow (OCF) = Earnings before interest and taxes + Depreciation – Taxes

Let’s use the information from the previous example to do a capital budgeting analysis.

Project operating cash flow (OCF):

• EBIT: $8,000
• Depreciation: +$7,000
• Taxes: -$2,720
• Operating Cash Flow: $12,280

📐 Formula: OCF = EBIT + Depreciation – Taxes

📌 Example: OCF = $8,000 + $7,000 - $2,720 = $12,280

Project Cash Flow Summary

The firm must spend $21,000 up front for fixed assets and invest an additional $10,000 in net working capital. So the immediate outflow is $31,000. The recovery of $10,000 tied up in NWC in the last year will lead to a cash inflow of the same amount.

Capital Budgeting Evaluation

Based on the projected cash flows, we can compute the following capital budgeting metrics:

• NPV = -$31,000 + $12,280/1.20¹ + $12,280/1.20² + $22,280/1.20³ = $655
• IRR = 21%

💡 Why this matters: A positive NPV of $655 and an IRR (21%) greater than the required return (20%) suggest the project adds value and should be undertaken.

• Payback = 2.3 years
• AAR = $5,280 / {(31,000 + 24,000 + 17,000 + 10,000) / 4} = 25.76%

📐 Formula: Average Accounting Return (AAR) = Average Net Income / Average Book Value of Investment

📌 Example: AAR = $5,280 / ($82,000 / 4) = $5,280 / $20,500 = 25.76%

The firm should invest in this project because the NPV is positive and the IRR exceeds the required return.

⭐ Key Takeaways

The foundation of capital investment analysis is identifying incremental cash flows—the changes in the firm's total cash flow directly caused by the project. It's critical to avoid common errors by ignoring sunk costs and including opportunity costs (at current market value), adjusting for side effects like cannibalism, accounting for investments in net working capital (which are recovered at the end), and excluding financing costs. The stand-alone principle allows us to analyze a project as a "minifirm" using pro forma statements to calculate its operating cash flow (OCF) and total project cash flow. Finally, a project should be accepted if it has a positive NPV and an IRR greater than the required return, which signal that the project adds value to the firm.

🧠 Quick Revision Questions

1. What is the stand-alone principle, and why is it useful in project evaluation?
2. Explain why a sunk cost is not a relevant cash flow, but an opportunity cost is relevant.
3. How does the phenomenon of erosion affect the calculation of a new project's incremental cash flows?
4. Why is the initial investment in net working capital treated as a cash outflow, and why is its recovery treated as an inflow?
5. Based on the ND Enterprises example, calculate the project's total cash flow in year 3, explaining each component.

📘 Lecture 30 — Pro Forma Financial Statements

📖 Overview: This lecture teaches how to prepare pro forma financial statements for capital budgeting projects and use them to evaluate project cash flows and investment decisions. It covers operating cash flow calculation, the tax shield approach, net working capital adjustments, and MACRS depreciation methods.

🗂️ Topics Covered

The lecture covers pro forma income statements and balance sheets for a sample project (ND Enterprises), project cash flow calculation and capital budgeting evaluation using NPV, IRR, payback, and AAR. It then explores the tax shield approach to OCF, a closer examination of net working capital effects on cash flow including accounts receivable and payable adjustments, and concludes with MACRS depreciation methods and property classes.

📝 Lecture Summary

Pro Forma Financial Statements

A project at ND Enterprises is analyzed with sales of 10,000 units/year at $5/unit, variable costs of $3/unit, and fixed costs of $5,000/year. The project cost is $21,000 with $7,000/year depreciation, $10,000 investment in net working capital (NWC), a required return of 20%, and a tax rate of 34%. The projected income statement shows sales of $50,000, variable costs of $30,000, gross profit of $20,000, fixed costs of $5,000, depreciation of $7,000, EBIT of $8,000, taxes of $2,720, and net income of $5,280. The projected balance sheet shows NWC constant at $10,000 each year, net fixed assets declining from $21,000 to $14,000 to $7,000 to $0 over years 0 through 3, with total assets falling from $31,000 to $10,000.

Project Cash Flows

Operating Cash Flow (OCF) is calculated starting from EBIT of $8,000, adding back depreciation of $7,000, and subtracting taxes of $2,720, giving $12,280 per year. The project requires an immediate outflow of $31,000 ($21,000 for fixed assets plus $10,000 for NWC). In year 3, the recovery of $10,000 in NWC adds to the cash flow. Total project cash flows are -$31,000 in year 0, $12,280 in years 1 and 2, and $22,280 in year 3.

🔑 Definition — Operating Cash Flow (OCF): The cash generated from a project's normal operations, calculated as EBIT + Depreciation - Taxes.

📐 Formula: OCF = EBIT + Depreciation – Taxes → Measures the actual cash produced by operations after accounting for tax payments.

📌 Example: For ND Enterprises, EBIT = $8,000, Depreciation = $7,000, Taxes = $2,720, so OCF = $8,000 + $7,000 - $2,720 = $12,280.

Capital Budgeting Evaluation

The Net Present Value (NPV) of the project is calculated as -$31,000 + $12,280/1.20¹ + $12,280/1.20² + $22,280/1.20³ = $655. The Internal Rate of Return (IRR) is 21%. The Payback period is 2.3 years. The Average Accounting Return (AAR) is $5,280 divided by the average book value of assets ($31,000 + $24,000 + $17,000 + $10,000)/4 = $20,500, giving 25.76%. Since NPV is positive ($655) and IRR (21%) exceeds the required return (20%), the firm should invest in this project.

💡 Why this matters: A positive NPV means the project adds value to the firm, while an IRR above the required return confirms the investment meets the firm's profitability threshold.

The Tax Shield Approach

The tax shield definition of OCF is: OCF = (Sales – Costs) × (1 – T) + Depreciation × T, where T is the corporate tax rate (34%). For ND Enterprises, (Sales – Costs) = $50,000 – ($30,000 + $5,000) = $15,000, so OCF = $15,000 × 0.66 + $7,000 × 0.34 = $9,900 + $2,380 = $12,280. This shows OCF has two components: the project's "would be" cash flows without depreciation ($9,900) and the depreciation tax shield ($2,380).

📐 Formula: OCF = (Sales – Costs) × (1 – T) + Depreciation × T → Separates operating cash flow into after-tax operating income plus the tax savings from depreciation.

📌 Example: With Sales=$50,000, Costs=$35,000, T=34%, Depreciation=$7,000, OCF = $15,000×0.66 + $7,000×0.34 = $9,900 + $2,380 = $12,280.

A Closer Look on NWC

When sales include credit and costs include unpaid amounts, cash flow adjusts via changes in NWC. For a sample year with sales $500, costs $310, and net income $190, if accounts receivable rise by $30 (to $910 from $880) and accounts payable rise by $55 (to $605 from $550), NWC decreases by $25 (from $330 to $305). Cash revenues are sales minus the increase in receivables = $500 – $30 = $470. Cash costs are costs minus the increase in payables = $310 – $55 = $255. Net cash flow is $470 – $255 = $215, matching the formula Total Cash Flow = OCF – Change in NWC – Capital Spending = $190 – (-$25) – $0 = $215.

🔑 Definition — Change in NWC: The difference in net working capital (current assets minus current liabilities) between two periods, used to adjust operating cash flow for credit sales and unpaid costs.

📌 Example: With sales $500, costs $310, ΔAR = +$30, ΔAP = +$55, ΔNWC = -$25, cash flow = $190 – (-$25) – 0 = $215.

The Pencil Company Example

For a year with sales of $998 and costs of $734, accounts receivable rose from $100 to $110 (+$10), inventory fell from $100 to $80 (-$20), and accounts payable fell from $100 to $70 (-$30). NWC changed from $100 to $120 (+$20). Cash revenues = $998 – $10 = $988. Cash costs = $734 – $20 + $30 = $744. Net cash flow = $988 – $744 = $244.

Depreciation

Accounting depreciation is a non-cash deduction that affects cash flow only through its influence on the tax bill. The Modified Accelerated Cost Recovery System (MACRS) assigns each asset to a property class (3-year, 5-year, 7-year) with fixed depreciation percentages. For example, a $12,000 automobile in the 5-year class has depreciation of 20% ($2,400) in year 1, 32% ($3,840) in year 2, 19.2% ($2,304) in year 3, 11.52% ($1,382.40) in years 4 and 5, and 5.76% ($691.20) in year 6. The ending book value after year 6 is $0.

🔑 Definition — MACRS: A depreciation method that assigns assets to property classes with fixed annual percentages, ignoring salvage value and actual economic life for tax purposes.

📐 Formula: Depreciation = Cost of Asset × MACRS Percentage for that year → Calculates annual depreciation deduction for tax purposes.

📌 Example: For a $12,000 automobile, year 1 depreciation = $12,000 × 20% = $2,400; year 2 = $12,000 × 32% = $3,840; total over 6 years = $12,000.

⭐ Key Takeaways

Students must remember that OCF can be calculated both directly (EBIT + Depreciation – Taxes) and via the tax shield approach (OCF = (Sales – Costs)(1 – T) + Depreciation × T), both yielding the same result. Changes in NWC crucially adjust cash flow for credit sales and unpaid costs, with cash revenues = sales – increase in receivables and cash costs = costs – increase in payables + increase in inventory. MACRS depreciation uses fixed percentages based on property class (3, 5, or 7 years) and ignores salvage value, with the depreciation tax shield (Depreciation × T) being the key cash flow benefit. A positive NPV and IRR greater than the required return indicate the project should be accepted.

🧠 Quick Revision Questions

1. For ND Enterprises, what is the operating cash flow (OCF) for each year using the direct method?
2. How do you calculate the tax shield component of OCF, and what is its value in the ND Enterprises example?
3. If accounts receivable increase by $30 and accounts payable increase by $55, how do you compute cash revenues and cash costs from sales of $500 and costs of $310?
4. For a 5-year MACRS property costing $12,000, what is the depreciation in year 3?
5. What does a positive NPV of $655 and IRR of 21% (above 20%) tell you about the ND Enterprises project?

📘 Lecture 31 — DEPRECIATION

📖 Overview: This lecture explains the Modified Accelerated Cost Recovery System (MACRS) for depreciation and its impact on tax calculations and project cash flows. It demonstrates how depreciation affects taxable income, asset sale tax consequences, and net present value analysis through detailed examples, including a comprehensive capital budgeting project for The M Inc.

🗂️ Topics Covered

The lecture covers MACRS depreciation tables and calculations, book value versus market value concepts, tax implications of asset sales including depreciation recapture and capital gains, and a complete project cash flow analysis for The M Inc. including revenue projections, operating cash flows, net working capital changes, capital spending, and project evaluation using NPV, IRR, and payback period.

📝 Lecture Summary

DEPRECIATION

The lecture begins with a MACRS (Modified Accelerated Cost Recovery System) depreciation example for an automobile costing $12,000, classified as 5-year property. The depreciation percentages are: Year 1: 20.00% ($2,400), Year 2: 32.00% ($3,840), Year 3: 19.20% ($2,304), Year 4: 11.52% ($1,382.40), Year 5: 11.52% ($1,382.40), and Year 6: 5.76% ($691.20), totaling 100% depreciation.

The book value declines each year as depreciation is subtracted. For Year 1, beginning book value is $12,000, depreciation is $2,400, ending book value is $9,600. By Year 6, ending book value reaches $0.

🔑 Definition — Book Value: The original cost of an asset minus accumulated depreciation.

📐 Formula: Ending Book Value = Beginning Book Value – Depreciation

Book Value versus Market Value

If the car is sold after 5 years for an estimated market value of 25% of purchase price ($3,000), there is a difference between market price ($3,000) and book value ($691.20) of $2,308.80. This difference is subject to taxes at 34%: 0.34 × $2,308.80 = $784.99.

The reason for tax payment is that the difference between market and book value represents excess depreciation that must be recaptured when the asset is sold. This is not a tax on capital gain, which occurs only if the market price exceeds the original cost. If book value exceeds market value, the difference is treated as a loss for tax purposes.

💡 Why this matters: Understanding the tax treatment of asset sales is crucial for calculating accurate after-tax cash flows in capital budgeting.

🔑 Definition — Depreciation Recapture: The gain from selling a depreciated asset that is taxed as ordinary income up to the amount of depreciation taken.

The SS Company

The SS Company purchased an IT system for $160,000 (5-year MACRS property). Yearly depreciation allowances are: Year 1: 20.00% ($32,000, ending book value $128,000), Year 2: 32.00% ($51,200, $76,800), Year 3: 19.20% ($30,720, $46,080), Year 4: 11.52% ($18,432, $27,648), Year 5: 11.52% ($18,432, $9,216), Year 6: 5.76% ($9,216, $0).

If sold after 4 years for $10,000, the book value is $27,648, creating a tax loss of $17,648. The company receives $10,000 from the buyer and saves 0.34 × $17,648 = $6,000 in taxes. The total after-tax cash flow from the sale is $10,000 + $6,000 = $16,000 cash inflow.

📌 Example: For SS Company, selling a system with book value $27,648 for $10,000 creates a $17,648 tax loss, resulting in tax savings of $6,000 and total after-tax proceeds of $16,000.

The M Inc.

The M Inc. is evaluating a new product line with projected unit sales over 8 years: 3,000, 5,000, 6,000, 6,500, 6,000, 5,000, 4,000, and 3,000 units. The product sells for $120 per unit for the first three years, dropping to $110 thereafter due to competition. Net working capital requires $20,000 initially, then 15% of sales each year. Variable costs are $60 per unit, fixed costs are $25,000 per year. Equipment costs $800,000 (7-year MACRS property) and will be worth 20% of cost ($160,000) in 8 years. Tax rate is 34%, required return is 15%.

Revenue projections for Year 1: $120 × 3,000 = $360,000; Year 2: $120 × 5,000 = $600,000; Year 3: $120 × 6,000 = $720,000; Year 4: $110 × 6,500 = $715,000; Year 5: $110 × 6,000 = $660,000; Year 6: $110 × 5,000 = $550,000; Year 7: $110 × 4,000 = $440,000; Year 8: $110 × 3,000 = $330,000.

🔑 Definition — Net Working Capital (NWC): Current assets minus current liabilities; changes in NWC represent cash flows related to operating liquidity needs.

Operating Cash Flow Calculations (Years 1-4)

For Year 1: Revenues $360,000 – Variable Costs ($60 × 3,000 = $180,000) – Fixed Costs $25,000 – Depreciation $114,320 = EBIT $40,680. Taxes (34%): $13,831. Net Income: $26,849.

For Year 2: Revenues $600,000 – VC $300,000 – FC $25,000 – Depreciation $195,920 = EBIT $79,080. Taxes: $26,887. Net Income: $52,193.

For Year 3: Revenues $720,000 – VC $360,000 – FC $25,000 – Depreciation $139,920 = EBIT $195,080. Taxes: $66,327. Net Income: $128,753.

For Year 4: Revenues $715,000 – VC $390,000 – FC $25,000 – Depreciation $99,920 = EBIT $200,080. Taxes: $68,027. Net Income: $132,053.

Operating Cash Flow Calculations (Years 5-8)

For Year 5: Revenues $660,000 – VC $360,000 – FC $25,000 – Depreciation $71,440 = EBIT $203,560. Taxes: $69,210. Net Income: $134,350.

For Year 6: Revenues $550,000 – VC $300,000 – FC $25,000 – Depreciation $71,440 = EBIT $153,560. Taxes: $52,210. Net Income: $101,350.

For Year 7: Revenues $440,000 – VC $240,000 – FC $25,000 – Depreciation $71,440 = EBIT $103,560. Taxes: $35,210. Net Income: $68,350.

For Year 8: Revenues $330,000 – VC $180,000 – FC $25,000 – Depreciation $35,600 = EBIT $89,400. Taxes: $30,396. Net Income: $59,004.

Changes in Net Working Capital

NWC starts at $20,000 (Year 0 cash outflow). For Year 1, NWC becomes 15% × $360,000 = $54,000, requiring an additional investment of $54,000 – $20,000 = $34,000 (cash outflow).

Year 2: NWC = 15% × $600,000 = $90,000, increase = $90,000 – $54,000 = $36,000 outflow. Year 3: NWC = 15% × $720,000 = $108,000, increase = $18,000 outflow. Year 4: NWC = 15% × $715,000 = $107,250, decrease = $107,250 – $108,000 = -$750 (cash inflow of $750). Year 5: NWC = 15% × $660,000 = $99,000, decrease = $99,000 – $107,250 = -$8,250 inflow. Year 6: NWC = 15% × $550,000 = $82,500, decrease = $82,500 – $99,000 = -$16,500 inflow. Year 7: NWC = 15% × $440,000 = $66,000, decrease = $66,000 – $82,500 = -$16,500 inflow. Year 8: NWC = 15% × $330,000 = $49,500, decrease = $49,500 – $66,000 = -$16,500 inflow (total NWC recovered).

Capital Spending

The initial equipment investment is $800,000 at Year 0 (outflow). At the end of the project (Year 8), the equipment has a market value of $160,000 but a book value of $0. This $160,000 excess is taxable at 34%, so after-tax proceeds = $160,000 × (1 – 0.34) = $105,600 (cash inflow in Year 8).

📌 Example: For the equipment, market value $160,000 minus book value $0 = $160,000 gain, taxed at 34% = $54,400 tax, leaving $105,600 after-tax proceeds.

Project Total Cash Flows

Year 0: Operating CF $0 – NWC $20,000 – Capital Spending $800,000 = -$820,000 Year 1: OCF $141,169 – NWC $34,000 = $107,169 Year 2: OCF $248,113 – NWC $36,000 = $212,113 Year 3: OCF $268,113 – NWC $18,000 = $250,673 Year 4: OCF $231,973 – NWC -$750 = $232,723 Year 5: OCF $205,790 – NWC -$8,250 = $214,040 Year 6: OCF $172,790 – NWC -$16,500 = $189,290 Year 7: OCF $139,790 – NWC -$16,500 = $156,290 Year 8: OCF $94,064 – NWC -$66,000 + Capital Spending $105,600 = $266,204

Project Evaluation

The Net Present Value (NPV) at 15% is calculated as $65,488, indicating the project is acceptable. The Internal Rate of Return (IRR) is 17.24%, also above the required return of 15%. The Payback Period is 4.08 years.

🔑 Definition — Net Present Value (NPV): The sum of present values of all project cash flows discounted at the required rate of return; a positive NPV indicates value creation.

📐 Formula: NPV = Σ (CFₜ / (1 + r)ᵗ) – Initial Investment → Measures whether a project adds value above the required return.

📌 Example: For The M Inc., discounted cash flows at 15%: Yr 0: -$820,000; Yr 1: $93,190; Yr 2: $160,388; Yr 3: $164,821; Yr 4: $133,060; Yr 5: $106,416; Yr 6: $81,835; Yr 7: $58,755; Yr 8: $87,023. Sum = $65,488 positive NPV.

⭐ Key Takeaways

The key concepts from this lecture are that MACRS depreciation provides accelerated depreciation schedules for different asset classes, and the tax treatment of asset sales depends on the difference between market value and book value (depreciation recapture if market > book, tax loss if book > market). For capital budgeting, total project cash flows combine operating cash flows, net working capital changes, and capital spending (including after-tax proceeds from asset sales). The M Inc. case demonstrates that a project with positive NPV ($65,488) and IRR (17.24%) exceeding the required return (15%) should be accepted, with a payback period of 4.08 years.

🧠 Quick Revision Questions

1. What is the difference between depreciation recapture and a capital gain when selling an asset?
2. How do you calculate the after-tax cash flow from selling an asset when market value exceeds book value?
3. In the M Inc. project, why does net working capital become a cash inflow in later years?
4. What is the formula for operating cash flow (OCF) and how is it calculated from net income and depreciation?
5. Why is the total after-tax proceeds from selling the equipment in Year 8 ($105,600) less than its market value ($160,000)?

📘 Lecture 32 — RETURNS

📖 Overview: This lecture examines how financial managers assess investment returns by understanding both dollar and percentage returns from market history. It introduces the critical concepts of return variability, variance, and standard deviation as measures of investment risk, establishing the fundamental relationship between risk and reward.

🗂️ Topics Covered

The lecture covers the components of dollar returns including income and capital gains, calculation of percentage returns through dividend yield and capital gains yield, the variability of returns across different asset classes, and the statistical measurement of risk using variance and standard deviation with practical examples.

📝 Lecture Summary

RETURNS

One of the financial manager's key responsibilities is to assess the value of proposed investments. The minimum return required from a non-financial investment must be at least as large as what can be obtained from buying financial assets of similar risk. Lessons from market history teach us that there is a reward for bearing risk, and the greater the potential reward, the greater the risk.

Any gain or loss from an investment is called the return on investment, typically expressed as dollar returns with two components:

• Income earned (Dividends)
• Capital gain (change in asset value)

Dollar returns equal the sum of cash received plus the change in dollar value of the asset.

🔑 Definition — Return on Investment: The gain or loss from an investment, consisting of income earned plus capital gains.

📐 Formula: Dollar Return = Cash Received + (Ending Value – Beginning Value)

📌 Example: You bought 100 shares one year ago at $25 each ($2,500 total investment). Over the year, you received $20 in dividends ($0.20/share × 100 shares). At year-end, stock sells for $30/share ($3,000 total). Dollar gain = $20 + ($3,000 – $2,500) = $520. If you sell, total cash inflow = $2,500 + $520 = $3,020. If you hold, the capital gain is still part of your return.

Percentage Returns

Percentage returns are more convenient because they do not depend on how much you actually invest.

🔑 Definition — Dividend Yield: Dividend divided by beginning price.

🔑 Definition — Capital Gains Yield: (Ending price – Beginning price) divided by beginning price.

📐 Formula: Total Percentage Return = Dividend Yield + Capital Gains Yield

📐 Formula: Percentage Return = Dollar Return ÷ Beginning Market Value

📌 Example: From the previous example: Dividend Yield = $20/$2,500 = 0.8%. Capital Gains Yield = ($3,000 – $2,500)/$2,500 = 20%. Total Percentage Return = 0.8% + 20% = 20.8%.

📌 Example: You buy stock at $25/share. Year-end price is $35/share. You receive $2 dividend per share. Dividend Yield = $2/$25 = 8%. Capital Gains Yield = ($35 – $25)/$25 = 40%. Total Percentage Return = 8% + 40% = 48%. If you invested $1,000, you would have $1,480 at year-end.

Variability of Returns

Year-to-year returns on common stocks tend to be more volatile than returns on long-term bonds. Measuring this variability is key to examining risk.

A frequency distribution of common stock returns over 72 years shows returns ranging from -55% to +55%, with the highest frequency (16 years) in the 10-20% range.

To measure the spread in returns, we need to know how far actual returns deviate from the average return. The most commonly used measures are variance and its square root, the standard deviation.

🔑 Definition — Variance: Measures the average squared differences between actual returns and the average return. The larger the number, the more actual returns tend to differ from the average.

🔑 Definition — Standard Deviation: The square root of variance, measuring the spread of returns. The larger the standard deviation, the more spread out the returns.

📐 Formula: Variance = Sum of Squared Deviations ÷ (n – 1)

📐 Formula: Standard Deviation = √Variance

📌 Example: Investment returns: 10%, 12%, 3%, and -9% over four years.

Average Return = (0.10 + 0.12 + 0.03 – 0.09)/4 = 0.04 = 4%

Variance = 0.0270/(4 – 1) = 0.009

Standard Deviation = √0.009 = 0.09487 = 9.487%

💡 Why this matters: Standard deviation quantifies investment risk. A higher standard deviation means greater return volatility, directly relating to the risk-reward tradeoff in financial decision making.

⭐ Key Takeaways

Dollar returns consist of income (dividends) plus capital gains, while percentage returns standardize this as dividend yield plus capital gains yield. Market history confirms a positive relationship between risk and reward, with common stocks showing greater volatility than bonds. Variance and standard deviation measure this volatility by quantifying how actual returns deviate from the average return. The calculation uses squared deviations divided by (n-1) to account for sample bias. Understanding these measures is essential for evaluating any investment opportunity.

🧠 Quick Revision Questions

1. What are the two components of dollar returns on an investment?
2. How do you calculate total percentage return from dividend yield and capital gains yield?
3. If a stock has returns of 15%, -5%, 8%, and 2% over four years, what is the average return?
4. Why do we divide by (n-1) instead of n when calculating variance from sample data?
5. What does a larger standard deviation indicate about an investment's returns?

📘 Lecture 33 — Variability of Returns

📖 Overview: This lecture examines how to measure and interpret the variability (risk) of investment returns using variance and standard deviation. It introduces the concepts of expected returns, risk premiums, and portfolio diversification, showing how combining assets can fundamentally alter an investor's risk profile.

🗂️ Topics Covered

The lecture covers calculating variance and standard deviation for historical returns, computing expected returns under different probability scenarios, determining risk premiums, calculating variance for expected returns, and building portfolios with multiple assets to manage risk through diversification.

📝 Lecture Summary

Variability of Returns

In general, the variance for T historical returns is calculated as: Var(R) = [(R₁ - R̄)² + ... + (Rₜ - R̄)²] / (T - 1). The standard deviation is always the square root of the variance and provides a measure of return volatility in the same units as the original returns.

For Company X and Company Y with four years of returns:

• Company X average return: R̄ₓ = (-.20 + .50 + .30 + .10)/4 = .175 (17.5%)
• Company Y average return: R̄ᵧ = (.05 + .09 - .12 + .20)/4 = .055 (5.5%)

🔑 Definition — Variance: The average squared deviation of returns from their mean, measuring the dispersion of returns. 📐 Formula: Var(R) = Σ(Rₜ - R̄)² / (T-1) → Calculates the average squared difference between each return and the mean return.

For Company X, deviations are: -.375, .325, .125, -.075 with squared deviations of .140625, .105625, .015625, .005625, summing to .267500. Variance = .2675/3 = .0892, Standard Deviation = √.0892 = .2987 (29.87%).

Standard deviation for Company X (29.87%) is more than twice Company Y's (13.27%), indicating Company X is the more volatile investment.

📌 Example: Company X had returns of -20%, 50%, 30%, and 10% over four years. The average return is 17.5%. The variance calculation shows the extreme deviations (-37.5% and +32.5%) produce large squared terms, resulting in a high standard deviation of 29.87%, confirming high volatility.

Expected Return

Given a single period, Stock L has an expected return of 25% and Stock U has 20%. Stock L may go up to 70% in an economic boom or slide to -20% in a recession, while Stock U may earn 30% in a recession and 10% during a boom.

🔑 Definition — Expected Return: The weighted average of possible returns, where the weights are the probabilities of each state occurring.

With equal probabilities (0.5 each for recession and boom):

• E(Rₗ) = (0.5 × -0.20) + (0.5 × 0.70) = 0.25 (25%)
• E(Rᵤ) = (0.5 × 0.30) + (0.5 × 0.10) = 0.20 (20%)

📌 Example: For Stock L, with a 50% chance of a recession (return -20%) and 50% chance of a boom (return 70%), the expected return is 25%. For Stock U, with the same probabilities, returns of 30% and 10% produce an expected return of 20%.

Risk Premium

The risk premium is the difference between the return on a risky investment and that on a risk-free investment (Rƒ). If risk-free investments offer 8%:

• Risk Premium (U) = E(Rᵤ) - Rƒ = 20% - 8% = 12%
• Risk Premium (L) = 25% - 8% = 17%

🔑 Definition — Risk Premium: The excess return an investor expects to receive for bearing the risk of an investment over a risk-free alternative.

Unequal Probabilities Case: With an 80% chance of recession and 20% chance of boom:

• E(Rₗ) = (0.8 × -0.20) + (0.2 × 0.70) = -0.02 (-2%)
• E(Rᵤ) = (0.8 × 0.30) + (0.2 × 0.10) = 0.26 (26%)

If risk-free rate is 10%:

• Risk Premium (U) = 26% - 10% = 16%
• Risk Premium (L) = -2% - 10% = -12% (negative risk premium)

📌 Example: When recession probability rises to 80%, Stock L's expected return becomes negative (-2%), producing a negative risk premium of -12% when the risk-free rate is 10%. This means investors would expect to lose money relative to the risk-free alternative.

Calculating the Variance

To calculate variance of expected returns: (1) Determine squared deviations from the expected return, (2) Multiply each squared deviation by its probability, (3) Sum all the products.

For Stock L with equal probabilities: σ²ₗ = 0.5(-.20 - .25)² + 0.5(.70 - .25)² = 0.5(0.2025) + 0.5(0.2025) = 0.2025, σₗ = √0.2025 = 45% For Stock U: σ²ᵤ = 0.5(.30 - .20)² + 0.5(.10 - .20)² = 0.5(0.01) + 0.5(0.01) = 0.0100, σᵤ = √0.0100 = 10%

📐 Formula: σ² = Σ[P(state) × (Return - E(R))²] → The probability-weighted average of squared deviations from the expected return.

💡 Why this matters: Stock L has higher expected return (25%) but also higher risk (45% standard deviation). Stock U has lower expected return (20%) but much lower risk (10% standard deviation). The choice depends on the investor's risk tolerance.

For unequal probabilities (80% recession, 20% boom):

• Stock L: σ²ₗ = 0.8(-.20 + .02)² + 0.2(.70 - .02)² = 0.8(0.0324) + 0.2(0.5184) = 0.12960, σₗ = √0.1296 = 36%
• Stock U: σ²ᵤ = 0.8(.30 - .26)² + 0.2(.10 - .26)² = 0.8(0.0016) + 0.2(0.0256) = 0.00640, σᵤ = √0.0064 = 8%

📌 Example: With unequal probabilities, Stock L's variance is 0.1296 (standard deviation 36%) while Stock U's variance is only 0.0064 (standard deviation 8%). Stock U's expected return (26%) is now higher than Stock L's (-2%), making U clearly superior on both return and risk.

Portfolios

A portfolio is a group of assets such as stocks and bonds held by an investor. Portfolio weights are the percentages of the total portfolio's value invested in each portfolio asset. If you have $50 in one asset and $150 in another (total $200), weights are 0.25 and 0.75.

🔑 Definition — Portfolio Expected Return: The weighted average of the expected returns of the individual assets: E(Rₚ) = x₁ × E(R₁) + x₂ × E(R₂) + ... + xₙ × E(Rₙ)

With equal weights (0.50 each) in Stocks L and U:

• Returns if recession occurs: 0.5 × (-20%) + 0.5 × 30% = 5%
• Returns if boom occurs: 0.5 × 70% + 0.5 × 10% = 40%
• E(Rₚ) = 0.50 × 25% + 0.50 × 20% = 22.5%

Portfolio variance: σ²ₚ = 0.5(0.05 - 0.225)² + 0.5(0.40 - 0.225)² = 0.5(0.030625) + 0.5(0.030625) = 0.030625, σₚ = √0.030625 = 17.5%

With different weights (2/11 in Stock L, 9/11 in Stock U):

• Returns if recession: 2/11 × (-20%) + 9/11 × 30% = 20.91%
• Returns if boom: 2/11 × 70% + 9/11 × 10% = 20.91%
• The returns are identical, showing zero variance

📌 Example: By allocating 2/11 of the portfolio to Stock L and 9/11 to Stock U, the portfolio returns become identical (20.91%) regardless of economic conditions. This demonstrates that combining assets can eliminate risk entirely through proper diversification.

💡 Why this matters: Combining assets into portfolios can substantially alter the risks faced by the investor. Portfolio variance is NOT a simple combination of asset variances—diversification can reduce or even eliminate risk.

⭐ Key Takeaways

Variance and standard deviation are the fundamental measures of return variability, with higher values indicating greater risk. Expected returns are probability-weighted averages, and risk premiums quantify the compensation investors require for bearing risk above risk-free investments. The most critical insight is that portfolio risk is not simply the average of individual asset risks—through proper diversification (choosing appropriate portfolio weights), investors can substantially reduce or even eliminate risk while maintaining returns. The portfolio with 2/11 in Stock L and 9/11 in Stock U perfectly illustrates how diversification can produce identical returns across all states (20.91%), achieving zero variance.

🧠 Quick Revision Questions

1. Using the formula Var(R) = Σ(Rₜ - R̄)² / (T-1), calculate the variance for a stock with returns of 10%, -5%, and 15% over three years (average return = 6.67%).
2. If Stock A has expected return of 12% with 70% probability of boom (return 20%) and 30% probability of recession, what must be the recession return to achieve this expected return?
3. With a risk-free rate of 5%, what is the risk premium for a stock with expected return of 14%?
4. A portfolio has $200 in Asset X (expected return 8%) and $300 in Asset Y (expected return 15%). What is the portfolio expected return?
5. If two stocks have perfectly offsetting returns (one rises when the other falls), what portfolio weights would achieve zero variance?

📘 Lecture 34 — Portfolio

📖 Overview: This lecture introduces portfolio expected return and variance calculations for different weighting schemes. It then explains the crucial distinction between systematic and unsystematic risk, demonstrating how diversification can eliminate the latter but not the former, establishing the concept of nondiversifiable risk.

🗂️ Topics Covered

This lecture covers the calculation of portfolio expected returns under two different weighting schemes (equal and unequal weights), including the computation of portfolio variance and standard deviation for a specific weighting example. It then defines systematic and unsystematic risk, breaking down the actual return into its expected and surprise components. The lecture concludes by exploring diversification and portfolio risk through empirical data, the principle of diversification, and the summary of total risk into its two main components.

📝 Lecture Summary

PORTFOLIO

We have projections on three stocks (A, B, C) across two economic states (Boom and Bust) with given probabilities. The expected returns for each stock are calculated as: E(RA) = 8.8%, E(RB) = 8.4%, E(RC) = 8.0%. For a portfolio with equal investment in each asset (weights of 1/3 each), the portfolio expected return is 8.4%. For a portfolio where Stock A has half the investment (1/2 weight) and the remainder is divided equally between B and C (1/4 each), the portfolio expected return is 8.5%.

For the unequal weighting case (A = 50%, B = 25%, C = 25%), the portfolio returns in each state are calculated: 13.75% during Boom (0.50 x 10% + 0.25 x 15% + 0.25 x 20%) and 5.00% during Bust (0.50 x 8% + 0.25 x 4% + 0.25 x 0%). The variance is calculated as σ² = 0.40 x (0.1375 - 0.085)² + 0.60 x (0.05 - 0.085)² = 0.0018375. The Standard Deviation is calculated to be 4.3%, while for the equally weighted portfolio, the standard deviation is about 5.4%.

🔑 Definition — Portfolio Expected Return [E(RP)]: The weighted average of the expected returns of the individual assets in the portfolio, where the weights are the proportions of the total investment allocated to each asset. 📐 Formula: E(RP) = Σ (wi x E(Ri)) for all i assets → The expected return of the portfolio is the sum of each asset's weight multiplied by its expected return. 📌 Example: For a portfolio with equal weights (1/3 each) in stocks with E(RA)=8.8%, E(RB)=8.4%, E(RC)=8.0%, the calculation is E(RP) = (1/3 x 8.8%) + (1/3 x 8.4%) + (1/3 x 8.0%) = 8.4%.

Risk

The true risk of an investment is the unanticipated or surprising part of the return. If we always receive exactly what we expect, then the investment will be risk-free. Systematic Risk (also called market risk) is a risk that influences a large number of assets, such as Gross Domestic Product (GDP), interest rates, and inflation, which affect wages, costs of supplies, asset values, and selling prices. Unsystematic Risk (also called unique or asset-specific risks) is a risk that affects a single or at most a small number of assets.

The actual return (R) of an asset can be broken down into its expected and surprise components: R = E(R) + U, where U is the surprise component. The surprise component has a systematic portion (m) and an unsystematic portion (ε), so: R = E(R) + m + ε.

💡 Why this matters: Understanding the difference between systematic and unsystematic risk is fundamental because diversification can only eliminate one type (unsystematic), not the other. This distinction is the foundation of modern portfolio theory and asset pricing models.

🔑 Definition — Systematic Risk: A risk that influences a large number of assets, also called market risk, which is nondiversifiable. 🔑 Definition — Unsystematic Risk: A risk that affects a single or at most a small number of assets, also called unique or asset-specific risk, which can be eliminated through diversification. 📐 Formula: R = E(R) + m + ε → The actual return equals the expected return plus the systematic surprise component plus the unsystematic surprise component.

Diversification and Portfolio Risk

If the standard deviation of annual return on a portfolio of 500 large common stocks is 20%, that does NOT mean the standard deviation of annual returns of a single stock in that portfolio is 20%. Empirical data from "How Many Stocks Make a Diversified Portfolio?" shows that the standard deviation of annual returns for a single stock is 49.24% (ratio 1.00). As the number of stocks increases, the portfolio standard deviation declines — to 23.93% with 10 stocks, 19.69% with 100 stocks, and 19.21% with 1,000 stocks. The ratio to a single stock falls to 0.49 with 10 stocks and 0.39 with 100 or more stocks.

Principle of Diversification: The benefit in terms of risk reduction from adding securities drops off as we add more securities. With 10 securities, most of the effect is already utilized, and with 30, there is very little remaining benefit. Two key points are: (1) some of the riskiness associated with individual assets can be eliminated by forming portfolios (the process called diversification), and (2) there is a minimum level of risk that cannot be eliminated simply by diversifying, called nondiversifiable risk.

If we hold a single stock, the value of our investment fluctuates because of company-specific events. If we hold a large portfolio, some stocks go up and others may go down due to company-specific events, so the net effect on the overall portfolio value is relatively small. Unsystematic risk is essentially eliminated by diversification, while systematic risk cannot be eliminated because it affects almost all assets to some degree. The size or type of portfolio has little effect on systematic risk, making it nondiversifiable risk.

Summarizing: Total risk = Systematic risk + Unsystematic risk. Systematic risk is also called nondiversifiable risk or market risk.

💡 Why this matters: The table showing standard deviation for portfolios of different sizes provides the empirical evidence for why holding a diversified portfolio (around 30-100 stocks) is the most efficient way to reduce risk without sacrificing expected return.

⭐ Key Takeaways

You must understand that portfolio expected return is simply a weighted average of individual asset returns and can be calculated for any set of weights. The critical distinction for risk is that systematic risk (market risk) affects many assets and cannot be eliminated by diversification, while unsystematic risk (unique risk) is specific to individual assets and can be essentially eliminated by holding a diversified portfolio. The data shows that by holding 100 randomly chosen stocks, the portfolio's standard deviation declines by about 60% from 49% to 20%, but after 30 stocks, the benefit from additional diversification is very small, revealing an irreducible level of nondiversifiable risk.

🧠 Quick Revision Questions

1. In the lecture's example, what is the portfolio expected return for equal investment in all three stocks with E(RA)=8.8%, E(RB)=8.4%, and E(RC)=8.0%?
2. What are the two types of risk that constitute the "surprise component" (U) in the formula R = E(R) + U?
3. According to the empirical data, approximately how much does the portfolio standard deviation decline (in percentage terms) when moving from 1 stock to 100 stocks?
4. What is the principle of diversification, and what is the name for the minimum level of risk that cannot be eliminated?
5. Why can a large portfolio eliminate unsystematic risk but not systematic risk?

📘 Lecture 35 — COST OF CAPITAL

📖 Overview: This lecture explains how firms calculate the cost of capital — the minimum return required to compensate investors for financing projects. It covers the cost of equity, debt, and preferred stock, along with capital structure weights and the tax effect on debt costs, which are essential for making sound investment decisions.

🗂️ Topics Covered

The lecture defines the cost of capital and its relationship to risk, then explains how to estimate the cost of equity using the dividend growth model, including estimating growth rates. It covers the cost of debt via yield to maturity, the cost of preferred stock as a perpetuity, calculating capital structure weights using market values, and the tax effect that makes debt cheaper after taxes.

📝 Lecture Summary

Cost of Capital

The cost of capital is the required return on an investment — the minimum return a firm must earn to compensate investors for the capital used. For a risk-free project, the cost of capital equals the risk-free rate. For a risky project, the cost of capital is higher than the risk-free rate. The terms required return, appropriate discount rate, and cost of capital are used interchangeably. The cost of capital depends on the risk of the investment (the use of money), not the source of money. A firm's overall cost of capital reflects the required return on its assets as a whole and is a mixture of the returns needed to compensate creditors (debt) and stockholders (equity).

💡 Why this matters: The cost of capital is the benchmark for evaluating new projects — if a project's return is below this cost, it destroys value.

Cost of Equity

The cost of equity (Rₑ) is the return required by stockholders. Under the dividend growth model, assuming dividends grow at a constant rate g, the price per share (P₀) is:
P₀ = D₁ / (Rₑ – g), where D₁ = D₀ × (1 + g).
Rearranging gives:
📐 Formula: Rₑ = D₁ / P₀ + g → The cost of equity equals the dividend yield plus the growth rate.

To estimate Rₑ, we need D₀ (dividend just paid), P₀ (current stock price), and g (estimated growth rate).

📌 Example: GSS Company paid a dividend of $4 per share last year (D₀). Stock price is $60. Dividends grow at 6% (g = 0.06).
Step 1: D₁ = $4 × 1.06 = $4.24
Step 2: Rₑ = $4.24 / $60 + 0.06 = 0.0707 + 0.06 = 13.07%

🔑 Definition — g (growth rate): The estimated annual growth rate of dividends, calculated from historical dividend changes or analysts' forecasts.

📌 Example: A company had dividends: 1999: $1.10; 2000: $1.20 (9.09% change); 2001: $1.35 (12.50%); 2002: $1.40 (3.70%); 2003: $1.55 (10.71%). Average growth rate = (9.09 + 12.50 + 3.70 + 10.71) / 4 = 9%.

Limitations of dividend growth approach:

• Only applicable to companies paying constant growth dividends.
• Estimated cost of equity is very sensitive to the estimated growth rate.
• Does not explicitly consider risk.

Cost of Debt

The cost of debt (Rᴅ) is the return demanded by creditors on new borrowings. It can be observed from interest rates in financial markets or estimated using the firm's bond ratings. The coupon rate on outstanding debt is irrelevant because it reflects past costs, not current costs.

📌 Example: GenTech issued a 30-year, 7% bond 8 years ago. The bond now sells for 96% of face value ($960). Using bond valuation, the yield to maturity is approximately 7.37%, so the cost of debt (Rᴅ) = 7.37%.

Cost of Preferred Stock

Preferred stock pays a fixed dividend every period forever, making it a perpetuity.
📐 Formula: Rᴘ = D / P₀ → The cost of preferred stock equals the fixed dividend divided by the current price per share.

📌 Example: CG Inc. has two preferred stock issues:

• Issue 1: D = $1.78, P₀ = $25.35 → Rᴘ = $1.78 / $25.35 = 7.02%
• Issue 2: D = $1.72, P₀ = $24.90 → Rᴘ = $1.72 / $24.90 = 6.91%
  Cost of preferred stock is between 6.9% and 7%.

Capital Structure Weights

Capital structure weights show the proportion of financing from equity and debt.

• Market value of equity (E) = shares outstanding × price per share.
• Market value of debt (D) = market price per bond × number of bonds outstanding (summed across issues).
• For non-traded debt, estimate market value using yields on similar traded debt.
• For short-term debt, book value approximates market value.
  Total market value: V = E + D
  Weights: E/V (equity percentage) and D/V (debt percentage).

📌 Example: If equity market value = $200 million and debt market value = $50 million, V = $250 million.
E/V = $200 / $250 = 80% (equity)
D/V = $50 / $250 = 20% (debt)

The Tax Effect

Interest paid on debt is tax-deductible, while dividends are not. This makes debt cheaper because the government effectively pays part of the interest cost.
📐 Formula: After-tax cost of debt = Rᴅ × (1 – Tᴄ), where Tᴄ = corporate tax rate.

📌 Example: A firm borrows $1 million at 9% (Rᴅ = 9%), with a tax rate of 34% (Tᴄ = 0.34).

• Total interest = $1,000,000 × 0.09 = $90,000
• Tax savings = $90,000 × 0.34 = $30,600
• After-tax interest = $90,000 – $30,600 = $59,400
• After-tax interest rate = $59,400 / $1,000,000 = 5.94%
  Using the formula: 9% × (1 – 0.34) = 5.94%

⭐ Key Takeaways

The cost of capital is the minimum return a firm must earn to satisfy investors and varies with investment risk. The cost of equity can be estimated using the dividend growth model (Rₑ = D₁/P₀ + g), but this method is sensitive to growth estimates and assumes constant growth. The cost of debt is the yield to maturity on current bonds, and the after-tax cost (Rᴅ × (1 – Tᴄ)) is lower due to the tax deductibility of interest. Capital structure weights (E/V and D/V) based on market values determine the overall cost of capital. The tax effect is critical — debt financing becomes cheaper after taxes, encouraging firms to use debt.

🧠 Quick Revision Questions

1. What is the cost of capital for a risk-free project, and how does it differ for a risky project?
2. Using the dividend growth model, how do you calculate the cost of equity?
3. Why is the coupon rate on existing debt irrelevant when calculating the cost of debt?
4. How do you calculate capital structure weights using market values?
5. A firm borrows at 8% with a 30% tax rate. What is the after-tax cost of debt?

📘 Lecture 36 — WEIGHTED AVERAGE COST OF CAPITAL

📖 Overview: This lecture explains how to calculate a firm’s overall cost of capital by combining the costs of different financing sources (equity, debt, and preferred stock). Understanding WACC is essential because it serves as the required return and discount rate for evaluating new projects with similar risk to existing operations.

🗂️ Topics Covered

This lecture covers the definition and calculation of the Weighted Average Cost of Capital (WACC), including its formula and components. It walks through a complete example of using WACC to evaluate a warehouse renovation project with an NPV analysis. Then, it presents a detailed case study of EMN Corporation showing how to estimate the cost of equity using the dividend growth model, compute the weighted average cost of debt from multiple bond issues, and calculate WACC using both book value and market value weights. Finally, it summarizes how to obtain costs of equity, debt, and WACC.

📝 Lecture Summary

WEIGHTED AVERAGE COST OF CAPITAL

To calculate the firm’s overall cost of capital, we multiply the capital structures with the associated costs and add up the pieces. The result is called the Weighted Average Cost of Capital (WACC).

🔑 Definition — WACC: The overall return the firm must earn on its existing assets to maintain the value of the stock; it is also the required return on any investments by the firm that have the same risks as existing operations. So for evaluating the cash flows of a proposed expansion project, this is the discount rate to be used.

📐 Formula: WACC = (E/V) × R_E + (D/V) × R_D × (1 – T_C) → The weighted sum of the cost of equity and the after-tax cost of debt.

For a firm using preferred stock, the formula expands to: WACC = (E/V) × R_E + (P/V) × R_P + (D/V) × R_D × (1 – T_C)

📌 Example: A company wants to renovate its warehouse distribution system. The plan will cost $50 million and is expected to save $12 million per year after taxes over the next six years. The company has a target debt-equity ratio of 1/3 (i.e., E/V = 0.75 and D/V = 0.25). The company has a cost of debt of 10% and a cost of equity of 20%. Assuming a tax rate of 34%, should the company go for the project?

Step 1: Calculate WACC WACC = (0.75 × 20%) + (0.25 × 10% × (1 – 0.34)) WACC = 15% + 1.65% = 16.65%

Step 2: Calculate NPV using WACC as the discount rate Since cash flows are an ordinary annuity: NPV = -$50 + [$12 × (1 – (1/(1 + 0.1665)^6) / 0.1665] NPV = -$50 + [$12 × 3.6222] NPV = -$50 + $43.47 = -$6.53 million

The negative NPV means that the financial market offers superior projects in the same risk class, so the project should be rejected.

EMN Corporation

EMN Corporation has 77.3 million shares of stock outstanding. The book value per share is $17.62, but the stock actually sells for $45.41. The total equity is about $1.36 billion on a book value basis but is closer to $3.51 billion on a market value basis.

EMN paid $1.76 per share in dividends last year and analysts estimate this dividend to grow by 7% through the next 5 years.

📐 Formula: The estimated cost of equity using the dividend growth model is: R_E = [D_0 × (1 + g) / P_0] + g R_E = [$1.76 × (1 + 0.07) / $45.41] + 0.07 R_E = 0.1115 or 11.15%

EMN has four long-term bond issues that account for essentially all of its long-term debt. To calculate the cost of debt, we combine these four issues by computing a weighted average.

To calculate the weighted average cost of debt, we take the percentage of the total debt represented by each issue and multiply by the yield on the issue.

Whether market values or book values are used, the cost of debt remains 6.34% because market values and book values are similar, and EMN has no preferred stock.

WACC on Book Value Basis:

• Equity (book): $1.362 billion
• Debt (book): $1.489 billion
• Total value: $2.851 billion
• E/V = $1.362b/$2.851b = 0.48
• D/V = $1.489b/$2.851b = 0.52
• WACC = (0.48 × 11.15%) + (0.52 × 6.34% × (1 – 0.34))
• WACC = 5.352% + 2.176% = 7.53%

WACC on Market Value Basis:

• Equity (market): $3.510 billion
• Debt (market): $1.540 billion
• Total value: $5.050 billion
• E/V = $3.510b/$5.050b = 0.70
• D/V = $1.540b/$5.050b = 0.30
• WACC = (0.70 × 11.15%) + (0.30 × 6.34% × (1 – 0.34))
• WACC = 7.805% + 1.255% = 9.06%

Using market value weights gives 9.06% for EMN’s WACC, which is much higher than 7.53% using book values. So using book values can lead to trouble, particularly if equity book values are used. EMN’s market-to-book ratio is about 2.6, so book values significantly overstate the percentage of EMN’s financing that comes from debt.

💡 Why this matters: Using book values instead of market values can seriously understate the true cost of capital, leading firms to accept projects that destroy shareholder value because the discount rate used is too low.

Summary of Capital Cost

• The Cost of Equity R_E: The dividend growth model gives R_E = D_1/P_0 + g, where D_1 is the expected dividend in one period, g is the dividend growth rate, and P_0 is the current stock price.
• The Cost of Debt R_D: For a firm with publicly held debt, the cost of debt can be measured as the yield to maturity on the outstanding debt. The coupon rate is irrelevant. If the firm has no publicly traded debt, the cost of debt can be measured as the yield to maturity on similarly rated bonds.
• The Weighted Average Cost of Capital (WACC): The firm’s WACC is the overall required return on the firm as a whole. It is the appropriate discount rate to use for cash flows similar in risk to the overall firm.
• WACC Calculation: WACC = (E/V) × R_E + (D/V) × R_D × (1 – T_C), where T_C is the corporate tax rate, E is the market value of the firm’s equity, D is the market value of the firm’s debt, V = E + D, E/V is the percentage of financing that is equity, and D/V is the percentage that is debt.

⭐ Key Takeaways

The Weighted Average Cost of Capital (WACC) is the overall return required on a firm and serves as the discount rate for evaluating projects with similar risk to existing operations. It is calculated by weighting the cost of equity and the after-tax cost of debt by their respective proportions of total financing. Market value weights should always be used instead of book value weights because book values can significantly distort the true cost of capital, especially when the market-to-book ratio is high. For the cost of equity, use the dividend growth model; for the cost of debt, use the yield to maturity on outstanding or similarly rated bonds, not the coupon rate. A project should only be accepted if its NPV computed using WACC is positive.

🧠 Quick Revision Questions

1. What is the formula for WACC when a firm uses only equity and debt financing?
2. Why must market value weights be used instead of book value weights when calculating WACC?
3. What is the correct measure to use for the cost of debt—the coupon rate or the yield to maturity?
4. A firm has a WACC of 16.65% and evaluates a project with a negative NPV of -$6.53 million. Should the project be accepted or rejected, and why?
5. How do you calculate the cost of equity using the dividend growth model?

📘 Lecture 37 — CAPITAL STRUCTURE

📖 Overview: This lecture examines how a firm's mix of debt and equity (capital structure) affects its value, cost of capital, and shareholder returns. It introduces the concept of financial leverage, shows how leverage impacts EPS and ROE, and explores the critical idea of homemade leverage—demonstrating that investors can replicate corporate leverage on their own.

🗂️ Topics Covered

The lecture covers the guiding principle of capital structure decisions based on maximizing firm value and minimizing WACC, financial leverage and its impact on EPS and ROE under different economic scenarios, calculation of the break-even EBIT point, and the concept of homemade leverage showing investors can adjust leverage personally through borrowing or lending.

📝 Lecture Summary

CAPITAL STRUCTURE

The guiding principle in choosing the debt-equity ratio is to choose a course of action that maximizes the value of a share of stock. When it comes to capital structure decisions, this is the same thing as maximizing the value of the whole firm. The WACC tells us that the firm's overall cost of capital is the weighted average of the costs of various components of the firm's capital structure. Usually, while describing WACC, we take the capital structure of the firm as given. But what happens to the cost of capital when we vary the amount of debt financing, or debt-equity ratio? Since values and discount rates move in opposite directions, the value of the firm's cash flows (or the value of the firm) is maximized when the WACC is minimized. One capital structure is better than another if it results in a lower weighted average cost of capital. A particular debt-equity ratio represents the optimal capital structure if it results in the lowest possible WACC. This optimal capital structure is also called the firm's target capital structure.

🔑 Definition — Optimal Capital Structure: The debt-equity ratio that results in the lowest possible WACC, thereby maximizing the value of the firm.

💡 Why this matters: Capital structure decisions are fundamental because they directly impact the firm's cost of capital and, ultimately, its market value. Managers must find the right balance between debt and equity to minimize financing costs.

Financial Leverage

Financial leverage refers to the extent to which a firm relies on debt. The more debt financing a firm uses in capital structure, the more financial leverage it employs. Financial leverage can dramatically alter the payoffs to the shareholders in the firm, but it may not affect the overall cost of capital. While illustrating how financial leverage works, we ignore taxes here and describe the impact of leverage in terms of its effect on earnings per share (EPS) and return on equity (ROE) . For meaningful analysis, we use cash flows instead of these accounting figures, but results will be the same.

The TA Corporation currently has no debt in its capital structure. The company is considering a restructuring that would involve issuing debt and using proceeds to buy back some of the outstanding equity. The table below presents both current and proposed capital structures:

EPS and ROE under current capital structure:

EPS and ROE under proposed capital structure:

The impact of leverage is evident when examining the restructuring effect on EPS and ROE. Particularly, the variability in both EPS and ROE is much larger under the proposed capital structure, illustrating how financial leverage acts to magnify gains and losses to shareholders.

📌 Example: Under the expected scenario, EPS increases from $2.50 (no debt) to $3.00 (with debt), while under the recession scenario, EPS drops from $1.25 to $0.50. This shows leverage amplifies both gains and losses.

Calculating Break-Even Point

To find the break-even EBIT where EPS is the same under both capital structures:

A. With no debt: EPS = EBIT/400,000

B. With $4,000,000 in debt at 10%: EPS = (EBIT - $400,000)/200,000

C. Solve for the break-even EBIT (EBITBE): EBITBE/400,000 = (EBITBE - $400,000)/200,000

D. With algebra: EBITBE = $800,000 And EPSBE = $2.00/share

The graph shows that when EBIT is below $800,000, the no-debt structure gives higher EPS (disadvantage to debt). When EBIT is above $800,000, the debt structure gives higher EPS (advantage to debt).

📐 Formula: Break-even EBIT: EBITBE/Current Shares = (EBITBE - Interest)/New Shares

📌 Example: The MPD Corporation currently uses no-debt financing and has decided to incorporate $1 million debt at 9%. MPD has 200,000 shares outstanding and a share price of $20. Under the old structure: EPS = EBIT/200,000. Under the new structure, interest = $1,000,000 × 0.09 = $90,000. The company repurchases $1,000,000/$20 = 50,000 shares, leaving 150,000 outstanding. EPS = (EBIT - $90,000)/150,000. Equating: EBIT/200,000 = (EBIT - $90,000)/150,000, giving EBIT = (4/3) × (EBIT - $90,000), so EBIT = $360,000 and EPS = $1.80. Management expects EPS to exceed this figure.

From the above discussion, the following conclusions can be drawn:

• The effect of financial leverage depends on the company's EBIT. When EBIT is relatively high, leverage is beneficial.
• Under the expected scenario, leverage increases returns to shareholders as measured by ROE and EPS.
• Shareholders are exposed to more risk under the proposed capital structure since EPS and ROE are much more sensitive to changes in EBIT.
• Because of the impact financial leverage has on both the expected return to stockholders and the riskiness of the stock, capital structure is an important consideration.

Homemade Leverage

The last conclusion is not necessarily correct because shareholders can adjust the amount of financial leverage by borrowing and lending on their own. The use of personal borrowing to alter the degree of financial leverage is called homemade leverage. Returning to the TA corporation, we can illustrate that it makes no difference whether or not TA uses the proposed capital structure.

Proposed Capital Structure (replicating with leverage):

Original capital structure and homemade leverage:

The proposed capital structure results in a debt-equity ratio of 1. To replicate this capital structure at the personal level, the stockholder must borrow enough to create this same debt-equity ratio of 1. Notice that the net earnings ($50, $300, $550) are identical under both approaches, and the net cost is also identical ($2,000). Therefore, an investor can achieve the same payoff by buying shares in the unlevered firm and borrowing personally.

🔑 Definition — Homemade Leverage: The use of personal borrowing or lending to alter the degree of financial leverage an investor experiences from owning shares in a firm.

Unlevering

Under the condition that TA management adopted the proposed capital structure, suppose an investor who owned 100 shares preferred the original capital structure. To create leverage, investors borrow on their own; to unlever, investors must loan out the money. In TA, the corporation borrowed an amount equal to half its value. The investor can unlever the stock by simply loaning out the money in the same proportion. The investor sells 50 shares for $1,000 total and then loans out $1,000 at 10%.

These payoffs ($125, $250, $375) match exactly what the investor would have received by owning 100 shares in the unlevered firm ($1.25 × 100, $2.50 × 100, $3.75 × 100). This demonstrates that corporate leverage decisions can be undone by investors through personal lending.

⭐ Key Takeaways

The optimal capital structure minimizes WACC and maximizes firm value. Financial leverage magnifies both gains and losses for shareholders, making EPS and ROE more sensitive to changes in EBIT. The break-even EBIT is the point where EPS is identical under different capital structures, and leverage is beneficial only when actual EBIT exceeds this break-even point. Most importantly, through homemade leverage and unlevering, investors can replicate or reverse corporate leverage decisions on their own, suggesting that in a world without taxes and bankruptcy costs, capital structure may not affect firm value—a foundation of the Modigliani-Miller proposition.

🧠 Quick Revision Questions

1. What is the relationship between WACC and firm value, and why does the optimal capital structure minimize WACC?
2. How does financial leverage affect EPS and ROE under different economic scenarios (recession, expected, expansion)?
3. Calculate the break-even EBIT for a firm with 300,000 shares outstanding (no debt) considering adding $2,000,000 debt at 8% interest, with a share price of $25.
4. Explain how an investor can use homemade leverage to replicate the returns of a levered firm by borrowing personally.
5. What is unlevering, and how can an investor undo the effects of corporate leverage through personal lending?

📘 Lecture 38 — M&M Propositions

📖 Overview: This lecture introduces the Modigliani and Miller (M&M) propositions on capital structure, first in a world without taxes and then with corporate taxes. It explains why capital structure matters (or doesn't) for firm value and cost of capital.

🗂️ Topics Covered

The lecture covers M&M Proposition 1 and 2 without taxes, showing how cost of equity changes with leverage while WACC remains constant. It then introduces business risk versus financial risk, followed by the impact of corporate taxes on capital structure, introducing the interest tax shield and M&M Proposition 1 with taxes.

📝 Lecture Summary

M&M PROPOSITIONS

Corporate borrowing is relatively less significant for corporate structure because investors can borrow or lend on their own. The stock price remains almost the same whichever capital structure a company chooses, based on the argument by Franco Modigliani and Merton Miller (commonly known as M&M).

The 1st proposition states that it is completely irrelevant how a firm chooses to arrange its finances. The size of the pie (firm's total value) does not depend on how it is sliced. Although changing the capital structure may not change the firm's total value, it does cause important changes in the firm's debt and equity.

We know that WACC = (E/V) x RE + (D/V) x RD where V = E + D. WACC can be interpreted as the required return on the firm's overall assets (RA). Thus RA = (E/V) x RE + (D/V) x RD. Rearranging: RE = RA + (RA – RD) x (D/E). This 2nd proposition tells us that the cost of equity depends on three things: the required return on firm's assets RA, the firm's cost of debt RD, and the firm's debt-equity ratio D/E.

As the firm raises its debt-equity ratio, the increase in leverage raises the risk of the equity and therefore the required return or cost of equity (RE). WACC remains the same, supporting M&M proposition 1.

📐 Formula: RE = RA + (RA – RD) x (D/E) → The cost of equity equals the return on assets plus a premium that increases with the debt-equity ratio.

📌 Example: RCD corporation has a WACC of 12% (ignoring taxes). It can borrow at 8%. With a target capital structure of 80% equity and 20% debt, D/E = 0.2/0.8 = 0.25, so RE = 12% + (12% - 8%) x 0.25 = 13%. With 50% equity, D/E = 1.0, so RE = 12% + (12% - 8%) x 1.0 = 16%. WACC in first case = 0.80 x 13% + 0.20 x 8% = 12%. In second case = 0.50 x 16% + 0.50 x 8% = 12%. So WACC is 12% in both cases.

Business and Financial Risk

M&M proposition 2 shows that the firm's cost of equity can be broken into two components. The required return on firm's assets, RA, depends on the nature of the firm's operating activities. The risk inherent in the firm's operations is called the business risk, which depends on the systematic risk of the firm's assets.

The component (RA – RD) x (D/E) is determined by the firm's financial structure. For an all-equity firm, this component is zero. The increase in debt financing raises the required return on equity because the risk born by the investors increases. This extra risk is called financial risk.

🔑 Definition — Business Risk: The risk inherent in the firm's operations, dependent on the systematic risk of the firm's assets. 🔑 Definition — Financial Risk: The extra risk borne by equity holders that results from debt financing.

Corporate Taxes & Capital Structure

Debt features two key aspects: interest paid on debt is tax deductible (a benefit for the firm), and failure to meet debt financing may lead to bankruptcy (a cost of debt financing).

Consider Firm U (unlevered) and Firm L (levered), identical on the left side of the balance sheet. EBIT is $1,000 every year for both firms. Firm L has issued $1,000 worth of perpetual bonds at 8% interest every year.

Cash flow from assets = EBIT – Taxes. Firm U = $700, Firm L = $724. Total cash flow to Firm L is $24 more, as its tax bill is $24 less. Interest being tax deductible has generated a tax saving equal to interest payment multiplied by tax rate, i.e. $80 x 0.30 = $24. This tax saving is called the Interest Tax Shield.

Since debt is perpetual, the same $24 shield will be generated every year forever. Since Firm L's cash flow is always $24 greater, its worth is more than Firm U by the value of this $24 perpetuity. Because the tax shield is generated by paying interest, it has the same risk as the debt, and 8% is therefore the appropriate discount rate.

PV = $24 / 0.08 = $300, which equals 0.30 x $1,000 = $300.

📐 Formula: PV of interest tax shield = (TC x D x RD) / RD = TC x D

The value of Firm L, VL, exceeds the value of Firm U, VU, by the present value of the interest tax shield, TC x D.

🔑 Definition — Interest Tax Shield: The tax saving generated by the tax deductibility of interest payments, equal to interest payment multiplied by the tax rate.

M&M Proposition 1 With Taxes

M&M Proposition 1 with taxes states that: VL = VU + TC x D

🔑 Definition — M&M Proposition 1 (with taxes): The value of the levered firm equals the value of the unlevered firm plus the present value of the interest tax shield.

💡 Why this matters: This proposition suggests that debt financing is highly advantageous and in the extreme, a firm's optimal capital structure is 100% debt. A firm's WACC decreases as the firm relies more heavily on debt financing.

M&M Summary

The No-Tax Case

• Proposition 1: The value of the firm levered (VL) is equal to the firm unlevered (VU): VL = VU. Implications: A firm's capital structure is irrelevant. A firm's WACC is the same no matter what mixture of debt and equity is used.
• Proposition 2: The cost of equity, RE is: RE = RA + (RA – RD) x D/E. Implications: Cost of equity rises as the firm increases its use of debt financing. The risk of the equity depends on business risk (which determines RA) and financial leverage (determined by D/E).

The Tax Case

• Proposition 1 with taxes: The value of the firm levered (VL) is equal to the value of the firm unlevered (VU) plus the present value of the interest tax shield: VL = VU + TC x D. Implications: Debt financing is highly advantageous and in the extreme a firm's optimal capital structure is 100% debt. A firm's WACC decreases as the firm relies more heavily on debt financing.

⭐ Key Takeaways

Without taxes, M&M propositions show that capital structure is irrelevant—firm value and WACC remain unchanged regardless of debt-equity mix. The cost of equity increases with leverage (RE = RA + (RA – RD) x D/E) to exactly offset the benefit of cheaper debt, keeping WACC constant. Business risk comes from operations, while financial risk is the additional risk borne by equity holders from debt financing. With corporate taxes, debt becomes advantageous because interest payments create a tax shield valued at TC x D, increasing firm value and reducing WACC. This leads to the extreme implication that optimal capital structure would be 100% debt under the tax-only view.

🧠 Quick Revision Questions

1. What does M&M Proposition 1 (no taxes) state about the relationship between firm value and capital structure?
2. Using M&M Proposition 2 (no taxes), if a firm has RA = 15%, RD = 10%, and a debt-equity ratio of 0.5, what is its cost of equity?
3. What is the difference between business risk and financial risk according to M&M?
4. How is the interest tax shield calculated, and why does it increase firm value?
5. According to M&M Proposition 1 with taxes, what is the optimal capital structure for a firm?

📘 Lecture 39 — Bankruptcy Costs

📖 Overview: This lecture examines the static theory of capital structure, which balances the tax benefits of debt against the costs of financial distress. It explains how firms determine their optimal capital structure and introduces the fundamental concepts of net working capital management, including how to identify sources and uses of cash.

🗂️ Topics Covered

This lecture covers bankruptcy costs (direct and indirect), financial distress costs, the static theory of capital structure, and the concept of optimal capital structure. It then illustrates these concepts through three comparative cases (M&M with no taxes, M&M with taxes, and static theory), followed by managerial recommendations regarding leverage. The lecture concludes with an introduction to net working capital, current assets and liabilities, and the sources and uses of cash.

📝 Lecture Summary

Bankruptcy Costs

Direct Bankruptcy Costs are the costs directly associated with the bankruptcy process, such as legal and administrative expenses. Indirect Bankruptcy Costs are the costs of avoiding a bankruptcy filing, which are incurred by a firm that is already in financial distress.

🔑 Definition — Financial Distress Costs: The total of both the direct and indirect costs associated with going bankrupt or experiencing financial distress.

Static Theory of Capital Structure

The Static Theory of Capital Structure states that a firm borrows up to the point where the tax benefit from an extra dollar of debt is exactly equal to the cost that comes from the increased probability of financial distress. This theory leads to the concept of an Optimal Capital Structure, which is the debt level (D*) that maximizes the firm's value (V_L*). The difference between the firm's value under the static theory and the M&M value with taxes is the loss in value from the possibility of financial distress. The difference between the static theory value and the M&M value with no taxes is the net gain from leverage.

📐 Formula: Optimal Capital Structure: The firm's value is maximized at V_L* when debt equals D*. The capital structure is composed of D*/ V_L* in debt and (1 - D*/ V_L*) in equity. The capital structure that maximizes firm value also minimizes the Weighted Average Cost of Capital (WACC).

Case 1, 2, and 3

Case 1 (M&M with no taxes, no bankruptcy costs): The value of the firm (V_L) and its WACC are not affected by capital structure. The firm's value remains constant at V_U regardless of debt, and WACC remains constant regardless of the debt-equity ratio.

Case 2 (M&M with corporate taxes, no bankruptcy costs): The value of the firm increases and the WACC decreases as the amount of debt goes up. This is due to the PV of the tax shield on debt (T_C x D). The firm value line slopes upward.

Case 3 (Static theory with corporate taxes and bankruptcy costs): The value of the firm (V_L) reaches a maximum at D*, the optimal amount of borrowing. At the same time, the WACC is minimized at the debt-equity ratio D*/E* (WACC*). The firm value increases initially due to the tax shield, but then decreases due to the PV of bankruptcy costs. The net gain from leverage is the difference between the firm's value under static theory and its value with no debt (V_U).

📌 Example: In Case 3, the value of the firm is initially V_U (value with no debt). As debt is added, the value rises due to the tax shield. However, as debt increases further, the probability and cost of financial distress rise, subtracting value from the firm. The firm reaches its maximum value at a specific debt level (D*), which is lower than the value predicted by M&M with taxes.

Some Managerial Recommendations

• Tax Benefits: Tax benefits from leveraging are only important to firms that are in a tax-paying position. Firms with substantial losses or tax shields from other sources (like depreciation) will get less benefit from leverage.
• Risk of Distress: Firms with a greater risk of experiencing financial distress will borrow less than firms with a lower risk.
• Assets: The cost of financial distress depends on the firm's assets and how easily their ownership can be transferred. Tangible assets are easier to transfer than intangible assets, making distress less costly for firms with tangible assets.

Net Working Capital

Net working capital (NWC) is the difference between current assets and current liabilities. Often, short-term financing is called net working capital management. Current assets are cash and other assets expected to convert to cash within one year (e.g., cash, marketable securities, accounts receivable, inventories). Current liabilities are obligations requiring cash payment within one year (e.g., accounts payable, expenses payable, notes payable).

📐 Formula: Balance Sheet Identity: NWC + Fixed assets = Long-term debt + Equity 📐 Formula: Cash Identity: Cash = Long-term debt + Equity + Current liabilities - Current assets (other than cash) - Fixed assets

Sources and Uses of Cash

• Activities that Increase Cash (Sources): Increasing long-term debt, equity, or current liabilities; decreasing current assets (other than cash) or fixed assets.
• Activities that Decrease Cash (Uses): Decreasing long-term debt, equity, or current liabilities; increasing current assets (other than cash) or fixed assets.
• Sources of cash always involve increasing a liability (or equity) account or decreasing an asset account.
• Uses of cash involve decreasing a liability (or equity) or increasing an asset account.

📌 Example: If accounts payable go up by $100, it is a source of cash (the firm borrowed $100 from its suppliers). If accounts receivable go up by $100, it is a use of cash (the firm has not yet collected $100 from its customers).

⭐ Key Takeaways

The static theory of capital structure is the central concept, which balances the tax shield benefit of debt against the increasing costs of financial distress. This trade-off creates a unique optimal capital structure (D*) that maximizes firm value and minimizes WACC, contrasting with M&M's earlier models where value either stays constant or increases indefinitely with debt. Managers must consider their firm's tax position, risk profile, and asset tangibility when making leverage decisions. Finally, understanding the difference between sources and uses of cash is fundamental to managing net working capital.

🧠 Quick Revision Questions

1. Define direct and indirect bankruptcy costs.
2. What is the fundamental trade-off in the static theory of capital structure?
3. In the static theory model, what happens to the firm's value and its WACC at the optimal capital structure (D*)?
4. Name two factors that reduce the benefit of leverage for a firm.
5. If a company increases its inventory, is this a source or a use of cash?

📘 Lecture 40 — OPERATING CYCLE AND CASH CYCLE

📖 Overview: This lecture explains the short-term financial activities of a manufacturing firm, focusing on the timing of cash flows. It defines and calculates the operating cycle and cash cycle, showing how long it takes a firm to convert inventory into cash and how to manage the gap between cash outflows and inflows.

🗂️ Topics Covered

The lecture covers the sequence of events and decisions in short-run activities, introduces the concepts of operating cycle (inventory period + accounts receivable period) and cash cycle (operating cycle minus accounts payable period), explains how to calculate these cycles using financial ratios, and discusses the interpretation and management of the cash cycle for profitability.

📝 Lecture Summary

Short-Run Activities and Cash Flow Timing

For a typical manufacturing firm, short-run activities consist of a sequence of events (buying raw materials, paying cash, manufacturing, selling, collecting cash) and corresponding decisions (how much inventory to order, whether to borrow, production technology, credit extension, and collection methods). These activities are unsynchronized because payment for purchases may not happen at the same time as receipts from sales, and they are uncertain because future sales and costs cannot be precisely predicted.

Consider the following chronological events:

• Day 0: Acquire inventory on credit (no cash effect)
• Day 30: Pay for inventory (-$1,000)
• Day 60: Sell inventory on credit (no cash effect)
• Day 105: Collect on sale (+$1,400)

Operating Cycle

The operating cycle is the time period between the acquisition of inventory and the collection of cash from receivables. In the example, it is 105 days.

The inventory period is the time it takes to acquire and sell inventory (60 days in the example). The accounts receivable period is the time between the sale of inventory and collection of the receivable (45 days in the example).

🔑 Definition — Operating Cycle: The sum of the inventory period and the accounts receivable period. It describes how a product moves through current asset accounts: it begins as inventory, is converted to a receivable when sold, and is converted to cash when collected.

📐 Formula: Operating cycle = Inventory period + Accounts receivable period → This tells the total time from purchasing inventory to receiving cash from its sale.

📌 Example: 105 days = 60 days + 45 days

Cash Cycle

The accounts payable period is the time between receipt of inventory and payment for it. In the example, payment is made after 30 days.

The cash cycle is the time between cash disbursement and cash collection. Since cash is spent on day 30 but not collected until day 105, the firm must finance $1,000 for 75 days.

🔑 Definition — Cash Cycle: The difference between the operating cycle and the accounts payable period. It represents the gap between short-term cash outflows and inflows that must be financed, either by borrowing or by holding a liquidity reserve.

📐 Formula: Cash cycle = Operating cycle – Accounts payable period → This tells how many days the firm needs to arrange financing for its operations.

📌 Example: 75 days = 105 days – 30 days

The gap can be filled either by borrowing or by holding a liquidity reserve in the form of cash or marketable securities. Alternatively, the gap can be shortened by changing the inventory, receivable, and payable periods.

Roles in Managing Operating Cycle

Various managers influence the short-term financial management of assets and liabilities:

• Cash Manager: Handles collection, concentration, disbursement, short-term investment, short-term borrowing, and bank relations (affects cash, marketable securities, short-term loans)
• Credit Manager: Monitors and controls accounts receivable and makes credit policy decisions (affects accounts receivable)
• Marketing Manager: Makes credit policy decisions (affects accounts receivable)
• Purchase Manager: Decides on purchases, supplies, and may negotiate payment terms (affects inventory, accounts payable)
• Production Manager: Sets production schedules and materials requirements (affects inventory, accounts payable)
• Payables Manager: Decides on payment policies and whether to take discounts (affects accounts payable)
• Controller: Provides accounting information on cash flows, reconciles accounts receivable, and applies payments (affects accounts receivable, accounts payable)

Calculating Operating and Cash Cycle

Using balance sheet information (in thousands) and an income statement with Net Sales of $11,500 and Cost of Goods Sold of $8,200:

Average Inventory = $2,500, Average Accounts Receivable = $1,800, Average Accounts Payable = $875

📐 Formula — Inventory Turnover: Cost of goods sold / Average Inventory → Tells how many times inventory is sold and replaced during the year.

📌 Example: Inventory turnover = $8.2 million / $2.5 million = 3.28 times

📐 Formula — Inventory Period: 365 days / Inventory Turnover → Tells the average number of days inventory sits before being sold.

📌 Example: Inventory period = 365 / 3.28 = 111.3 days

Assuming all sales were credit sales:

📐 Formula — Receivables Turnover: Credit Sales / Average Accounts Receivable → Tells how many times receivables are collected during the year.

📌 Example: Receivables turnover = $11.5 million / $1.8 million = 6.4 times

📐 Formula — Receivables Period: 365 days / Receivable Turnover → Tells the average number of days customers take to pay.

📌 Example: Receivables period = 365 / 6.4 = 57 days (also called days' sales in receivables or average collection period)

📌 Example: Operating cycle = 111 days + 57 days = 168 days

📐 Formula — Payables Turnover: Cost of goods sold / Average Payables → Tells how many times payables are paid off during the year.

📌 Example: Payables turnover = $8.2 million / $0.875 million = 9.4 times

📐 Formula — Payables Period: 365 days / Payables Turnover → Tells the average number of days the firm takes to pay its suppliers.

📌 Example: Payables period = 365 / 9.4 = 39 days

📌 Example: Cash cycle = 168 days – 39 days = 129 days

Example: SP Company

SP Company has the following figures: Inventory (beginning $5,000, ending $7,000), Accounts Receivable (beginning $2,700, ending $2,400), Accounts Payable (beginning $750, ending $4,800), Credit Sales = $50,000, Cost of Goods Sold = $30,000.

📌 Calculations:

• Average Inventory = ($5,000 + $7,000)/2 = $6,000
• Average Receivables = ($2,700 + $2,400)/2 = $2,000
• Average Payables = ($750 + $4,800)/2 = $3,750
• Inventory turnover = $30,000/$6,000 = 5 times
• Receivable turnover = $50,000/$2,000 = 25 times
• Payable turnover = $30,000/$3,750 = 8 times
• Inventory period = 365/5 = 73 days
• Receivable period = 365/25 = 14.6 days
• Payable period = 365/8 = 45.6 days
• Operating cycle = 73 + 14.6 = 87.6 days
• Cash cycle = 87.6 – 45.6 = 42 days

Interpreting Cash Cycle

These calculations reveal that the cash cycle depends on inventory, receivable, and payable turnovers. It increases if inventory and receivables periods get longer, and decreases if the payable period is lengthened.

Most firms have a positive cash cycle and require more financing for inventories and receivables for longer cash cycles. The link between the firm's cash cycle and its profitability is provided by Total Assets Turnover (Sales/Total Assets). The higher this ratio, the greater the firm's accounting Return on Assets (ROA) and Return on Equity (ROE). Therefore, the shorter the cash cycle, the lower the firm's investment in inventories and receivables, the lower total assets, and the higher total asset turnover.

💡 Why this matters: A shorter cash cycle means the firm needs less external financing, has lower asset investments, and achieves higher profitability through better asset utilization.

⭐ Key Takeaways

The operating cycle (inventory period + receivables period) measures the total time from inventory acquisition to cash collection, while the cash cycle (operating cycle minus payables period) measures the net financing gap. A shorter cash cycle reduces the need for external financing and improves profitability by increasing total asset turnover, return on assets, and return on equity. The cash cycle can be managed by adjusting inventory, receivable, and payable periods through coordinated actions of cash, credit, marketing, purchase, production, and payables managers.

🧠 Quick Revision Questions

1. What is the operating cycle, and how is it calculated?
2. What is the cash cycle, and how is it different from the operating cycle?
3. How does a longer inventory period affect the cash cycle?
4. Using the formula, calculate the cash cycle if a firm has an inventory period of 73 days, a receivable period of 14.6 days, and a payable period of 45.6 days.
5. Why does a shorter cash cycle improve a firm's profitability?

📘 Lecture 41 — Short-Term Financial Policy

📖 Overview: This lecture explores short-term financial policy, focusing on how firms determine the size and financing of current assets. It explains the trade-offs between flexible and restrictive policies, introduces the concept of carrying costs versus shortage costs, and demonstrates how to use a cash budget for short-term financial planning.

🗂️ Topics Covered

The lecture covers the size of investments in current assets under flexible and restrictive policies, the financing of current assets with short-term versus long-term debt, carrying costs and shortage costs, alternative financing policies including temporary and permanent current assets, the three policy types (Flexible F, Restrictive R, and Compromise C), and a detailed example of constructing a cash budget for PT Inc.

📝 Lecture Summary

Size of investments in current assets

A flexible policy maintains a high ratio of current assets to sales, keeping larger cash/marketable securities balances, larger inventory investments, and more liberal credit terms leading to higher accounts receivable. A restrictive policy maintains a low ratio of current assets to sales, keeping lower cash balances, smaller inventory investments, and tight or no credit sales with minimal accounts receivable. The optimum level of investment depends on a trade-off between costs of restrictive versus flexible policies. Flexible policies are costly because they require greater investment in current assets, but expected future cash-flows are higher. A restrictive policy reduces future sales levels compared to a flexible policy.

Financing of current assets

Under a flexible policy, firms use less short-term debt and more long-term debt. Under a restrictive policy, firms use more short-term debt and less long-term debt.

Carrying costs and shortage costs

Managing short-term assets involves a trade-off between carrying costs and shortage costs. Carrying costs increase with increased levels of current assets and include costs to store and finance assets, as well as opportunity costs (e.g., inventories vs. short-term investments). Shortage costs decrease with increased levels of current assets and include trading or order costs (avoiding stock-outs through more frequent orders) and costs related to lack of safety reserves (lost sales, customers, and production stoppages).

🔑 Definition — CA*: The optimal amount of current assets that minimizes total costs (carrying costs + shortage costs).

📐 Formula: Total cost of holding current assets = Carrying costs + Shortage costs → At CA*, the sum of these two costs is minimized.

📌 Example: A firm with low carrying costs relative to shortage costs should use a flexible policy (high CA). A firm with high carrying costs relative to shortage costs should use a restrictive policy (low CA). The minimum point on the total cost curve determines CA*.

Alternative Financing Policies

Total asset requirements for a growing firm change over time due to a general growth trend, seasonal variation, and unpredictable fluctuations. Temporary current assets are additional current assets carried during peak times that decrease as sales occur. Permanent current assets are the minimum level of current assets carried at all times, considered permanent because the level is constant.

📌 Example: Policy F (Flexible) implies a short-term cash surplus and large investment in cash and marketable securities. Policy R (Restrictive) uses long-term financing only for permanent asset requirements and short-term borrowing for seasonal variations.

💡 Why this matters: Choosing between Policy F and Policy R affects liquidity, risk, and profitability. Policy F provides safety but lower returns, while Policy R is cheaper but riskier.

Which is the Best Policy?

Cash Reserves — Pros: firms are less likely to experience financial distress and can handle emergencies or take unexpected opportunities. Cons: cash and marketable securities earn lower returns and are zero NPV investments.

Maturity Hedging — Try to match financing maturities with asset maturities: finance temporary current assets with short-term debt; finance permanent current assets and fixed assets with long-term debt and equity.

Interest Rates — Short-term rates are normally lower than long-term rates, so short-term debt may be cheaper. However, firms can get into trouble if rates increase quickly or if they have difficulty making payments and cannot refinance.

Compromise Policy — The firm keeps a reserve of liquidity to initially finance seasonal variations. Short-term borrowing is used when the reserve is exhausted.

Cash Budget

A cash budget is a forecast of cash inflows and outflows over the next short-term planning period. It is the primary tool in short-term financial planning, helping determine when the firm will have cash surpluses or need to borrow. It records estimates of cash receipts and disbursements.

🔑 Definition — Cash Budget: A forecast of cash inflows and outflows used to plan short-term financing needs.

📌 Example — PT Inc. Cash Budget:

• Sales estimates (in millions): Q1=500, Q2=600, Q3=650, Q4=800, Q1 next year=550

• Beginning receivables = $250; Average collection period = 30 days (2/3 collected in quarter made, 1/3 next quarter)

• Cash Collections:

  • Q1: Beginning receivables $250 + (2/3 × 500 = 333) = $583; Ending receivables = 1/3 × 500 = $167
  • Q2: $167 + 400 = $567; Ending = $200
  • Q3: $200 + 433 = $633; Ending = $217
  • Q4: $217 + 533 = $750; Ending = $267

• Accounts payable: Purchases = 50% of next quarter's sales; Payables period = 45 days (half paid each quarter, half next)

  • Q1 purchases = 50% × 600 = 300
  • Q2 purchases = 50% × 650 = 325
  • Q3 purchases = 50% × 800 = 400
  • Q4 purchases = 50% × 550 = 275

• Cash Disbursements:

  • Q1: Payment of accounts = beginning payables $125 + half of Q1 purchases (150) = $275; Wages (25% of 500=125); Interest $50 = Total $450
  • Q2: Payment = half of Q1 purchases (150) + half of Q2 purchases (162.5) = $312.5? Wait, recalculate: Beginning payables $125 paid in Q1. So Q1 payments = $125 + (0.5 × 300 = 150) = $275. Q2 payments = (0.5 × 300 = 150) + (0.5 × 325 = 162.5) = $312.5? But lecture shows $438. Let me check: Actually, the lecture says payables period is 45 days = half of purchases. So for Q1, purchases = 300. Half paid in Q1 = 150, half in Q2 = 150. Beginning payables = 125 all paid in Q1. So Q1 payments = 125 + 150 = 275. Q2: 150 (from Q1) + half of Q2 purchases (325/2 = 162.5) = 312.5? But lecture says 438. There's a discrepancy. Let me re-read: "Beginning payables = 125" and "Payables period is 45 days, so half of the purchases will be paid for each quarter and the remaining will be paid the following quarter." So Q1 purchases = 50% × 600 = 300. Half paid Q1 = 150, half Q2 = 150. Q2 purchases = 50% × 650 = 325. Half paid Q2 = 162.5, half Q3 = 162.5. Q3 purchases = 50% × 800 = 400. Half paid Q3 = 200, half Q4 = 200. Q4 purchases = 50% × 550 = 275. Half paid Q4 = 137.5, half Q1 next year.

• Cash Disbursements per lecture:

  • Q1: Payment of accounts = $275 (beg payables 125 + half of Q1 purchases 150); Wages 125; Interest 50 = Total $450
  • Q2: Payment of accounts = $438 (half of Q1 150 + half of Q2 162.5 + ? Beginning payables already done. Wait, 150+162.5=312.5. Lecture says 438. Actually maybe beginning payables of 125 is only for Q1. So Q2: 150 + 162.5 = 312.5 plus wages 150 plus capital exp 200 plus interest 50 = 712.5? Lecture says 438 just for payment of accounts? Hmm. Let me recheck: Q2 payments = from Q1 purchases (150) + from Q2 purchases (162.5) = 312.5. But lecture says 438. Actually, maybe: Beginning payables $125 paid in Q1. Then Q1 purchases = 300 → 150 paid Q1, 150 paid Q2. Q2 purchases = 325 → 162.5 paid Q2, 162.5 paid Q3. So Q2 payments = 150 + 162.5 = 312.5. But lecture says 438. There's an error in the lecture text or my interpretation. Let's go with what the lecture states.

  The lecture states: Q1 = $450, Q2 = $838, Q3 = $575, Q4 = $588.

⭐ Key Takeaways

The key concepts to remember are: the trade-off between flexible and restrictive short-term financial policies determines the optimal level of current assets (CA*), where carrying costs and shortage costs are minimized. Firms must distinguish between temporary and permanent current assets and choose financing policies (Flexible F, Restrictive R, Compromise C) that balance cash reserves, maturity hedging, and interest rate risks. The cash budget is the essential tool for forecasting cash inflows (collections) and outflows (disbursements) to plan for surpluses or financing needs, using collection periods and payables periods to calculate timing.

🧠 Quick Revision Questions

1. What are the key differences between a flexible policy and a restrictive policy in terms of cash balances, inventory, and accounts receivable?
2. How do carrying costs and shortage costs behave as the amount of current assets increases, and where is the optimal point CA* located?
3. Under the maturity hedging approach, how should temporary current assets and permanent current assets be financed?
4. What are the pros and cons of maintaining large cash reserves versus using short-term debt?
5. Using the cash budget example, if the average collection period is 30 days, what fraction of sales is collected in the current quarter, and what fraction is collected in the next quarter?

📘 Lecture 42 — Short-Term Borrowing

📖 Overview: This lecture covers the various sources of short-term financing available to firms, distinguishing between unsecured and secured loans. It also introduces the process of creating a short-term financial plan and explains the concepts of float, cash management, and the motives for holding cash.

🗂️ Topics Covered

The lecture begins by detailing types of unsecured loans (line of credit, revolving credit, letter of credit) and secured loans (accounts receivable financing through assigning and factoring, and inventory loans via blanket lien, trust receipt, and field warehouse financing). It then presents a quantitative example of a short-term financial plan for PT Inc., calculating interest costs and debt levels. Finally, it covers the reasons for holding cash (speculative, transaction, and precautionary motives) and the benefits and opportunity costs of cash holdings.

📝 Lecture Summary

Short-Term Borrowing

Short-term borrowing can be categorized as unsecured loans, which are not backed by collateral, and secured loans, which are backed by specific assets like receivables or inventory. Unsecured options include a line of credit (an informal or formal arrangement with a bank), a committed line of credit (a formal arrangement involving a commitment fee), and a non-committed line of credit (an informal channel with less paperwork). A revolving credit arrangement is a formal line of credit that is open for two or more years. A letter of credit is another form of unsecured guarantee.

Secured loans involve pledging specific assets. Accounts receivable financing can be done through assigning, where the borrower is responsible even if the receivables are not collected, or factoring, where the receivable is discounted and sold to the lender (factor) who then bears the risk of default. Maturity factoring is a type where the factor forwards the money on an agreed-upon future date.

Inventory loans are another form of secured financing. A blanket inventory lien gives the lender a lien against all of the borrower's inventories. A trust receipt (also called floor planning) allows the borrower to hold specific inventory in “trust” for the lender. Field warehouse financing uses an independent company specialized in inventory management to act as a control agent.

Other sources of short-term funding include commercial paper, which are short-term notes issued by large and highly rated firms, and trade credit, which involves increasing the accounts payable period by delaying payments to suppliers.

A Short-Term Financial Plan

This section presents a financial plan for PT Inc., which arranges to borrow any needed funds on a short-term basis at an interest rate of 20% APR, calculated on a quarterly basis (20%/4 = 5%). The initial short-term debt is zero.

The plan uses projected cash flows for four quarters (in millions): Q1: Beginning cash $20, Net inflow $40 → Ending cash $60 Q2: Beginning cash $60, Net inflow -$110 → Ending cash -$50 Q3: Beginning cash -$50, Net inflow $55 → Ending cash $5 Q4: Beginning cash $5, Net inflow -$15 → Ending cash -$10

After accounting for a minimum cash balance of $10 million, the cumulative surplus (deficit) for each quarter is: Q1: $50, Q2: -$60, Q3: -$5, Q4: -$20. To cover the deficits, PT Inc. borrows funds.

The final plan shows:

• Q1: Beginning cash $20, Net inflow $40, No borrowing needed, Ending cash $60.
• Q2: Beginning cash $60, Net inflow -$110, New short-term borrowing of $60, Ending cash $10.
• Q3: Beginning cash $10, Net inflow $55, Interest on short-term borrowing (5% of $60 = $3), Short-term borrowing repaid of $52, Ending cash $10.
• Q4: Beginning cash $10, Net inflow -$15, New short-term borrowing of $15.4 (to cover the deficit plus the new interest), Ending cash $10.

The ending short-term debt for each quarter is: Q1: $0, Q2: $60, Q3: $8, Q4: $23.4. The final debt of $23.4 million equals the cumulative deficit for the entire year ($20 million) plus total interest paid during the year ($3 + 0.4 = $3.4 million). This plan, which ignores the tax deductibility of interest and interest earnings on cash surplus, illustrates that financing the firm’s short-term needs will cost about $3.4 million in interest before taxes for the year.

📐 Formula: Interest = Beginning Short-Term Debt × Quarterly Interest Rate. (e.g., Q3 Interest = $60 million × 5% = $3 million) 📌 Example: In Q3, PT Inc. had $60 million in beginning short-term debt. The interest cost for the quarter is $60 million × 0.05 = $3 million. The company then repays $52 million of its debt, leaving an ending balance of $60 + $3 - $52 = $8 million.

Float and Cash Management

The basic objective in cash management is to keep the investment in cash as low as possible while still operating the firm’s activities efficiently and effectively. The key principle is to collect early and pay late. The firm must invest temporarily idle cash in short-term marketable securities, which have lower default risk and are highly liquid.

The three reasons for holding cash are:

• Speculative Motive: The need to hold cash to take advantage of additional investment opportunities, such as bargain purchases, attractive interest rates, and favorable exchange rate fluctuations. This also relates to reserve borrowing utility and holding marketable securities.
• Transaction Motive: The need to hold cash to satisfy normal disbursement and collection activities associated with a firm’s ongoing operations.
• Precautionary Motive: The need to hold cash as a safety margin to act as a financial reserve.

🔑 Definition — Opportunity Cost of Holding Cash: The interest income that could be earned in the next best use if the cash were not held idle. 💡 Why this matters: Holding excessive cash has a real cost (foregone interest income). The firm must balance this cost against the need to have sufficient liquidity for transactions and the risk of a "cash-out" situation, which might force it to raise cash on a short-term basis by borrowing or selling current assets.

⭐ Key Takeaways

The lecture categorizes short-term borrowing into unsecured loans (like lines of credit) and secured loans (using receivables or inventory as collateral). The short-term financial plan example demonstrates that the cost of borrowing is calculated on a quarterly basis, leading to an annual interest expense that must be added to the cumulative deficit to arrive at the final short-term debt. The core goal of cash management is to minimize idle cash while ensuring enough liquidity for operations, driven by transaction, precautionary, and speculative motives. The primary cost of holding excessive cash is the opportunity cost of forgone interest income from alternative investments.

🧠 Quick Revision Questions

1. What is the difference between a "committed" and a "non-committed" line of credit?
2. In accounts receivable financing, what is the key difference between assigning and factoring?
3. For PT Inc., what was the total amount of interest paid on short-term debt over the entire year?
4. Name the three main motives for holding cash and briefly describe each.
5. What is the "opportunity cost" of a firm holding excessive cash balances?

📘 Lecture 43 — Float and Cash Management

📖 Overview: This lecture explains the concept of float—the difference between a firm's book balance and bank balance—and how it impacts cash management. It covers strategies for accelerating cash collections, controlling disbursements, and investing idle cash, while also introducing the components of credit policy. Understanding float is critical for managing a firm's liquidity and minimizing financing costs.

🗂️ Topics Covered

The lecture defines float, including disbursement, collection, and net float, and explains how cheques create timing differences. It then breaks down cash collection and disbursement processes into mailing, processing, and availability delays, and introduces tools like lockboxes, concentration banks, and zero-balance accounts. Finally, it covers the components of credit policy—terms of sale, credit analysis, and collection policy—and explains trade credit terms like 2/10, net 30.

📝 Lecture Summary

Float and Cash Management

The difference between bank cash and book cash, representing the net effect of cheques in the process of clearing, is called float. Cheques written by a firm generate disbursement float, causing a decrease in the firm’s book balance but no change in its available balance. Cheques collected by the firm create collection float, which increases book balances but does not immediately change available balance.

🔑 Definition — Float: The difference between a firm's available balance (bank cash) and its book balance (accounting cash), caused by cheques in transit. 📐 Formula: Float = Firm’s available balance – Firm’s book balance 📐 Formula: Net float = Disbursement float + Collection float → The overall timing difference from all payment and collection activities. 📌 Example: GM Inc. has $100,000 on deposit. On June 8, it pays with a $100,000 cheque. The book balance drops to $0 immediately, but the available balance stays $100,000 until the cheque clears on June 14. Disbursement float = $100,000 – $0 = $100,000. 📌 Example: You have $5,000 on deposit. You write a $1,000 cheque (disbursement float = $1,000) and deposit a $2,000 cheque (collection float = -$2,000). Net float = $1,000 + (-$2,000) = -$1,000. Your available balance is $1,000 less than your book balance.

Components of Collection and Disbursement Time

Total collection or disbursement time can be broken into three parts: mailing time (cheques trapped in the postal system), processing delay (time to process and deposit the cheque), and availability delay (time to clear the cheque through the banking system). Electronic Data Interchange (EDI) eliminates paper invoices and cheques, sharply reducing or eliminating float.

💡 Why this matters: Reducing any of these delays accelerates cash availability, improving liquidity and reducing borrowing needs.

Cash Collection and Concentration

To speed up collections, firms can use multiple collection points, lockboxes (post office boxes where banks collect and process payments directly), or preauthorized payment systems. Cash concentration is the process of moving funds from multiple collection points (e.g., local banks) into a single main account, often at a concentration bank, to reduce the number of accounts to track and centralize cash management.

Cash Disbursement and Ethical Issues

The goal in managing disbursement float is to slow down disbursements by increasing mailing, processing, and availability delays. Strategies include writing cheques on a distant bank, mailing from a distant post office, or holding payment for several days. However, financial managers must always work with collected company cash balances, not book balances—using uncleared funds without the bank’s knowledge raises serious ethical and legal questions.

🔑 Definition — Zero-balance account: A disbursement account where the firm maintains a zero balance, transferring funds from a master account only as needed to cover cheques presented for payment. 🔑 Definition — Controlled disbursement account: A disbursement account where the firm transfers an amount sufficient to cover demands for payment.

Investing Idle Cash

Firms with surplus cash can invest in the money market, often via money market mutual funds (funds that invest in short-term financial assets for a fee). Surplus cash arises from seasonal/cyclical activities or planned expenditures. For example, when seasonal demand for current assets is low, surplus is invested in short-term marketable securities (Time 1); when demand is high, the deficit is financed by selling securities or borrowing (Time 2).

Credits and Receivables

Granting credit stimulates sales but involves costs: the chance of non-payment and the cost of carrying receivables. Credit policy decisions involve a trade-off between increased sales and these costs. Its three components are: terms of sale (conditions for cash or credit), credit analysis (determining the probability of customer payment), and collection policy (procedures for collecting accounts receivable).

Terms of Sale

The terms of sale include the credit period (time to pay in full), cash discounts and discount period, and credit instruments. For example, terms of 2/10, net 30 mean the customer has 30 days to pay the full amount, but can take a 2% discount if payment is made within 10 days.

📌 Example: A buyer places a $1,000 order under terms 2/10, net 60. They can either pay $1,000 × (1 – 0.02) = $980 in 10 days, or pay the full $1,000 in 60 days.

⭐ Key Takeaways

Float is the difference between available and book balances, and it can be positive (disbursement float > collection float) or negative. Managing float involves accelerating collections (via lockboxes, concentration banks) and controlling disbursements (via zero-balance accounts, distant banks), while always operating on collected, not book, balances. Idle cash should be invested in money market instruments. Finally, credit policy—including terms of sale like 2/10, net 30—balances the benefit of increased sales against the costs of delayed receipts and default risk.

🧠 Quick Revision Questions

1. If a firm has an available balance of $50,000 and a book balance of $40,000, what is the net float, and what does it imply about disbursement versus collection float?
2. What are the three components of total collection time, and which one does a lockbox primarily reduce?
3. A firm uses a zero-balance account for payroll. What happens when payroll cheques are presented for payment?
4. Under trade terms of 3/15, net 45, what is the effective discount percentage, and when must the full payment be made?
5. Why is it unethical for a financial manager to write cheques against uncollected deposits?

📘 Lecture 44 — CREDITS AND RECEIVABLES

📖 Overview: This lecture explains how firms manage credit offered to customers, including the structure of credit periods, the trade-offs of offering cash discounts, and the factors that influence optimal credit policy. It also covers how firms analyze customer creditworthiness and implement collection policies to manage receivables effectively.

🗂️ Topics Covered

The lecture covers credit period components and influencing factors, cash discounts and their cost calculations, credit instruments, optimal credit policy with carrying and opportunity costs, trade credit conditions, credit analysis using the 5 C's, and collection policy including aging schedules and collection procedures.

📝 Lecture Summary

Credits and Receivables

Credit Period is the basic length of time for which credit is granted. If a cash discount is offered, the credit period has two components: the net credit period (length of time customer has to pay) and the cash discount period (time during which discount is available). The invoice date is the shipping date or billing date. The two most important factors influencing credit period length are the buyer's inventory period and operating cycle – the shorter these are, the shorter the credit period. By extending credit, we finance a portion of our buyer's operating cycle and shorten the buyer's cash cycle. If our credit period exceeds the buyer's inventory period, we are financing not only inventory purchases but also part of the buyer's receivables. If our credit period exceeds the buyer's operating cycle, we are providing financing for the customer's business beyond the immediate sale, meaning the buyer has a loan from us even after the merchandise is resold.

💡 Why this matters: Understanding how credit periods interact with the buyer's operating cycle helps firms avoid effectively becoming long-term lenders to their customers.

Other factors influencing credit period include:

• Perishability and collateral value – perishable items have rapid turnover and low collateral value, so credit periods are shorter.
• Consumer demand – well-established products have rapid turnover, while newer or slow-moving products require longer credit periods.
• Cost, profitability and standardization – inexpensive and standardized products have lower markups and higher turnover rates, leading to shorter credit periods.
• Credit risk – higher credit risk leads to shorter credit periods.
• Size of the account – smaller accounts may have shorter credit periods as they are more costly to manage.
• Product market competition – in highly competitive markets, longer credit periods may be offered.
• Customer type – determined on a case-to-case basis.

Cash discounts are discounts given to induce prompt payment, also called sales discount. This reduces the amount of credit offered, and the firm must trade this off against the cash discount. Buyers only use credit after the discount expires, making this a way to charge higher prices on credit sales. An example is "3/10 net 30" – the customer can take a 3% discount if they pay within 10 days but must pay within 30 days. A firm offering "3/10 net 30" is essentially offering customers a 20‑day loan. For a $1,000 sale, some customers pay on day 10 taking the discount, while others pay on day 30 forgoing the discount. A customer who forgoes the 3% discount to pay on day 30 is borrowing $970 for 20 days and paying $30 interest.

🔑 Definition — Cash Discount: A discount given to induce prompt payment, also called a sales discount. 📐 Formula: $(1 + r)^{20/365} = \frac{$1,000}{$970}$ → $r = \left(\frac{$1,000}{$970}\right)^{365/20} - 1 = 0.7435 = 74.35%$ 📌 Example: A firm offers "3/10 net 30" on a $1,000 sale. Customer pays on day 30 forgoing the 3% discount. They borrow $970 for 20 days and pay $30 interest. The effective annual interest rate is 74.35%.

Credit instrument is the basic evidence of indebtedness. Most credit is offered on open account — the invoice is the only credit instrument. Promissory notes are IOUs signed after delivery of goods. Commercial drafts call for a customer to pay a specific amount by a specific date; the draft is sent to the customer's bank, and when signed, the goods are sent. Banker's acceptances allow a bank to substitute its creditworthiness for the customer, for a fee. Conditional sales contracts let the seller retain legal ownership of the goods until the customer has completed payment.

Optimal Credit Policy

The optimal amount of credit is determined by the point where incremental cash flows from increased sales exactly equal the incremental costs of carrying the increased investment in accounts receivable. Carrying costs associated with granting credit are of three types: the required return on receivables, losses from bad debts, and the cost of managing credit and credit collection. For a restrictive credit policy, all these costs will be low. Shortage of credit creates an opportunity cost of extra potential profit from credit sales that is low because credit is refused — this forgone benefit comes from increased quantity sold and higher prices. Carrying costs are positively related to the amount of credit extended, while opportunity costs go down when credit is granted. The sum of carrying costs and opportunity costs is called the credit cost curve.

💡 Why this matters: The optimal credit policy balances the costs of granting credit against the profits from increased sales, and this optimum depends on the specific characteristics of each firm.

Trade credit is more likely to be granted if: the selling firm has a cost advantage over other lenders; can engage in price discrimination; can obtain favorable tax treatment; has no established reputation for quality; or perceives a long-term strategic relationship. The optimal credit policy depends on particular firm characteristics including excess capacity, low variable operating costs, and repeat customers.

Credit Analysis

Credit analysis refers to the process of deciding whether to extend credit to a particular customer by gathering relevant information and determining creditworthiness. Credit information sources include financial statements, credit reports on the customer's payment history with other firms, banks, and the customer's payment history with the firm. Credit evaluation uses the traditional 5 C's of credit: Character (willingness to pay), Capacity (ability to pay), Capital (financial reserves), Collateral (pledged assets), and Conditions (relevant economic conditions). Credit scoring refers to calculating a numerical rating for a customer based on collected information; credit is granted or refused based on the result.

🔑 Definition — Credit Analysis: The process of deciding whether or not to extend credit to a particular customer by gathering relevant information and determining creditworthiness. 🔑 Definition — Credit Scoring: The process of calculating a numerical rating for a customer based on information collected; credit is then granted or refused based on the result.

Collection Policy

Collection refers to obtaining payment on past-due accounts. Collection Policy is composed of the firm's willingness to extend credit as reflected in the firm's investment in receivables and the collection effort. To track payments, the firm focuses on its Average Collection Period (ACP). Alternatively, an Aging Schedule can be used to monitor receivables, classifying credit accounts by age.

📌 Example: A firm has $100,000 in receivables with the following aging schedule:

If this firm has a credit period of 60 days, then 25% of its accounts are late. The seriousness depends on the nature of the firm's collections and customers. The longer an account has been unpaid, the less likely it is to be paid. Percentages on aging schedules keep changing for firms with seasonal sales.

Collection Effort – most firms follow a protocol for past-due customers: send a delinquency letter, make a telephone call to the customer, employ a collection agency, and/or take legal action against the customer. The firm may also refuse to grant additional credit to customers until arrearages are cleared up.

⭐ Key Takeaways

The credit period has two components when a cash discount is offered: net credit period and cash discount period, and its length is primarily influenced by the buyer's inventory period and operating cycle. Cash discounts like "3/10 net 30" effectively create a high-cost loan (up to 74.35% APR) for customers who forgo the discount. Optimal credit policy balances carrying costs (positively related to credit extended) against opportunity costs (negatively related to credit extended) at the point where total costs are minimized. Credit analysis uses the 5 C's framework (Character, Capacity, Capital, Collateral, Conditions) and credit scoring to evaluate customer creditworthiness. Collection policy uses aging schedules and a progressive protocol from delinquency letters to legal action to manage past-due accounts.

🧠 Quick Revision Questions

1. What are the two components of a credit period when a cash discount is offered, and how do they relate to the invoice date?
2. If a firm's credit period exceeds the buyer's operating cycle, what does this imply about the financing being provided?
3. Calculate the effective annual interest rate for a "2/10 net 30" credit term on a $500 sale, showing all steps.
4. What are the three types of carrying costs associated with granting credit, and how do they behave relative to the amount of credit extended?
5. Describe the traditional 5 C's of credit and explain how each factor contributes to determining a customer's creditworthiness.

📘 Lecture 45 — INVENTORY MANAGEMENT

📖 Overview: This lecture examines how firms manage their inventory to balance carrying costs and shortage costs while supporting the operating cycle. It introduces key inventory management concepts including the ABC approach, the Economic Order Quantity (EOQ) model, and practical considerations like safety stock and reorder points.

🗂️ Topics Covered

The lecture covers inventory types and their liquidity characteristics, inventory costs including carrying and shortage costs with their trade-off relationship, the ABC approach for prioritizing inventory management, the Economic Order Quantity (EOQ) model for determining optimal order sizes with mathematical derivation, and practical inventory management concepts including safety stock and reorder points.

📝 Lecture Summary

Inventory Types

The firm's operating cycle is made up of its inventory period and receivables period. Both credit policy and inventory policy coordinate to derive sales and ensure smooth processing of acquiring, selling inventory, and collecting on sales. Inventory comes in three types: Raw Material (starting point in production), Work-in-Progress (size depends on production process length), and Finished Goods. One company's raw material can be another's finished good, such as steel sheets for automobile manufacturing.

Various inventory types differ in liquidity. Commodity-like or standardized raw materials are easily converted to cash, while work-in-progress can be quite illiquid. Derived or Dependent Demand refers to demand for an inventory item that becomes part of another item. The firm's demand for finished goods is not derived from demand for other inventory items.

Inventory Costs

Carrying costs include all direct and opportunity costs of keeping inventory on hand: storage and tracking costs, insurance and taxes, losses due to obsolescence/deterioration/theft, and the opportunity cost of capital for the invested amount.

Shortage costs are associated with having inadequate inventory on hand. These include restocking costs (costs of placing orders with suppliers or setting up production runs) and safety reserve costs (opportunity losses from inadequate inventory like lost sales and goodwill).

A trade-off exists: carrying costs increase with inventory levels while shortage or restocking costs decline with inventory levels. The goal of inventory management is to minimize the sum of these two costs.

ABC Approach

The basic idea of the ABC approach is to divide inventory into three or more groups. A small portion of inventory in terms of quantity may represent a large portion in terms of inventory value. For example, a production process may involve expensive high-tech components (Group A, 10% of items but 57% of value) as well as inexpensive basic materials (Group C, 50% of items but 16% of value).

🔑 Definition — ABC Approach: An inventory management method that categorizes inventory into groups based on their relative value, allowing firms to focus management attention on high-value items.

Economic Order Quantity Model

The Economic Order Quantity (EOQ) model is the best known approach to explicitly establish an optimal inventory level. The actual cost of inventory is not included since total inventory needed is dictated by sales. The model determines the order size the firm should use when restocking inventory.

Assuming inventory is sold at a steady rate until zero, then restocked to an optimal level: suppose a firm starts with 3,600 units, annual sales are 46,800 units (about 900 per week). All inventory sells in four weeks, then the firm restocks 3,600 units and repeats. This produces a sawtooth pattern for inventory holdings.

Carrying costs are assumed directly proportional to inventory levels. If CC is the carrying cost per unit per year:

• Total carrying costs = Average inventory × Carrying costs per unit = (Q/2) × CC
• For CC = $0.75 per unit per year with Q = 3,600: (1,800 × $0.75) = $1,350 per year

For restocking costs (assuming fixed costs per order):

• Total restocking costs = Fixed cost per order × Number of orders = F × (T/Q)
• Where T = total unit sales per year, Q = order quantity
• For T = 46,800, Q = 3,600: 13 orders × $50 = $650 per year

Total costs = Carrying costs + Restocking costs = (Q/2) × CC + F × (T/Q)

📐 Formula: Total Inventory Cost = (Q/2) × CC + F × (T/Q) → Sum of annual carrying costs plus annual restocking costs

📌 Example: For CC = $0.75, F = $50, T = 46,800:

• Q = 500: Costs = $187.50 + $4,680 = $4,867.50
• Q = 2,000: Costs = $750 + $1,170 = $1,920
• Q = 2,500: Costs = $937.50 + $936 = $1,873.50
• Q = 3,000: Costs = $1,125 + $780 = $1,905

The minimum point is found by equating carrying and restocking costs:

• (Q*/2) × CC = F × (T/Q*)
• (Q*)² = 2T × F / CC
• Q* = (2T × F / CC)^½

🔑 Definition — Economic Order Quantity (EOQ): The optimal order quantity that minimizes total inventory costs, found where carrying costs equal restocking costs.

📐 Formula: EOQ = (2T × F / CC)^½ → The square root of (twice annual sales times fixed order cost divided by carrying cost per unit)

📌 Example: For T = 46,800, F = $50, CC = $0.75:

• Q* = [(2 × 46,800) × $50 / 0.75]^½ = 2,498 units

📌 Example — R Shoes: T = 600 pairs/year, F = $20/order, CC = $3/pair

• EOQ = [(2 × 600) × $20 / 3]^½ = 89.44 units
• Restocking frequency = 600/89.44 = 6.71 times per year
• Total restocking costs = $20 × 6.71 = $134.16
• Average inventory = 89.44/2 = 44.72
• Carrying costs = $3 × 44.72 = $134.16
• Total costs = $268.33

Safety Stock and Reorder Points

In reality, firms reorder before inventory runs to zero to minimize stock-out risk and cover lead time between order and delivery. Safety stock is the minimum level of inventory kept on hand; inventories are reordered when the level falls to the safety stock level. Reorder points are the times at which the firm will actually place inventory orders, even before reaching critical level.

🔑 Definition — Safety Stock: The minimum level of inventory a firm keeps on hand to protect against stock-outs during lead time.

🔑 Definition — Reorder Point: The inventory level at which a firm places a new order, set to ensure inventory arrives before stock runs out given lead time.

💡 Why this matters: Without safety stock and proper reorder points, firms face stock-outs that can halt production or lose sales, while excessive safety stock increases carrying costs unnecessarily.

⭐ Key Takeaways

The goal of inventory management is to minimize the sum of carrying costs and shortage costs, achieved by finding the optimal order quantity where these costs are equal. The EOQ model provides a mathematical formula (Q* = √(2TF/CC)) for determining this optimal order size, balancing the costs of holding inventory against the costs of ordering. The ABC approach helps prioritize management attention on high-value inventory items. Practical inventory management requires safety stock and reorder points to account for lead times and prevent stock-outs, ensuring continuous operations.

🧠 Quick Revision Questions

1. What are the three types of inventory and how do they differ in liquidity?
2. What are the two main categories of inventory costs, and how do they behave as inventory levels change?
3. How is the Economic Order Quantity (EOQ) formula derived, and what does it minimize?
4. A firm sells 1,000 units per year with ordering costs of $25 per order and carrying costs of $2 per unit. What is the EOQ?
5. Why do firms use safety stock and how do reorder points relate to lead time?