Reading 45: Cost of Capital LOSa习题精选 capital, average, interpret, following, 2010

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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

 

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In calculating the weighted average cost of capital (WACC), which of the following statements is least accurate?

A) Different methods for estimating the cost of common equity might produce different results.

B) The cost of preferred equity capital is the preferred dividend divided by the price of preferred shares.

C) The cost of debt is equal to one minus the marginal tax rate multiplied by the coupon rate on outstanding debt.

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After-tax cost of debt = bond yield ? tax savings = k_d ? k_dt = k_d(1 ? t)

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A company has the following capital structure:

• Target weightings: 30% debt, 20% preferred stock, 50% common equity.
• Tax Rate: 35%.
• The firm can issue $1,000 face value, 7% semi-annual coupon debt with a 15-year maturity for a price of $1,047.46.
• An 8% dividend preferred stock issue has a value of $35 per share.
• The company’s growth rate is estimated at 6%.
• The company's common shares have a value of $40 and a dividend in year 0 of D₀ = $3.00.

The company's weighted average cost of capital is closest to:

A) 9.84%.

B) 9.28%.

C) 10.53%.

Step 1: Determine the after-tax cost of debt:

The after-tax cost of debt [k_d (1 – t)] is used to compute the weighted average cost of capital. It is the interest rate on new debt (k_d) less the tax savings due to the deductibility of interest (k_dt).

Here, we are given the inputs needed to calculate k_d: N = 15 × 2 = 30; PMT = (1,000 × 0.07) / 2 = 35; FV = 1,000; PV = -1,047.46; CPT → I = 3.25, multiply by 2 = 6.50%.

Thus, k_d (1 – t) = 6.50% × (1 – 0.35) = 4.22%

Step 2: Determine the cost of preferred stock:

Preferred stock is a perpetuity that pays a fixed dividend (D_ps) forever. The cost of preferred stock (k_ps) = D_ps / P

where:	Dps = preferred dividends.
	P = price

Here, D_ps = 0.08 × $35.00 = $2.80, so k_ps = D_ps / P = $2.80 / $35 = 0.08, or 8.0%.

Step 3: Determine the cost of common equity:

k_ce = (D₁ / P₀) + g

where:	D1 = Dividend in next year
	P0 = Current stock price
	g = Dividend growth rate

Here, D₁ = D₀ × (1 + g) = $3.00 × (1 + 0.06) = $3.18.

k_ce = (3.18 / 40) + 0.06 = 0.1395 or 13.95%.

Step 4: Calculate WACC:

WACC = (w_d)(k_d) + (w_ps)(k_ps) + (w_ce)(k_ce)

where w_d, w_ps, and w_ce are the weights used for debt, preferred stock, and common equity.

Here, WACC = (0.30 × 4.22%) + (0.20 × 8.0%) + (0.50 × 13.95%) = 9.84%.

Note: Your calculation may differ slightly, depending on whether you carry all calculations in your calculator, or round to two decimals and then calculate.

honeycfa

Helmut Humm, manager at a large U.S. firm, has just been assigned to the capital budgeting area to replace a person who left suddenly. One of Humm’s first tasks is to calculate the company’s weighted average cost of capital (WACC) – and fast! The CEO is scheduled to present to the board in half an hour and needs the WACC – now! Luckily, Humm finds clear notes on the target capital component weights. Unfortunately, all he can find for the cost of capital components is some handwritten notes. He can make out the numbers, but not the corresponding capital component.  As time runs out, he has to guess.

Here is what Humm deciphered:

• Target weights: w_d = 30%, w_ps = 20%, w_ce = 50%, where w_d, w_ps, and w_ce are the weights used for debt, preferred stock, and common equity.
• Cost of components (in no particular order): 6.0%, 15.0%, and 8.5%.
• The cost of debt is the after-tax cost.

If Humm guesses correctly, the WACC is:

A) 9.2%.

B) 9.0%.

C) 11.0%.

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If Humm remembers to order the capital components from cheapest to most expensive, he can calculate WACC. The order from cheapest to most expensive is: debt, preferred stock (which acts like a hybrid of debt and equity), and common equity.

Then, using the formula for WACC = (w_d)(k_d) + (w_ps)(k_ps) + (w_ce)(k_ce)

where w_d, w_ps, and w_e are the weights used for debt, preferred stock, and common equity.

WACC = (0.30 × 6.0%) + (0.20 × 8.5%) + (0.50 × 15.00%) = 11.0%.

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The following data is regarding the Link Company:

• A target debt/equity ratio of 0.5
• Bonds are currently yielding 10%
• Link is a constant growth firm that just paid a dividend of $3.00
• Stock sells for $31.50 per share, and has a growth rate of 5%
• Marginal tax rate is 40%

What is Link's after-tax cost of capital?

A) 10.5%.

B) 12.0%.

C) 12.5%.

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Use the revised form of the constant growth model to determine the cost of equity. Use algebra to determine the weights for the target capital structure realizing that debt is 50% of equity. Substitute 0.5E for D in the formula below.

k_s = D₁ ÷ P₀ + growth = (3)(1.05) ÷ (31.50) + 0.05 = 0.15 or 15%

V = debt + equity = 0.5 + 1 = 1.5

WACC = (E ÷ V)(k_s) + (D ÷ V)(k_debt)(1 ? t)

WACC = (1 ÷ 1.5)(0.15) + (0.5 ÷ 1.5)(0.10)(1 ? 0.4) = 0.1 + 0.02 = 0.12 or 12%

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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) 12.3%.

C) 11.5%.

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

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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.

honeycfa

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.

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

A) An increase in expected inflation.

B) A reduction in the market risk premium.

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.

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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.