Exercise 1: BMW Corporation Is Comparing Two

Exercise 1 Bmw Corporation Is Comparing Two

BMW Corporation is comparing two different capital structures: an all-equity plan (Plan I) and a levered plan (Plan II). Under Plan I, BMW would have 265,000 shares of stock outstanding. Under Plan II, there would be 185,000 shares of stock outstanding and $2.8 million in debt outstanding. The interest rate on the debt is 10 percent and there are no taxes. If EBIT is $750,000, which plan will result in the higher EPS? If EBIT is $1,500,000, which plan will result in the higher EPS? What is the break-even EBIT?

Paper For Above instruction

BMW Corporation's strategic decision to evaluate different capital structures involves comparing an all-equity plan with a leveraged one to understand their impact on earnings per share (EPS). This analysis hinges on understanding how leverage influences corporate earnings and shareholders' returns at varying levels of EBIT (Earnings Before Interest and Taxes).

In the all-equity scenario (Plan I), BMW has 265,000 shares outstanding. Its value is solely derived from equity financing, and there's no debt obligation, implying that EPS directly correlates with EBIT as profits are distributed among the shareholders without interest deductions. Conversely, in the levered plan (Plan II), there are 185,000 shares outstanding with $2.8 million debt bearing a 10% interest rate, introducing fixed financing costs that influence the company's net income and EPS.

To compare EPS across both plans, let's derive their formulas:

Plan I: EPS = EBIT / Number of Shares = EBIT / 265,000

Plan II: EBIT is reduced by the interest expense ($2.8 million × 10% = $280,000). Net Income = (EBIT - Interest) since taxes are zero. Therefore, EPS = (EBIT - 280,000) / 185,000

Calculating for EBIT of $750,000:

Plan I: EPS = 750,000 / 265,000 ≈ 2.83

Plan II: EPS = (750,000 - 280,000) / 185,000 ≈ 470,000 / 185,000 ≈ 2.54

Calculating for EBIT of $1,500,000:

Plan I: EPS = 1,500,000 / 265,000 ≈ 5.66

Plan II: EPS = (1,500,000 - 280,000) / 185,000 ≈ 1,220,000 / 185,000 ≈ 6.59

From these calculations, at EBIT of $750,000, the all-equity plan (Plan I) results in higher EPS. At EBIT of $1,500,000, the levered plan (Plan II) yields a higher EPS. The break-even EBIT is where EPS under both plans are equal:

Set: EBIT / 265,000 = (EBIT - 280,000) / 185,000

Cross-multiplied:

185,000 × EBIT = 265,000 × (EBIT - 280,000)

185,000 × EBIT = 265,000 × EBIT - 265,000 × 280,000

Simplify:

(265,000 - 185,000) × EBIT = 265,000 × 280,000

80,000 × EBIT = 265,000 × 280,000

EBIT = (265,000 × 280,000) / 80,000 ≈ (74,200,000) / 80,000 ≈ $927,500

Thus, the break-even EBIT is approximately $927,500, at which point both plans yield the same EPS.

Exercise 2: Valuation of the Firm Under MM Proposition I

Using Modigliani and Miller (MM) Proposition I, which posits that in perfect markets the value of a firm is unaffected by its capital structure, we can assess the value of each plan and derive the stock price per share.

Plan I (All Equity): The firm's value equals its EBIT divided by the cost of equity (\(r_e\)). Assuming the dividend discount model approach:

\(V_{E} = \frac{\text{EBIT}}{r_e}\)

Since the cost of equity isn't specified, for simplicity, we'll assume a market-required rate similar to other comparable firms, say 12%. Therefore,

\(V_{E} = \frac{750,000}{0.12} = \$6,250,000\)

Number of shares outstanding is 265,000, so the price per share:

\(P_{E} = \frac{\$6,250,000}{265,000} ≈ \$23.58\)

Plan II: Since the firm's value under MM Proposition I remains unchanged by leverage, the total value of the firm is:

\(V_{L} = V_{E} = \$6,250,000\)

The value of debt is \$2.8 million, leaving equity valued at:

\(V_{E} = V_{L} - \text{Debt} = \$6,250,000 - \$2,800,000 = \$3,450,000\)

The new equity value is divided among 185,000 shares, so the price per share:

\(P_{E} = \frac{\$3,450,000}{185,000} ≈ \$18.65\)

Exercise 3: Capital Structure Effects on Returns – BestBuy and Staples

BestBuy is all equity financed with \$750,000 in stock. Staples uses both stock and perpetual debt, with its stock worth \$375,000 at an 8% interest rate. Both expect EBIT of \$86,000, and taxes are ignored for simplicity.

Richard owns \$30,000 of Staples stock. To find his expected return:

Staples' equity value: \$375,000, so Richard's ownership share is:

\(\frac{30,000}{375,000} = 8\%\)

His proportionate EBIT share is:

8% of EBIT: 0.08 × 86,000 = \$6,880

Interest on Staples' debt: 8% of \$375,000 = \$30,000

Net income for Staples' equity holders:

86,000 - 30,000 = \$56,000

Richard's expected return:

Return = (Net income / Investment) × 100 = (6,880 / 30,000) × 100 ≈ 22.93%

Alternatively, Richard can mimic this return through homemade leverage by investing in BestBuy and borrowing to replicate Staples' leverage. By investing \$30,000 in BestBuy and borrowing an additional \$30,000 at 8%, he can create cash flows equivalent to Staples' leverage.

Interest charge:

8% of \$30,000 = \$2,400

Dividends from BestBuy:

Total cash flow = EBIT - interest paid on borrowed amount = 86,000 - 2,400 = \$83,600

Richard's portion:

8% of total cash flow: 0.08 × 83,600 ≈ \$6,688

Return on his \$30,000 investment:

(6,688 / 30,000) × 100 ≈ 22.29%

The cost of equity for BestBuy is inferred from its expected returns, coinciding largely with the firm's EBIT and leverage. WACC for BestBuy is calculated considering equity and debt weights, with debt at 8% and equity reflecting the expected return. Given the similarities, the calculations align with standard leverage and cost of capital principles.

This scenario illustrates the principle of homemade leverage—investors can replicate a firm's leverage structure by adjusting their personal borrowing and investment decisions, fundamentally demonstrating the irrelevance of capital structure in perfect markets per MM propositions.

Exercise 4: Ford's Debt-Equity Ratio and WACC

Ford Inc. has a market value of equity of \$23 million and debt of \$7 million. The debt-to-equity ratio is:

\(\frac{7,000,000}{23,000,000} ≈ 0.304\)

The firm's beta is 1.15, with the risk-free rate at 5% and market return at 12%. The cost of equity, using the Capital Asset Pricing Model (CAPM):

\(r_e = 5\% + 1.15 \times (12\% - 5\%) = 5\% + 1.15 \times 7\% = 5\% + 8.05\% = 13.05\%\)

The WACC:

WACC = \(\frac{E}{V} r_e + \frac{D}{V} r_d\)

Where:

- \(E = \$23M\),

- \(D = \$7M\),

- Total value \(V = E + D = \$30M\),

- Cost of debt \(r_d = 5\%\).

Calculations:

WACC = (23/30) × 13.05% + (7/30) × 5% ≈ 0.7667 × 13.05% + 0.2333 × 5% ≈ 10.02% + 1.17% ≈ 11.19%

For an all-equity firm with the same EBIT and risk profile, the cost of capital aligns with the cost of equity:

Approximate cost of capital: 13.05%

Exercise 5: Value of Granny Corp.

Granny Corp has an EBIT of \$975,000 per year, expected to continue perpetually. Unlevered cost of equity is 14%, and the corporate tax rate is 35%. The value of the firm (levered or unlevered) can be calculated using the Modigliani-Miller formula with taxes:

\(V_{L} = \frac{EBIT \times (1 - T)}{r_{u}} + T \times \text{Value of debt}\)

Calculate:

Tax shield = Tax rate × Value of debt

First, the value of an unlevered firm:

\(V_{U} = \frac{975,000 \times (1 - 0.35)}{0.14} = \frac{975,000 \times 0.65}{0.14} ≈ \frac{633,750}{0.14} ≈ 4,526,786\)

Adding the present value of the tax shield (as debt is perpetual):

Assuming debt market value \(D = \$1.9 \text{ million}\), the tax shield:

Tax shield = 0.35 × 1,900,000 = \$665,000

Total firm value:

\(V_{L} = V_{U} + \text{Tax shield} ≈ 4,526,786 + 665,000 ≈ \$5,191,786\)

Exercise 6: Yu Jianguo’s Cash Flows and Leverage Strategies

Yu Jianguo’s earnings vary with his working hours, impacting the company's EBIT and his earnings. The company’s valuation is \$3.2 million, and it seeks a \$1.3 million infusion, which can be financed through equity or debt at 8%. Without taxes, the cash flows to Yu depend on the chosen financing.

Under debt financing, additional debt incurs interest:

Interest = 8% of \$1.3 million = \$104,000.

At 40 hours/week (EBIT = \$550,000):

Debt issue cash flows:

- Interest: \$104,000

- EBIT: \$550,000

- After debt payments, cash flow to Yu remains proportional to his ownership, but with additional debt:

Cash flows are primarily driven by EBIT, but his personal cash flow becomes more leveraged under debt.

Under equity financing, the \$1.3 million infusion increases equity by issuing new shares, diluting existing ownership but avoiding interest payments.

In terms of incentive:

- Under debt, Yu might work harder to ensure the firm’s EBIT exceeds interest obligations, maintaining debt coverage.

- Under equity, since there are no fixed payments, his motivation depends on future profit-sharing arrangements.

Exact calculations:

Debt Issue:

- 40-hour week: Cash flow to Yu ≈ proportional to EBIT minus interest, but for simplicity, assuming EBIT directly flows to shareholders:

- Based on EBIT, cash flows involve the residual after interest.

- At 40 hours: \( \$550,000 \) EBIT, less \$104,000 interest, yields net income; proportionally, his cash flow:

- \( (550,000 / \text{Total EBIT}) \times (EBIT - interest) \), but specifics depend on ownership share.

Equity Issue:

- No debt payments, so cash flows mirror EBIT directly.

- Working time increases EBIT, thus increasing cash flows proportionally.

Overall, Yu is likely to work harder under debt financing because the fixed interest payment creates pressure to maintain high EBIT to meet debt obligations, aligning incentives for increased effort.

Exercise 7: Bankruptcy Costs and Firm Value

MGM Inc. has a debt of \$6 million and, if financed solely by equity, its value would be \$17.85 million. Its stock price is \$38 per share, with 350,000 shares outstanding. The corporate tax rate is 35%. To find the expected bankruptcy costs, we compare the firm's value with and without leverage:

Value of firm under all-equity financing: \$17.85 million.

Value with debt:

Value = Equity value + Debt = (\$38 × 350,000) + \$6 million = \$13.3 million + \$6 million = \$19.3 million

Expected bankruptcy costs = Difference between the value of an unlevered firm and the leveraged firm:

Expected bankruptcy costs = \$17.85 million - (\$19.3 million - the benefit of tax shields)

However, to find expected bankruptcy costs explicitly:

Expected bankruptcy costs = (Value without taxes) - (Value with taxes and debt), adjusted for probability.

Using Miller's theorem, assuming the firm's value is unaffected by taxes in the absence of bankruptcy costs, the decrease due to bankruptcy costs can be approximated as the difference in valuations due to expected costs. Given the data:

Expected bankruptcy costs = \$19.3 million - \$17.85 million = \$1.45 million

Hence, the expected present value of bankruptcy costs is approximately \$1.45 million, illustrating how leverage can induce bankruptcy risk, reducing firm value relative to its potential.

References

• Damodaran, A. (2010). Applied Corporate Finance. Wiley Finance.
• Modigliani, F., & Miller, M. H. (1958). The Cost of Capital, Corporation Finance and the Theory of Investment. The American Economic Review, 48(3), 261–297.
• Ross, S. A., Westerfield, R., & Jaffe, J. (2021). Corporate Finance. McGraw-Hill Education.
• Brealey, R. A., Myers, S. C., & Allen, F. (2017). Principles of Corporate Finance. McGraw-Hill Education.
• Frank, M. Z., & Goyal, V. K. (2009). Capital Structure Decisions: Which Factors Are Reliably Important? Financial Management, 38(1), 1–37.
• Fama, E. F., & French, K. R. (2002). The Equity Premium. The Journal of Finance, 57(2), 637–659.
• Titman, S., & Wessels, R. (1988). The Determinants of Capital Structure Choice. Journal of Finance, 43(1), 1–19.
• Myers, S. C. (1984). The Capital Structure Puzzle. Journal of Finance, 39(3), 575–592.
• Han, J., & Luo, S. (2018). The Impact of Capital Structure on Firm Performance. Journal of Financial