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

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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.

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A $100 par, 8% preferred stock is currently selling for $80. What is the cost of preferred equity?

A) 10.8%.

B) 8.0%.

C) 10.0%.

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k_ps = $8 / $80 = 10%

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The following information applies to a corporation:

• The company has $200 million of equity and $100 million of debt.
• The company recently issued bonds at 9%.
• The corporate tax rate is 30%.
• The company's beta is 1.125.

If the risk-free rate is 6% and the expected return on the market portfolio is 14%, the company’s after-tax weighted average cost of capital is closest to:

A) 12.1%.

B) 10.5%.

C) 11.2%.

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k_s = RFR + β(R_m ? RFR)
= 6% + 1.125(14% ? 6%) = 15%

WACC = [D/(D + E)] × k_d(1 ? t) + [E/(D + E)] × k_s
= (100/300)(9%)(1 ? 0.3) + (200/300)(15%) = 12.1%

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The cost of preferred stock is equal to the preferred stock dividend:

A) divided by the market price.

B) divided by its par value.

C) multiplied by the market price.

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The cost of preferred stock, k_ps, is D_ps ÷ price.

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• 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%

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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.

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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%.

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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)

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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%.

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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%.