Reading 45: Cost of Capital-LOS h 习题精选 日志

1215

Session 11: Corporate Finance
Reading 45: Cost of Capital

LOS h: Calculate and interpret the cost of equity capital using the capital asset pricing model approach, the dividend discount model approach, and the bond-yield-plus risk-premium approach.

 

 

If central bank actions caused the risk-free rate to increase, what is the most likely change to cost of debt and equity capital?

A) Both decrease.

B) One increase and one decrease.

C) Both increase.

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An increase in the risk-free rate will cause the cost of equity to increase. It would also cause the cost of debt to increase. In either case, the nominal cost of capital is the risk-free rate plus the appropriate premium for risk.

1215

Julius, Inc., is in a 40% marginal tax bracket. The firm can raise as much capital as needed in the bond market at a cost of 10%. The preferred stock has a fixed dividend of $4.00. The price of preferred stock is $31.50. The after-tax costs of debt and preferred stock are closest to:

Debt

Preferred stock

A) 6.0% 12.7%

B) 10.0% 7.6%

C) 6.0% 7.6%

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After-tax cost of debt = 10% × (1 – 0.4) = 6%.
Cost of preferred stock = $4 / $31.50 = 12.7%.

1215

Genoa Corp. is estimating its weighted average cost of capital (WACC). They have several pieces of data to consider. The firm pays 40% of its earnings out in dividends. The return on equity (ROE) is 15%. Last year’s earnings were $5.00 per share and the dividend was just paid to shareholders. The current price of shares is $42.00. Genoa's 8% coupon bonds have a yield to maturity of 7.5%. The firm's tax rate is 30%.

The cost of common equity is closest to:

A) 13.76%.

B) 16.14%.

C) 14.19%.

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ROE × retention ratio = growth rate.

15% × (1 – 0.40) = 9%

D₀ = $5.00 × 0.40 = $2.00

[$2.00(1.09) / $42.00] + 0.09 = 14.19%

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The after-tax cost of debt is closest to:

A) 7.5%.

B) 5.3%.

C) 5.6%.

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7.5 × (1 ? 0.3) = 5.25%

1215

A firm has $3 million in outstanding 10-year bonds, with a fixed rate of 8% (assume annual payments). The bonds trade at a price of $92 per $100 par in the open market. The firm’s marginal tax rate is 35%. What is the after-tax component cost of debt to be used in the weighted average cost of capital (WACC) calculations?

A) 9.26%.

B) 5.40%.

C) 6.02%.

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If the bonds are trading at $92 per $100 par, the required yield is 9.26%, and the market value of the issue is $2.76 million.

The equivalent after-tax cost of this financing is: 9.26% (1 – 0.35) = 6.02%.

1215

A company has the following data associated with it:

• A target capital structure of 10% preferred stock, 50% common equity and 40% debt.
• Outstanding 20-year annual pay 6% coupon bonds selling for $894.
• Common stock selling for $45 per share that is expected to grow at 8% and expected to pay a $2 dividend one year from today.
• Their $100 par preferred stock currently sells for $90 and is earning 5%.
• The company's tax rate is 40%.

What is the after tax cost of debt capital and after tax cost of preferred stock capital?

Debt Capital

Preferred Stock Capital

A) 4.2% 6.3%

B) 4.5% 5.6%

C) 4.2% 5.6%

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Debt
N = 20; FV = 1,000; PMT = 60; PV = -894; CPT → I = 7%
k_d = (7%)(1 ? 0.4) = 4.2%

Preferred Stock
k_ps = D_ps / P
k_ps = 5 / 90 = 5.56%

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What is the weighted average cost of capital (WACC)?

A) 9.2%.

B) 10.3%.

C) 8.5%.

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k_ce = (D₁ / P₀) + g
k_ce = 2 / 45 + 0.08 = 0.1244 = 12.44%
WACC = (0.4)(4.2) + (0.1)(5.6) + (0.5)(12.4) = 8.5%

1215

• The company has a target capital structure of 40% debt and 60% equity.
• Bonds pay 10% coupon (semi-annual payout), mature in 20 years, and sell for $849.54.
• The company stock beta is 1.2.
• Risk-free rate is 10%, and market risk premium is 5%.
• The company is a constant growth firm that just paid a dividend of $2.00, sells for $27.00 per share, and has a growth rate of 8%.
• The company's marginal tax rate is 40%.

The after-tax cost of debt is:

A) 8.0%.

B) 7.2%.

C) 9.1%.

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N = 40; PMT = 50; FV = 1,000; PV = 849.54; Compute i = 6%, double = 12%, now (12)(1 ? 0.4) = 7.2%.

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The cost of equity using the capital asset pricing model (CAPM) approach and the discounted cash flow approach is:

CAPM

Discounted Cash Flow

A) 16.0% 15.4%

B) 16.6% 15.4%

C) 16.0% 16.0%

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CAPM = 10 + (5)(1.2) = 16%.

Discounted Cash Flow: D₁ = 2(1.08) = 2.16, now (2.16 / 27) + 0.08 = 16%

1215

Which of the following statements about the cost of capital is CORRECT?

A) Ideally, historical measures of the component costs from prior financing should be used in estimating the appropriate weighted average cost of capital.

B) The cost of issuing new equity could possibly be lower than the cost of retained earnings if the market risk premium and risk-free rate decline by a substantial amount.

C) In the weighted average cost of capital calculation, the cost of preferred stock must be adjusted for the cost to issue new preferred stock.

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The marginal cost of capital will increase or stay the same as more capital is raised. Marginal costs of capital, not historical costs, should be used in estimating the weighted average cost of capital.

1215

A firm has $4 million in outstanding bonds that mature in four years, with a fixed rate of 7.5% (assume annual payments). The bonds trade at a price of $98 in the open market. The firm’s marginal tax rate is 35%. Using the bond-yield plus method, what is the firm’s cost of equity risk assuming an add-on of 4%?

A) 11.50%.

B) 12.11%.

C) 13.34%.

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If the bonds are trading at $98, the required yield is 8.11%, and the market value of the issue is $3.92 million. To calculate this rate using a financial calculator (and figuring the rate assuming a $100 face value for each bond), N = 4; PMT = 7.5 = (0.075 × 100); FV = 100; PV = -98; CPT → I/Y = 8.11. By adding the equity risk factor of 4%, we compute the cost of equity as 12.11%.

1215

A company has $5 million in debt outstanding with a coupon rate of 12%. Currently the YTM on these bonds is 14%. If the tax rate is 40%, what is the after tax cost of debt?

A) 8.4%.

B) 7.2%.

C) 5.6%.

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(0.14)(1 - 0.4)

1215

The expected annual dividend one year from today is $2.50 for a share of stock priced at $25. What is the cost of equity if the constant long-term growth in dividends is projected to be 8%?

A) 19%.

B) 15%.

C) 18%.

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K_s = (D₁ / P₀) + g = (2.5/25) + 0.08 = 0.18 or 18%.