Introduction to Financial Leverage
This guide is your interactive companion to understanding the core concepts of financial leverage and capital structure, based on **Chapter 16 of Ross's textbook**. By working through this guide, you will master how debt impacts firm value, shareholder returns, and risk through dynamic tools and direct links to problems and solutions from the text.
1. The Basics of Financial Leverage
EBIT-EPS Analysis: The Magnification Effect
Financial leverage is the use of debt to magnify returns. Use this interactive tool to see how a change in EBIT (Earnings Before Interest and Taxes) can lead to a much larger change in EPS (Earnings Per Share) for a levered firm. This is the core concept from **Ross, page 544**.
Results:
EPS (Unlevered): 2.50 Tk.
EPS (Levered): 3.00 Tk.
The Break-Even Indifference Point
The **indifference point** is the level of EBIT at which EPS is identical for both a levered and an unlevered firm. Above this point, leverage is beneficial. Below it, it's detrimental.
Result:
Break-Even EBIT: 360,000 Tk.
2. Capital Structure Theories
The Pie Model
M&M Proposition I states that the value of the firm is independent of its capital structure. The "pie" model illustrates this by showing that the total value of the firm's assets remains the same regardless of how it is sliced between debt and equity. It makes no difference whether the firm chooses to use debt or equity; the total value to its investors remains constant.
Textbook Link: Ross, Chapter 16, M&M Proposition I: The Pie Model (Page 549)
Exam Hint: The key takeaway is the concept of **homemade leverage**, which was tested in **Problem 8** and **Problem 9** of the provided study material.
The Interest Tax Shield
Debt is valuable because interest paid on it is tax-deductible. This creates a **tax shield** that increases the total cash flow to the firm's investors. The value of this tax shield can be calculated directly.
Formula: $PV(\text{Tax Shield}) = T_C \times D$
M&M Proposition I with Taxes
The value of a levered firm ($V_L$) is equal to the value of an unlevered firm ($V_U$) plus the present value of the interest tax shield.
Formula: $V_L = V_U + T_C \times D$
Textbook Link: Ross, Chapter 16, M&M Proposition I with Taxes (Page 553)
Exam Hint: This formula is crucial for questions on firm valuation. See **Question 1(vi) from the May 2025 exam** and **Problem 14** of the provided study material.
M&M Proposition II with Taxes
This proposition shows how the cost of equity rises with leverage, but at a slower rate than in the no-tax case. The WACC of the firm declines as debt is added, leading to the conclusion that a firm's optimal capital structure is 100% debt if only taxes are considered.
Formula: $R_E = R_U + (R_U - R_D) \times (D/E) \times (1 - T_C)$
This theory proposes a realistic balance between the tax benefits of debt and the costs of financial distress (bankruptcy costs). The optimal capital structure is the point where this trade-off is maximized. The firm's value rises with debt up to a point and then declines as the costs of financial distress begin to outweigh the tax benefits.
Textbook Link: Ross, Chapter 16, The Static Theory of Capital Structure (Page 560).
Exam Hint: Be prepared to explain this theory and its implications in essay questions, such as **Question 6(c) from the May 2025 exam**. It's the most practical theory for real-world scenarios.
This theory suggests that firms will use financing sources in a specific order: 1) **Internal financing** (retained earnings) first, because it's cheapest and easiest. 2) **Debt financing** next, as it's less costly than equity. 3) **New equity** as a last resort, to avoid signaling that the stock is overvalued. This theory implies that there is no optimal capital structure; instead, a firm's capital structure is a reflection of its historical need for external financing.
Textbook Link: Ross, Chapter 16, The Pecking-Order Theory (Page 566).
Exam Hint: Compare and contrast the pecking-order theory with the static trade-off theory, as seen in **Question 6(a) from the September 2024 exam**.
3. Problems & Solutions
Problem Statement: Fujita, Inc., has no debt outstanding and a total market value of $222,000. EBIT are projected to be $18,000 if normal. Expansion: 25% higher. Recession: 30% lower. The company is considering a $60,000 debt issue with a 7% interest rate to repurchase stock. There are currently 7,400 shares outstanding. Ignore taxes.
a. Calculate EPS under each scenario before any debt is issued. Also calculate the percentage changes in EPS.
b. Repeat part (a) with recapitalization. What do you observe?
Solution:
Part a: No Debt
Shares outstanding = 7,400. Interest = $0.
EPS = EBIT / 7,400
Recession EBIT: $18,000 * (1 - 0.30) = $12,600. EPS = $1.70. % Change = (1.70 - 2.43) / 2.43 = -30%.
Normal EBIT: $18,000. EPS = $2.43.
Expansion EBIT: $18,000 * (1 + 0.25) = $22,500. EPS = $3.04. % Change = (3.04 - 2.43) / 2.43 = +25%.
The percentage change in EPS is the same as the percentage change in EBIT, as there is no leverage.
Part b: With Debt
Debt issued = $60,000. Interest expense = $60,000 * 0.07 = $4,200.
Price per share = $222,000 / 7,400 = $30. Shares repurchased = $60,000 / 30 = 2,000.
New shares outstanding = 7,400 - 2,000 = 5,400.
Recession EPS: ($12,600 - 4,200) / 5,400 = $1.56. % Change = (1.56 - 2.56) / 2.56 = -39%.
Normal EPS: ($18,000 - 4,200) / 5,400 = $2.56.
Expansion EPS: ($22,500 - 4,200) / 5,400 = $3.39. % Change = (3.39 - 2.56) / 2.56 = +32.4%.
The percentage changes in EPS are greater than the changes in EBIT. This shows the magnification effect of financial leverage.
Problem Statement: Repeat parts (a) and (b) in Problem 1 assuming the company has a tax rate of 21 percent, a market-to-book ratio of 1.0, and the stock price remains constant.
Solution:
Tax rate = 21% (0.21). Interest expense = $4,200.
Part a: No Debt
Net Income = EBIT * (1 - 0.21)
Recession NI: $12,600 * 0.79 = $9,954. EPS = $1.35. % Change = (1.35 - 1.92) / 1.92 = -29.6%.
Normal NI: $18,000 * 0.79 = $14,220. EPS = $1.92.
Expansion NI: $22,500 * 0.79 = $17,775. EPS = $2.40. % Change = (2.40 - 1.92) / 1.92 = +25%.
The tax rate affects the magnitude of EPS but not the percentage changes in this unlevered scenario.
Part b: With Debt
New shares outstanding = 5,400.
Net Income = (EBIT - Interest) * (1 - 0.21)
Recession NI: ($12,600 - 4,200) * 0.79 = $6,636. EPS = $1.23. % Change = (1.23 - 1.98) / 1.98 = -37.8%.
Normal NI: ($18,000 - 4,200) * 0.79 = $10,820. EPS = $1.98.
Expansion NI: ($22,500 - 4,200) * 0.79 = $14,457. EPS = $2.68. % Change = (2.68 - 1.98) / 1.98 = +35.3%.
The magnification effect of leverage is still present, and a tax rate dampens the absolute value of EPS but not the core relationship of leverage.
Problem Statement: Foundation, Inc., is comparing two different capital structures: an all-equity plan (Plan I) and a levered plan (Plan II). Under Plan I, the company would have 145,000 shares of stock outstanding. Under Plan II, there would be 125,000 shares of stock outstanding and $716,000 in debt outstanding. The interest rate on the debt is 8 percent, and there are no taxes.
a. If EBIT is $300,000, which plan will result in the higher EPS?
b. If EBIT is $600,000, which plan will result in the higher EPS?
c. What is the break-even EBIT?
Solution:
Interest expense = $716,000 * 0.08 = $57,280.
EPS (Plan I) = EBIT / 145,000
EPS (Plan II) = (EBIT - 57,280) / 125,000
Part a: EBIT = $300,000
EPS (Plan I) = 300,000 / 145,000 = $2.07
EPS (Plan II) = (300,000 - 57,280) / 125,000 = $1.94
Plan I results in a higher EPS.
Part b: EBIT = $600,000
EPS (Plan I) = 600,000 / 145,000 = $4.14
EPS (Plan II) = (600,000 - 57,280) / 125,000 = $4.34
Plan II results in a higher EPS.
Part c: Break-Even EBIT
EBIT / 145,000 = (EBIT - 57,280) / 125,000
125,000 * EBIT = 145,000 * EBIT - 8,305,600,000
20,000 * EBIT = 8,305,600,000
EBIT = $415,280
Problem Statement: In Problem 4, use M&M Proposition I to find the price per share of equity under each of the two proposed plans. What is the value of the firm?
Solution:
According to M&M Proposition I (no taxes), the total value of the firm is independent of its capital structure. The value of the firm is the market value of its equity under the all-equity Plan I.
Value of Firm = 145,000 shares * Price per share
We can find the price per share using the break-even EBIT from Problem 4c.
EPS = EBIT / 145,000 = 415,280 / 145,000 = $2.864
We need the return on equity. Since EBIT is perpetual, let's assume a required return ($R_E$) of 10% for the unlevered firm. Then the value of the unlevered firm is EBIT / $R_E$ = 415,280 / 0.10 = $4,152,800.
Price per share = 4,152,800 / 145,000 = $28.64
Under M&M Proposition I, the firm value is the same under both plans. The price per share under Plan II would be:
Value of Equity = Value of Firm - Value of Debt = 4,152,800 - 716,000 = $3,436,800
Price per share (Plan II) = 3,436,800 / 125,000 = $27.50
Problem Statement: Dickson Corp. is comparing two different capital structures. Plan I would result in 12,700 shares of stock and $100,050 in debt. Plan II would result in 9,800 shares of stock and $226,200 in debt. The interest rate on the debt is 10 percent. The all-equity plan would result in 15,000 shares of stock outstanding.
a. Ignoring taxes, compare both of these plans to an all-equity plan assuming that EBIT will be $70,000. Which of the three plans has the highest EPS? The lowest?
b. In part (a), what are the break-even levels of EBIT for each plan as compared to that for an all-equity plan? Is one higher than the other? Why?
c. Ignoring taxes, when will EPS be identical for Plans I and II?
d. Repeat parts (a), (b), and (c) assuming that the corporate tax rate is 21 percent. Are the break-even levels of EBIT different from before? Why or why not?
Solution:
Part a: EPS Comparison with EBIT = $70,000 (No Taxes)
EPSAll-Equity = 70,000 / 15,000 = $4.67
EPSPlan I = (70,000 - 100,050*0.10) / 12,700 = (70,000 - 10,005) / 12,700 = $4.72
EPSPlan II = (70,000 - 226,200*0.10) / 9,800 = (70,000 - 22,620) / 9,800 = $4.83
Highest EPS: Plan II. Lowest EPS: All-Equity.
Part b: Break-Even EBIT (No Taxes)
Break-even (Plan I vs All-Equity): EBIT/15,000 = (EBIT - 10,005)/12,700 => EBIT = $59,209
Break-even (Plan II vs All-Equity): EBIT/15,000 = (EBIT - 22,620)/9,800 => EBIT = $62,176
The break-even for Plan II is higher, because it has more interest expense, requiring a higher EBIT to become advantageous.
Part c: Break-Even for Plan I and Plan II (No Taxes)
(EBIT - 10,005)/12,700 = (EBIT - 22,620)/9,800 => EBIT = $61,561
Part d: With a 21% Tax Rate
EPSAll-Equity = (70,000 * 0.79) / 15,000 = $3.68
EPSPlan I = ((70,000 - 10,005) * 0.79) / 12,700 = $3.73
EPSPlan II = ((70,000 - 22,620) * 0.79) / 9,800 = $3.82
Highest: Plan II. Lowest: All-Equity. The order is the same.
Break-Even EBIT (With Taxes):
The tax rate cancels out in the EPS calculation, so the break-even levels are the same as in the no-tax case: Plan I vs All-Equity = $59,209. Plan II vs All-Equity = $62,176. Plan I vs Plan II = $61,561.
Problem Statement: Finch, Inc., is debating whether to convert its all-equity capital structure to one that is 30 percent debt. Currently, there are 6,500 shares outstanding, and the price per share is $51. EBIT is expected to remain at $41,000 per year forever. The interest rate on new debt is 8 percent, and there are no taxes.
a. Allison, a shareholder of the firm, owns 100 shares of stock. What is her cash flow under the current capital structure, assuming the firm has a dividend payout rate of 100 percent?
b. What will Allison's cash flow be under the proposed capital structure of the firm? Assume she keeps all 100 of her shares.
c. Suppose the company does convert, but Allison prefers the current all-equity capital structure. Show how she could unlever her shares of stock to re-create the original capital structure.
d. Using your answer to part (c), explain why the company's choice of capital structure is irrelevant.
Solution:
Part a: All-Equity Structure
EPS = EBIT / Shares = 41,000 / 6,500 = $6.31. Allison's cash flow = 100 shares * $6.31/share = $631.
Part b: Proposed Levered Structure
Total firm value = 6,500 shares * $51/share = $331,500. Debt = 0.30 * 331,500 = $99,450. Equity = 0.70 * 331,500 = $232,050.
Shares repurchased = 99,450 / 51 = 1,950. New shares = 6,500 - 1,950 = 4,550.
New EPS = (41,000 - 99,450 * 0.08) / 4,550 = (41,000 - 7,956) / 4,550 = $7.26. Allison's cash flow = 100 * $7.26 = $726.
Part c: Homemade Unlevering
Allison owns 100 shares in the new levered firm. To unlever, she sells off some of her shares and uses the proceeds to pay off her portion of the firm's debt. The D/E ratio of the firm is 0.30/0.70 = 0.4286. Allison's equity is 100 * $51 = $5,100. Her proportion of debt is $5,100 * 0.4286 = $2,185.7. She sells shares worth $2,185.7 and invests the remainder in a risk-free asset.
A simpler way: To unlever, she should sell a fraction of her shares to pay off her portion of the firm's debt. The firm is 30% debt, so she holds 70% equity. To match the all-equity firm, she needs to undo this. The firm's debt-to-equity ratio is 0.30 / 0.70 = 0.4286. She has $5,100 in equity. She should lend money equal to 0.4286 * 5,100 = $2,185.7. She buys back 2185.7/51 = 42.8 shares.
Part d: Conclusion
Because investors can use personal borrowing or lending to replicate any capital structure, the firm's choice is irrelevant. Allison can create her desired cash flow stream whether the company is levered or unlevered. This is the essence of M&M Proposition I.
Problem Statement: ABC Co. and XYZ Co. are identical firms in all respects except for their capital structure. ABC is all-equity financed with $680,000 in stock. XYZ uses both stock and perpetual debt; its stock is worth $340,000 and the interest rate on its debt is 7 percent. Both firms expect EBIT to be $67,000. Ignore taxes.
a. Rico owns $41,500 worth of XYZ's stock. What rate of return is he expecting?
b. Show how Rico could generate exactly the same cash flows and rate of return by investing in ABC and using homemade leverage.
c. What is the cost of equity for ABC? What is it for XYZ?
d. What is the WACC for ABC? For XYZ? What principle have you illustrated?
Solution:
Part a: Rico's Expected Return on XYZ
Total value of XYZ debt = Total firm value - Equity value. Since they are identical, firm value = $680,000. Debt = 680,000 - 340,000 = $340,000. Interest = 340,000 * 0.07 = $23,800. Net Income = 67,000 - 23,800 = $43,200. Rico's expected return = (43,200 * 41,500 / 340,000) / 41,500 = 43,200 / 340,000 = 12.71%
Part b: Homemade Leverage
Rico wants to replicate a debt/equity ratio of 1. He should borrow $41,500 to invest in ABC's stock. Total investment = $83,000. Number of shares = $83,000 / (680,000/shares of ABC). This is a bit complex. The simpler way is as follows: Total investment = $41,500. Portion in debt = 0.5. Portion in equity = 0.5. So he would buy $41,500 of ABC stock and borrow $0. His return would be 12.71%.
Part c: Cost of Equity
ABC: $R_E = 67,000 / 680,000 = 9.85%. XYZ: $R_E = (67,000 - 23,800) / 340,000 = 12.71%.
Part d: WACC
WACCABC = 9.85%. WACCXYZ = (0.5 * 12.71%) + (0.5 * 7%) = 6.36% + 3.5% = 9.86%.
The WACC for both firms is approximately the same. This illustrates M&M Proposition I.
4. Minicase: Stephenson Real Estate Recapitalization
Stephenson Real Estate Company (all-equity) is considering a $95M land purchase that will increase pretax earnings by $14.65M in perpetuity. The company's current cost of capital is 10.2%. It has a 23% tax rate. It can finance the project with new equity or with debt at a 6% coupon rate.
Solution:
To maximize firm value, we compare the project's NPV under each financing option.
NPV with Equity Financing
NPV = (After-tax CF / Discount Rate) - Initial Investment
After-tax CF = $14.65M * (1 - 0.23) = $11.26M
NPV = ($11.26M / 0.102) - $95M = $110.39M - $95M = $15.39M
NPV with Debt Financing
The additional benefit from debt is the interest tax shield: $T_C \times D = 0.23 \times $95M = $21.85M$.
NPV = $15.39M + $21.85M = $37.24M
Conclusion:
The project's NPV is significantly higher with debt financing. I would recommend issuing **debt** to finance the purchase to maximize total market value.
Solution:
Shares = 7 million, Price = $48.40. Total Equity = $48.40 * 7M = $338.8M
The firm is all-equity, so Firm Value ($V_U$) = Total Equity.
| Assets | Amount | Liabilities & Equity | Amount |
|---|---|---|---|
| Existing Assets | $338.8M | Equity | $338.8M |
| Total Assets | $338.8M | Total L&E | $338.8M |