538 Brooks ◼ Financial Management: Core Concepts, 4e
5. Break-even EBIT (with and without taxes). Alpha Company is looking at two different
capital structures, one an all-equity firm, and the other a levered firm with $2 million of debt
financing at 8% interest. The all-equity firm will have a value of $4 million and 400,000
shares outstanding. The levered firm will have 200,000 shares outstanding.
a. Find the break-even EBIT for Alpha Company using EPS if there are no corporate taxes.
b. Find the break-even EBIT for Alpha Company using EPS if the corporate tax rate is 30%.
c. What do you notice about these two break-even EBITS for Alpha Company?
6. Break-even EBIT (with taxes). Beta, Gamma, and Delta Companies are similar in every way
except for their capital structures. Beta is an all-equity firm with $3,600,000 of value and
100,000 shares outstanding. Gamma is a levered firm with the same value as Beta, but with
$1,080,000 in debt at 9% and 70,000 shares outstanding. Delta is a levered firm with
$2,160,000 in debt at 12% and 40,000 shares outstanding. What are the break-even EBITs
for Beta and Gamma, Beta and Delta, and Gamma and Delta Companies if the corporate tax
rate is 40% for all three companies?
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7. Pecking order hypothesis. Rachel can raise capital from the following sources:
Source of Funds
Interest Rate
Borrowing Limit
Parents
0%
$10,000
Friends
5%
$2,000
Bank Loan
9%
$15,000
Credit Card
14.5%
$5,000
What is Rachel’s weighted average cost of capital if she needs to raise
a. $10,000?
b. $20,000?
c. $30,000?
ANSWER
542 Brooks ◼ Financial Management: Core Concepts, 4e
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ANSWER
RE = Ra + (Ra – RD) × (D/E)
Current required cost of equity: 0.20 + (0.20 – 0.10) (0) = 0.20 or 20%
New required cost of equity: 0.20 + (0.20 – 0.10) (0.5/0.5) = 0.30 or 30%
544 Brooks ◼ Financial Management: Core Concepts, 4e
Once again this problem can be solved by adding the tax shield to the current after tax equity
value without debt.
VE = $25,000,000 (1 – 0.4) = $15,000,000
VL = VE + (D × TC)
a. $15,000,000 + ($6,250,000 × 0.4) = $17,500,000
b. $15,000,000 + ($18,750,000 × 0.4) = $22,500,000
15. Size of tax shield. Using the information from Problems 11 and 13 on Air Seattle, determine
the size of the tax shield with a corporate tax rate of 15%, 25%, 35%, and 45% if Air Seattle’s
capital structure is 50/50 debt to equity.
ANSWER
16. Size of tax shield. Using the information from Problems 12 and 14 on Roxy Broadcasting,
determine the size of the tax shield with a corporate tax rate of 15%, 25%, 35%, and 45%
if Roxy’s capital structure is 1/3 debt to equity. Determine the same if the capital structure
is 3/1.
ANSWER
Equity Slice (b)
$11,250,000
$3,750,000
Equity Wealth (a + b)
$17,500,000
$22,500,000
Equity Increase
$2,500,000
$7,500,000
Tax Shield
$2,500,000
$7,500,000
Chapter 16 ◼ Capital Structure 545
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New debt issues with 25% debt = $25,000,000 × (0.25) = $6,250,000
Tax shield = (D × TC)
a. TC @15% ($6,250,000 × 0.15) = $937,500
b. TC @25% ($6,250,000 × 0.25) = $1,562,500
c. TC @35% ($6,250,000 × 0.35) = $2,187,500
d. TC @45% ($6,250,000 × 0.45) = $2,812,500
New debt issues with 75% debt = $25,000,000 × (0.75) = $18,750,000
Tax shield = (D × TC)
a. TC @15% ($18,750,000 × 0.15) = $2,812,500
b. TC @25% ($18,750,000 × 0.25) = $4,687,500
c. TC @35% ($18,750,000 × 0.35) = $6,562,500
d. TC @45% ($18,750,000 × 0.45) = $8,437,500
Chapter 16 ◼ Capital Structure 547
Solutions to Advanced Problems for Spreadsheet Application
1. Break-even EBIT for different capital structures in a world of no taxes.
Jordan Enterprises EBIT
Capital Structure 25,000,000.00$ 27,500,000.00$ 30,000,000.00$ 32,500,000.00$ 35,000,000.00$
All – Equity
EBIT 25,000,000.00$ 27,500,000.00$ 30,000,000.00$ 32,500,000.00$ 35,000,000.00$
Interest Expense –$ 5.00$ 10.00$ 15.00$ 20.00$
Net Income 25,000,000.00$ 27,499,995.00$ 29,999,990.00$ 32,499,985.00$ 34,999,980.00$
Shares 10,000,000 10,000,005 10,000,010 10,000,015 10,000,020
EPS 2.50$ 2.75$ 3.00$ 3.25$ 3.50$
25.0 % Debt
EBIT 25,000,000.00$ 27,500,000.00$ 30,000,000.00$ 32,500,000.00$ 35,000,000.00$
Interest Expense 7,500,000.00$ 7,500,000.00$ 7,500,000.00$ 7,500,000.00$ 7,500,000.00$
Net Income 17,500,000.00$ 20,000,000.00$ 22,500,000.00$ 25,000,000.00$ 27,500,000.00$
Shares 7,500,000 7,500,000 7,500,000 7,500,000 7,500,000
EPS 2.33$ 2.67$ 3.00$ 3.33$ 3.67$
50.0 % Debt
EBIT 25,000,000.00$ 27,500,000.00$ 30,000,000.00$ 32,500,000.00$ 35,000,000.00$
Interest Expense 15,000,000.00$ 15,000,000.00$ 15,000,000.00$ 15,000,000.00$ 15,000,000.00$
Net Income 10,000,000.00$ 12,500,000.00$ 15,000,000.00$ 17,500,000.00$ 20,000,000.00$
Shares 5,000,000 5,000,000 5,000,000 5,000,000 5,000,000
EPS 2.00$ 2.50$ 3.00$ 3.50$ 4.00$
$2.40
$2.60
$2.80
$3.00
$3.20
$3.40
$3.60
$3.80
$4.00
Earnings Per Share for Different Capital Structures
All Equity
12.5% Debt
25% Debt
37.5% Debt
50% debt
Chapter 16 ◼ Capital Structure 549
Solutions to Mini-Case
General Energy Storage Systems: How Much Debt and How Much Equity?
1. Why should GESS expect to pay a higher rate of interest if it borrows $4,000,000 rather
than $2,000,000?
2. Estimate earnings per share for plan A and plan B at EBIT levels of $800,000, $1,000,000,
and $1,200,000.
Plan A
EBIT
$ 800,000.00
$1,000,000.00
$1,200,000.00
Interest 9%
360,000.00
360,000.00
360,000.00
EBT
440,000.00
640,000.00
840,000.00
Tax 40%
176,000.00
256,000.00
336,000.00
Net Inc.
$264,000.00
$384,000.00
$504,000.00
Shares outstanding
300,000.00
300,000.00
300,000.00
E.P.S.
$0.88
$1.28
$1.68
Plan B
EBIT
$ 800,000.00
$1,000,000.00
$1,200,000.00
Interest 8%
160,000.00
160,000.00
160,000.00
EBT
640,000.00
840,000.00
1,040,000.00
Tax 40%
256,000.00
336,000.00
416,000.00
Net Inc.
$384,000.00
$504,000.00
$624,000.00
Shares outstanding
400,000.00
400,000.00
400,000.00
E.P.S.
$0.96
$1.26
$1.56
552 Brooks ◼ Financial Management: Core Concepts, 4e
Additional Problems with Solutions
1. Different loan rates. Diversified Holdings has four subsidiaries, each of which borrows funds
from the parent company and has a different success rate with the projects it undertakes.
Subsidiary A is successful with its projects 80% of the time, Subsidiary B gets it right 93% of
the time, Subsidiary C gets it 75% of the time, and Subsidiary D gets it 85% of the time. What
loan rates should Diversified Holdings charge each subsidiary for loans?
2. Benefits of borrowing. Loyola Turbo Engines is looking to expand its operations by adding
another manufacturing location. If successful, the company will make $750,000, but if it
fails, the company will lose $300,000. Loyola can borrow the required capital of 300,000 at
16%.
(a) If all their projections point to an 85% probability of success, should they borrow the
money and go ahead with the expansion?
(b) Above what minimum probability of success will the project be acceptable with a
discount rate of 16%?
Chapter 16 ◼ Capital Structure 555
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Equity value after tax with new structure = $7,692,307.70 × (1 – 0.35) = $5,000,000
New equity wealth after tax = $5,000,000 + $7,692,307.7 = $12,692,307.7
Or this problem can be solved by adding the current equity wealth unlevered to the tax
shield VL = VE + (D × TC)
$10,000,000 + ($7,692,307.70 × 0.35) = $12,692,307.7
5. Equity value in a levered firm. Sea Crest Corporation, which is an all-equity firm, has an
annual EBIT of $2,540,000, and a WACC of 15%. The current tax rate is 35%. Sea Crest Corp.
will have the same EBIT forever. If the company sells debt worth $3,250,000 with a cost of
debt of 10%, what is the value of equity in the unlevered and levered firm? What is the
value of debt in the levered firm? What is the government’s value in the unlevered and
levered firm?
ANSWER (Slides 16-48 to 16-49)