Reading 45: Cost of Capital-LOS a 习题精选 2011, face, following, interpret, structure

1215

Session 11: Corporate Finance
Reading 45: Cost of Capital

LOS a: Calculate and interpret the weighted average cost of capital (WACC) of a company.

 

 

A company has the following information:

• A target capital structure of 40% debt and 60% equity.
• $1,000 par value bonds pay 10% coupon (semi-annual payments), 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's marginal tax rate is 40%.

 

The weighted average cost of capital (WACC) is closest to:

A) 13.0%.

B) 13.5%.

C) 12.5%.

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K_s = 0.10 + (0.05)(1.2) = 0.16 or 16%

K_d = Solve for i: N = 40, PMT = 50, FV = 1,000, PV = -849.54, CPT I = 6 × 2 = 12%

WACC = (0.4)(12)(1 - 0.4) + (0.6)(16)= 2.88 + 9.6 = 12.48

1215

A company is planning a $50 million expansion. The expansion is to be financed by selling $20 million in new debt and $30 million in new common stock. The before-tax required return on debt is 9% and the required return for equity is 14%. If the company is in the 40% tax bracket, the marginal weighted average cost of capital is closest to:

A) 9.0%.

B) 10.0%

C) 10.6%.

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(0.4)(9%)(1 - 0.4) + (0.6)(14%) = 10.56%

1215

A firm is planning a $25 million expansion project. The project will be financed with $10 million in debt and $15 million in equity stock (equal to the company's current capital structure). The before-tax required return on debt is 10% and 15% for equity. If the company is in the 35% tax bracket, what cost of capital should the firm use to determine the project's net present value (NPV)?

A) 12.5%.

B) 9.6%.

C) 11.6%.

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WACC = (E / V)(R_E) + (D / V)(R_D)(1 ? TC)

WACC = (15 / 25)(0.15) + (10 / 25)(0.10)(1 ? 0.35) = 0.09 + 0.026 = 0.116 or 11.6%

1215

A firm has $100 in equity and $300 in debt. The firm recently issued bonds at the market required rate of 9%. The firm's beta is 1.125, the risk-free rate is 6%, and the expected return in the market is 14%. Assume the firm is at their optimal capital structure and the firm's tax rate is 40%. What is the firm's weighted average cost of capital (WACC)?

A) 8.6%.

B) 5.4%.

C) 7.8%.

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CAPM = R_E = R_F + B(R_M ? R_F) = 0.06 + (1.125)(0.14 ? 0.06) = 0.15

WACC = (E ÷ V)(R_E) + (D ÷ V)(R_D)(1 ? t)

V = 100 + 300 = 400

WACC = (1 ÷ 4)(0.15) + (3 ÷ 4)(0.09)(1 ? 0.4) = 0.078

1215

Hatch Corporation's target capital structure is 40% debt, 50% common stock, and 10% preferred stock. Information regarding the company's cost of capital can be summarized as follows:

• The company's bonds have a nominal yield to maturity of 7%.
• The company's preferred stock sells for $40 a share and pays an annual dividend of $4 a share.
• The company's common stock sells for $25 a share and is expected to pay a dividend of $2 a share at the end of the year (i.e., D₁ = $2.00). The dividend is expected to grow at a constant rate of 7% a year.
• The company has no retained earnings.
• The company's tax rate is 40%.

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

A) 10.18%.

B) 10.59%.

C) 10.03%.

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WACC = (w_d)(k_d)(1 ? t) + (w_ps)(k_ps) + (w_ce)(k_ce)

where:
w_d = 0.40
w_ce = 0.50
w_ps = 0.10
k_d = 0.07

k_ps = D_ps / P = 4.00 / 40.00 = 0.10

k_ce = D₁ / P₀ + g = 2.00 / 25.00 + 0.07 = 0.08 + 0.07 = 0.15

WACC = (0.4)(0.07)(1 ? 0.4) + (0.1)(0.10) + (0.5)(0.15) = 0.0168 + 0.01 + 0.075 = 0.1018 or 10.18%

1215

When calculating the weighted average cost of capital (WACC) an adjustment is made for taxes because:

A) equity earns higher return than debt.

B) equity is risky.

C) the interest on debt is tax deductible.

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Equity and preferred stock are not adjusted for taxes because dividends are not deductible for corporate taxes. Only interest expense is deductible for corporate taxes.

1215

Which of the following events will reduce a company's weighted average cost of capital (WACC)?

A) A reduction in the market risk premium.

B) An increase in expected inflation.

C) A reduction in the company's bond rating.

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An increase in either the company’s beta or the market risk premium will cause the WACC to increase using the CAPM approach. A reduction in the market risk premium will reduce the cost of equity for WACC.

1215

Assume a firm uses a constant WACC to select investment projects rather than adjusting the projects for risk. If so, the firm will tend to:

A) accept profitable, low-risk projects and accept unprofitable, high-risk projects.

B) accept profitable, low-risk projects and reject unprofitable, high-risk projects.

C) reject profitable, low-risk projects and accept unprofitable, high-risk projects.

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The firm will reject profitable, low-risk projects because it will use a hurdle rate that is too high. The firm should lower the required rate of return for lower risk projects. The firm will accept unprofitable, high-risk projects because the hurdle rate of return used will be too low relative to the risk of the project. The firm should increase the required rate of return for high-risk projects.

1215

Ravencroft Supplies is estimating its weighted average cost of capital (WACC). Ravencroft’s optimal capital structure includes 10% preferred stock, 30% debt, and 60% equity. They can sell additional bonds at a rate of 8%. The cost of issuing new preferred stock is 12%. The firm can issue new shares of common stock at a cost of 14.5%. The firm’s marginal tax rate is 35%. Ravencroft’s WACC is closest to:

A) 13.3%.

B) 11.5%.

C) 12.3%.

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0.10(12%) + 0.30(8%)(1 – 0.35) + 0.6(14.5%) = 11.46%.

1215

Assume that a company has equal amounts of debt, common stock, and preferred stock. An increase in the corporate tax rate of a firm will cause its weighted average cost of capital (WACC) to:

A) rise.

B) fall.

C) more information is needed.

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Recall the WACC equation:

WACC = [w_d × k_d × (1 ? t)] + (w_ps × k_ps) + (w_ce × k_s)

The increase in the corporate tax rate will result in a lower cost of debt, resulting in a lower WACC for the company.