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Chapter 11
The cost of
capital PROBLEMS
1. WACC
• Eric has another get-rich-quick idea, but needs
funding to support it. He chooses an all-debt
funding scenario. Eric will borrow $5,000 from
Wendy, who will charge him 5% on the loan. He
will also borrow $2,500 from Bebe, who will charge
8% on the loan, and $1,000 from Shelly, who will
charge 16% on the loan. What is the weighted
average cost of capital for Eric?
8-2
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1. WACC - answer
• Total funds borrowed = $5,000 + $2,500 + $1,000 = $8,500
• WACC = ($5,000/$8,500) X 0.05 + ($2,500/$8,500) X 0.08 +
($1,000/$8,500) X 0.16
• WACC = 0.5882 X 0.05 + 0.2941 X 0.08 + 0.1176 X 0.16
• WACC = 0.0294 + 0.0235 + 0.0188 = 0.0717 or 7.17%
8-3
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2.
WACC
• Grey’s Pharmaceuticals has a new project that will
require funding of $6 million. The company has
decided to pursue an all-debt scenario. Grey’s has
made an agreement with four lenders for the
needed financing. These lenders will advance the
following amounts and interest rates:
• What is the weighted average cost of capital for the
$6,000,000?
8-4
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2.
WACC - answer
• WACC = ($2.5/$6) X 0.13 + ($1.3/$6) X 0.10 +
($1.5/$6) X 0.06 + ($0.7/$6) X 0.08
• WACC = 0.4167 X 0.13 + 0.2167 X 0.10 + 0.25 X
0.06 + 0.11667 X 0.08
• WACC = 0.05417 + 0.02167 + 0.015 + 0.00933
=0.10017 = 10.017%
8-5
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3.
Cost of preferred stock
• Jerry is raising funds for his company by
selling preferred stock. The preferred stock
has a par value of $120 and a dividend rate
of 6%. The stock is selling for $90 in the
market. What is the cost of preferred stock
for Jerry?
8-6
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3.
Cost of preferred stock - anwer
• The dividend is $120 X 0.06 = $7.20
• And with a price of $80, the cost of
preferred stock is $7.20/$90 = 0.08 or 8%
8-7
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4.
Cost of equity: SML
• Stan is expanding his business and will sell
common stock for the needed funds. If the
current risk-free rate is 4% and the
expected market return is 12%, what is the
cost of equity for Stan if the beta of the
stock is
a.
b.
c.
d.
8-8
0.75?
0.90?
1.05?
1.20?
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4.
Cost of equity: SML - answer
a. Using the security market line we have,
E(ri) = rf + βi (E(rm) – rf)
Cost of Equity
= E(ri) = 0.04 + 0.75 (0.12 – 0.04)
Cost of Equity
= 0.04 + 0.75 (0.08) = 0.04 + 0.06 = 0.10 or 10%
b. Using the security market line we have,
E(ri) = rf + βi (E(rm) – rf)
Cost of Equity
= E(ri) = 0.04 + 0.90 (0.12 – 0.04)
Cost of Equity
= 0.04 + 0.90 (0.08) = 0.04 + 0.072 = 0.112 or
11.2%
c. Using the security market line we have,
E(ri) = rf + βi (E(rm) – rf)
Cost of Equity
= E(ri) = 0.04 + 1.05 (0.12 – 0.04)
Cost of Equity
= 0.04 + 1.05 (0.08) = 0.04 + 0.084 = 0.124 or
12.4%
d. Using the security market line we have,
E(ri) = rf + βi (E(rm) – rf)
Cost of Equity
= E(ri) = 0.04 + 1.20 (0.12 – 0.04)
Cost of Equity
= 0.04 + 1.20 (0.08) = 0.04 + 0.096 = 0.136 or
13.6%
8-9
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5.
Book value versus market value
components
Compare Trout Inc. with Salmon Enterprises using the balance sheet of
Trout and the market data of Salmon for the weights in the weighted
average cost of capital.
Trout Inc.
Current Assets: $2,000,000
Current Liabilities:
$1,000,000
Long-term Assets:$7,000,000 Long-Term Liabilities: $5,000,000
Total Assets
$9,000,000
Owner’s Equity:
$3,000,000
Salmon Enterprises
Bonds Outstanding 3,000 selling at $980
Common Stock Outstanding 260,000 selling at $23.40
If the after-tax cost of debt is 8% for both companies and the cost of
equity is 12% which company has the highest WACC?
8-10
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5.
Book value versus market value
components - answer
Trout Inc. Component Weights:
Debt = $5,000,000) / $8,000,000 = 0.625
Equity = $3,000,000 / $8,000,000 = 0.375
Salmon Enterprises Component Weights:
Market Value of Debt
= $980 × 3,000 = $2,940,000
Market Value of Equity
= $23.40 × 260,000 = $6,084,000
Debt Component
= $2,940,000 / ($2,940,000 +
$6,084,000) = 0.3258
Equity Component
= $6,084,000 / ($2,940,000 +
$6,084,000) = 0.6742
WACC for Trout = 0.625 × 8% + 0.375 × 12% = 9.5%
WACC for Salmont = 0.3258 × 8% + 0.6742 × 12% =
10.6968%
8-11
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6.
Adjusted WACC
Clark Explorers Inc., an engineering firm has the
following capital structure:
Using market value and book value (separately, of course), find the
adjusted WACC for Clark Explorers at the following tax rates:
a. 35%
b. 25%
c. 15%
d. 5%
8-12
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6.
Adjusted WACC - answer
Market Value Component weights are:
Equity Market Value
= $30 × 120,000 = $3,600,000
Preferred Stock Market Value
= $110 × 10,000 = $1,100,000
Debt Market Value
= $955 × 6,000 = $5,730,000
Total Market Value
= $3,600,000 + $1,100,000 + $5,730,000 =
$10,430,000
Equity Market Percent
= $3,600,000 / $10,430,000 = 0.3452
Preferred Stock Market Percent = $1,100,000 / $10,430,000 = 0.1055
Debt Market Percent
= $5,730,000 / $10,430,000 = 0.0.5494
Total Book Value
=$3,000,000 + $1,000,000 + $6,000,000 =
$10,000,000
Equity Book Percent
= $3,000,000 / $10,000,000 = 0.30
Preferred Book Market Percent
= $1,000,000 / $10,000,000 = 0.10
Debt Book Percent
= $6,000,000 / $10,000,000 = 0.60
8-13
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6.
Adjusted WACC - answer
a. Adjusted WACC, market value
= 0.3452 × 15% + 0.1055 × 12% + 0.5494 × 9% × (1 – 0.35)
= 5.1774% + 1.2656% + 3.2139% = 9.6568%
Adjusted WACC, book value
= 0.30 × 15% + 0.10 × 12% + 0.60 × 9% × (1 – 0.35)
= 4.5% + 1.2% + 3.51% = 9.21%
b. Adjusted WACC, market value
= 0.3452 × 15% + 0.1055 × 12% + 0.5494 × 9% × (1 – 0.25)
= 5.1774% + 1.2656% + 3.7083% = 10.1512%
Adjusted WACC, book value
= 0.30 × 15% + 0.10 × 12% + 0.60 × 9% × (1 – 0.25)
= 4.5% + 1.2% + 4.05% = 9.75%
8-14
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6.
Adjusted WACC - answer
c. Adjusted WACC, market value
= 0.3452 × 15% + 0.1055 × 12% + 0.5494 × 9% × (1 – 0.15)
= 5.1774% + 1.2656% + 4.2027% = 10.6457%
Adjusted WACC, book value
= 0.30 × 15% + 0.10 × 12% + 0.60 × 9% × (1 – 0.15)
= 4.5% + 1.2% + 4.59% = 10.29%
d. Adjusted WACC, market value
= 0.3452 × 15% + 0.1055 × 12% + 0.5494 × 9% × (1 – 0.05)
= 5.1774% + 1.2656% + 4.6972% = 11.1401%
Adjusted WACC, book value
= 0.30 × 15% + 0.10 × 12% + 0.60 × 9% × (1 – 0.05)
= 4.5% + 1.2% + 5.13% = 10.83%
8-15
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