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周教授CFA金融课程:2019/2020年CFA一二三级系列课程
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: wd = 30%, wps = 20%, wce = 50%, where wd, wps, and wce 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)
11.0%.
B)
9.2%.
C)
9.0%.



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 = (wd)(kd) + (wps)(kps) + (wce)(kce)

where wd, wps, and we 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%.

TOP

When calculating the weighted average cost of capital (WACC) an adjustment is made for taxes because:
A)
equity earns higher return than debt.
B)
the interest on debt is tax deductible.
C)
equity is risky.



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.

TOP

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)
12.5%.
B)
13.0%.
C)
13.5%.



Ks = 0.10 + (0.05)(1.2) = 0.16 or 16%
Kd = 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

TOP

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.
  • A preferred stock issue that pays a dividend of $2.80 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 [kd (1 – t)] is used to compute the weighted average cost of capital. It is the interest rate on new debt (kd) less the tax savings due to the deductibility of interest (kdt).
Here, we are given the inputs needed to calculate kd: 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, kd (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 (Dps) forever. The cost of preferred stock (kps) = Dps / P

where:

Dps = preferred dividends.


P = price

Here, kps = Dps / P = $2.80 / $35 = 0.08, or 8.0%.

Step 3: Determine the cost of common equity:

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

Step 4: Calculate WACC:

WACC = (wd)(kd) + (wps)(kps) + (wce)(kce)
where wd, wps, and wce 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.

TOP

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)
fall.
B)
rise.
C)
more information is needed.



Recall the WACC equation:

WACC = [wd × kd × (1 − t)] + (wps × kps) + (wce × ks)

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

TOP

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%.



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

TOP

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)
10.59%.
B)
10.03%.
C)
10.18%.



WACC = (wd)(kd)(1 − t) + (wps)(kps) + (wce)(kce)
where:
wd = 0.40
wce = 0.50
wps = 0.10
kd = 0.07
kps = Dps / P = 4.00 / 40.00 = 0.10
kce = 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%

TOP

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)
7.8%.
C)
5.4%.



CAPM = RE = RF + B(RM − RF) = 0.06 + (1.125)(0.14 − 0.06) = 0.15
WACC = (E ÷ V)(RE) + (D ÷ V)(RD)(1 − t)
V = 100 + 300 = 400
WACC = (1 ÷ 4)(0.15) + (3 ÷ 4)(0.09)(1 − 0.4) = 0.078

TOP

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%.


WACC = (E / V)(RE) + (D / V)(RD)(1 − TC)
WACC = (15 / 25)(0.15) + (10 / 25)(0.10)(1 − 0.35) = 0.09 + 0.026 = 0.116 or 11.6%

TOP

Which of the following choices best describes the role of taxes on the after-tax cost of capital in the U.S. from the different capital sources?
Common equity Preferred equityDebt
A)
No effectDecreaseDecrease
B)
DecreaseDecreaseNo effect
C)
No effectNo effectDecrease



In the U.S., interest paid on corporate debt is tax deductible, so the after-tax cost of debt capital is less than the before-tax cost of debt capital. Dividend payments are not tax deductible, so taxes do not decrease the cost of common or preferred equity.

TOP

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