Accounts Analysis

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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)?

Sample Solution

Following the Iranian Constitutional Revolution as well as the First World War, the Pahlavi regime led by Reza Shah attempted to consolidate the Kurdish tribal by stripping tribal leaders of their position and replacing them with governors. This led to a strong opposition by multiple Kurdish tribes (Ahmadzadeh and Stansfield, pg. 12). One of the main Kurdish leaders that opposed the centralization was Ismal Agha Simko of the Shakak tribe. He was very successful in uniting multiple Kurdish tribes and was eventually lured and assassinated by Iranian authorities. Simko’s success inspired the development of Kurdish nationalism (Ahmadzadeh and Stansfield, pg. 13). Eventually the British, sensing the Kurds’ restlessness as a result of this change as well as the Soviets agenda, stepped in. They advised the Iranian central government to appease the Kurds by restoring tribal leaders land and title. Unsuccessful compromises led to more Kurdish attacks and raids in Iran. Eventually, the Iranian authorities released the tribal leaders, however, the transition was not as smooth since chief authority lost its relevancy (Price, pg. 186).

Due to the beginning of World War II, British and Soviet influence over the government grew a stronger foothold over Reza Shah’s. Their presence led to the development of the Society for the Revival of the Kurds, or more commonly known as JK, in 1942. The JK’s goal was to form a Kurdish homeland but was held back by the ever-present tribal traditions. It was not until they joined with the Kurdistan Democratic Party (KDP), who were led by Qazi Mohammad, that the possibility of a Kurdish homeland gained footing (Ahmadzadeh and Stansfield, pg. 14). In 1946, the Mahabad Republic was established in northwestern Iran with assistance from the Soviets who were desperate to see a divided Iran (Purdy, pg. 3). However, no one except the Soviets recognized it as a country, so when the Soviets became weaker throughout World War II the Kurdish Republic was left vulnerable to the Iranian government who ended their rule in 1946 (Ahmadzadeh and Stansfield, pg. 15).

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