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Solidify your understanding on the applications of the cost of capital

topics.

Use a financial calculator or spreadsheet (Excel) to solve 10 problems (provided on

page 4) related to the cost of capital. You are required to show the following three steps for each problem

(a sample problem and solution is provided for guidance):

(i) Describe and interpret the assumptions related to the problem.

(ii) Apply the appropriate mathematical model to solve the problem.

(iii) Calculate the correct solution to the problem.

A company is expected to pay a $3.50 dividend at year-end, the dividends are expected to grow at a constant

rate of 6.50% a year, and the common stock currently sells for $62.50 per share. The before-tax cost of debt

is 7.50% and the tax rate is 40.00%. The target capital structure consists of 40.00% debt and 60.00%

common equity. What is the company’s WACC if all equity is from retained earnings?

Solution:

(i) Describe the assumptions related to the problem:

The problem assumes the dividends of the company will grow at 6.50% forever and next

periods dividend will be $3.50; a tax rate of 40.00% is also assumed for the firm.

(ii) Apply the appropriate mathematical model:

The cost of equity is based on the dividend growth model: 𝐑𝐄 =

𝐃𝟏

𝐏𝟎

+ 𝐠

RE = required return, D1 = next period’s dividend, P0 = current price, and g = constant growth

rate.

The cost of debt is based on the after-tax component model: 𝐑𝐃,𝐀𝐓 = 𝐑𝐃,𝐁𝐓(𝟏 − 𝐓𝐂)

RD,AT = after-tax cost of debt, RD,BT = before-tax cost of debt, and TC = the firm’s marginal tax

rate.

The weighted average cost of capital is based on the weighted average model: 𝐖𝐀𝐂𝐂 =

𝐄

𝐕

(𝐑𝐄

) +

𝐃

𝐕

(𝐑𝐃,𝐀𝐓) or 𝐖𝐀𝐂𝐂 = 𝐖𝐄

(𝐑𝐄

) + 𝐖𝐃(𝐑𝐃,𝐀𝐓)

E

V

= WE = weight of equity, D

V

= WD = weight of debt, RE = required return, and RD,AT = after tax cost of debt.

(iii) Calculation:

WACC = 9.06%

Step 1: RE =

$3.50

$62.50

+ 0.065 = 0.121 or 12.10%

Step 2: RD,AT = 7.50%(1 − 0.40) = 4.50%

Step 3: WACC = 0.60(12.10%) + 0.40(4.50%) = 9.06%

4

Homework Problems

1) A company has $10 million of debt outstanding with a coupon rate of 8.00%. Currently the yield to

maturity on these bonds is 10.50%. If the firm’s tax rate is 40.00%, what is relevant cost of debt

financing to this company (round your answer to two decimal places)?

2) Suppose a company currently has some bonds outstanding in the market. The bonds have 10 years until

maturity, they pay a coupon rate of 6% on a semiannual basis. If the company’s bonds are selling for

$965 now, and the company’s tax rate is 40%, what is its after-tax cost of debt (round your answer to

two decimal places)?

3) A company’s perpetual preferred stock currently trades at $87.50 per share and pays an $8.00 annual

dividend. What is the firm’s cost of preferred stock (round your answer to two decimal places)?

4) Assume that you have been provided with the following firm data: risk-free rate = 4%, market risk

premium = 5%, and beta = 1.15. What is the cost of equity from retained earnings based on the CAPM

approach (round your answer to two decimal places)?

5) A company hired you as a consultant to help them estimate its cost of capital. You have been provided

with the following data: D1 = $0.80, P0 = $22.50, and g = 5% (constant). Based on the DCF approach,

what is the cost of equity from retained earnings (round your answer to two decimal places)?

6) The expected dividend is $1.50 per share of common stock priced at $15.00. What is the cost of internal

common equity if the long-term growth in dividends is projected to be 4% indefinitely (round your

answer to two decimal places)?

7) A company is expected to pay a dividend of $1.90 next year. Dividends are expected to grow at a

constant rate of 3% per year, and the stock price is currently $12.50. The company’s marginal tax rate

is 40%. Compute the cost of internal equity (round your answer to two decimal places).

8) You were hired as a consultant to a company, whose target capital structure is 40.00% debt, 10.00%

preferred, and 50.00% common equity. The after-tax cost of debt is 6.00%, the cost of preferred stock

is 7.50%, and the cost of retained earnings is 13.25%. The firm will not be issuing any new stock. What

is its WACC (round your answer to two decimal places)?

9) A company’s capital structure consists of 40% debt and 60% equity. The before-tax cost of debt is 12%,

the cost of retained earnings is 15%, and the tax rate is 40%. What is this company’s WACC (round

your answer to two decimal places)?

10) A company plans to maintain its optimal capital structure of 30% debt, 20% preferred stock, and 50%

common stock into the future. The required return on each component is 10%, 11%, and 18%,

respectively. Assuming a 40% marginal tax rate, what is the WACC of this company (round your

answer to two decimal places)?

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