Chapter 15
Debt and Taxes
15-3.
Suppose the corporate tax rate is 25%. Consider a firm that earns $1000 before interest and taxes
each year with no risk. The firm’s capital expenditures equal its depreciation expenses each year,
and it will have no changes to its net working capital. The risk-free interest rate is 5%.
a.
Suppose the firm has no debt and pays out its net income as a dividend each year. What is the
value of the firm’s equity?
b. Suppose instead the firm makes interest payments of $500 per year. What is the value of equity?
What is the value of debt?
c.
What is the difference between the total value of the firm with leverage and without leverage?
d. The difference in part c is equal to what percentage of the value of the debt?
Solution：
a.
EBIT
1000
Interest expense
0
EBT
1000
tax
25%
Net income
750
Equity value: net income/ risk free rate= 750/5%= 15000.
b.
EBIT
1000
Interest expense
500
EBT
500
tax
25%
Net income
375
Debt value= 500/5%= 10000
Equity value= 375/5%=7500
c.
Without leverage, total value of the firm= 15000
With leverage, total value of the firm= 17500
d.
(17500-15000)/10000=25%
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15-4.
Braxton Enterprises currently has debt outstanding of $35 million and an interest rate of 8%. Braxton
plans to reduce its debt by repaying $7 million in principal at the end of each year for the next five
years. If Braxton’s marginal corporate tax rate is 25%, what is the interest tax shield from Braxton’s
debt in each of the next five years?
Solution:
15-9.
Year 1
Year 2
Year 3
Year 4
Year 5
debt
28
21
14
7
0
interest
2.24
1.68
1.12
0.56
0
Tax
rate
25%
25%
25%
25%
25%
Tax
shield
0.56
0.42
0.28
0.14
0
Safeco Inc. has no debt, and maintains a policy of holding $10 million in excess cash reserves, invested
in risk-free Treasury securities. If Safeco pays a corporate tax rate of 21%, what is the cost of
permanently maintaining this $10 million reserve? (Hint: what is the present value of the additional
taxes that Safeco will pay?)
PV(Interest tax shield)= tax rate* D= -21%* 10,000,000=-2,100,000
15-10.
Rogot Instruments makes fine violins and cellos. It has $1 million in debt outstanding, equity valued
at $2 million, and pays corporate income tax at a rate of 21%. Its cost of equity is 12% and its cost of
debt is 7%.
a.
What is Rogot’s pretax WACC?
b. What is Rogot’s (effective after-tax) WACC?
a. Pretax WACC= 1/3*7%+2/3*12%= 10.3%
b. After tax WACC= 1/3*7%*(1-21%)+2/3*12%=9.84%
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15-11.
Rumolt Motors has 30 million shares outstanding with a price of $15 per share. In addition, Rumolt
has issued bonds with a total current market value of $150 million. Suppose Rumolt’s equity cost of
capital is 10%, and its debt cost of capital is 5%.
a. What is Rumolt’s pre-tax weighted average cost of capital?
b. If Rumolt’s corporate tax rate is 21%, what is its after-tax weighted average cost of capital?
a.
Equity= $15*30million= $450 million
Pretax WACC= 150/600* 5% + 450/600*10%= 8.75%
b.
after tax WACC= 150/600* 5%*(1-21%) + 450/600*10%=8.49%
15-14.
Restex maintains a debt-equity ratio of 0.85, and has an equity cost of capital of 12%, and a debt cost
of capital of 7%. Restex’s corporate tax rate is 25%, and its market capitalization is $220 million.
a.
If Restex’s free cash flow is expected to be $10 million in one year, what constant expected
future growth rate is consistent with the firm’s current market value?
b. Estimate the value of Restex’s interest tax shield.
a. rWACC= D/(E+D)*rD*(1-tax rate)+E/(E+D)*rE= 0.85/(1+0.85)*0.75*7%+ 1/(1+0.85)*12%=8.90%
Present value of the firm= 220,000,000/(1/(1+0.85))=407,000,000
∵Present value= CF/(r-g) ,∴ 407,000,000= 10,000,000/(8.90%-g)
g= 6.44%
b. pretax WACC= D/(E+D)*rD+E/(E+D)*rE=0.85/(1+0.85)*7%+ 1/(1+0.85)*12%=9.7%
Pretax present value of the firm= CF/(r-g)=10,000,000/(9.7%-6.44%)=303,030,303
Tax shield= 407,000,000- 303,030,303=103,969,697
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15-19.
Rally, Inc., is an all-equity firm with assets worth $25 billion and 10 billion shares outstanding. Rally
plans to borrow $10 billion and use these funds to repurchase shares. The firm’s corporate tax rate
is 21%, and Rally plans to keep its outstanding debt equal to $10 billion permanently.
a.
Without the increase in leverage, what would Rally’s share price be?
b. Suppose Rally offers $2.60 per share to repurchase its shares. Would shareholders sell for this
price?
c.
Suppose Rally offers $3.00 per share, and shareholders tender their shares at this price. What
will Rally’s share price be after the repurchase?
d. What is the lowest price Rally can offer and have shareholders tender their shares? What will its
stock price be after the share repurchase in that case?
a. Share price= $25 billion/10 billion= $2.5 per share
b. Vleveraged=asset= Vunleveraged+cash+ tax shield= 25billion+10billion+21%*10billion = 37.1billion
Share price before repurchase= 37.1billion/10 billion= 3.71＞2.6
Shareholder will not sell for this price
c. After repurchase
Shares= 10 billion- $10 billion/$3=6.67billion
Equity= Asset- debt= 25billion+21%*10billion-10 billion= 17.1billion
Share price after repurchase= 17.1billion/6.67billion= $2.56
d. Before repurchasing
Fair value1= Equity/ sharesoutstanding= (37.1billion-10 billion)/10 billion= 2.71
During the repurchasing process:
Shares= 10 billion- $10 billion/$2.71= 6.31billion
Price= Equity/ shares= 17.1billion/6.31billion=$2.71
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15-21.
Facebook, Inc. had no debt on its balance sheet in 2014, but paid $2 billion in taxes. Suppose
Facebook were to issue sufficient debt to reduce its taxes by $250 million per year permanently.
Assume Facebook’s marginal corporate tax rate is 35% and its borrowing cost is 5%.
a.
How much debt would Facebook need to issue?
b. If Facebook’s investors do not pay personal taxes (because they hold their Facebook stock in
tax-free retirement accounts), how much value would be created (what is the value of the tax
shield)?
c.
Suppose Facebook issues the amount of debt in (a), but suppose Facebook’s investors pay a
20% tax rate on income from equity and a 39.6% tax rate on interest income. What is the value
of the tax shield from the new debt in this case?
a. Reduced Earning before tax= 250 million/ 35%= 714.29 million
Debt= 714.29 million/ interest= 714.29 million/ 5%= 14.29 billion
b. b. Tax shield= tax rate* D= 0.35* 14.29 billion= 5 billion
15-22.
Markum Enterprises is considering permanently adding $100 million of debt to its capital structure.
Markum’s corporate tax rate is 25%.
a.
Absent personal taxes, what is the value of the interest tax shield from the new debt?
b. If investors pay a tax rate of 37% on interest income, and a tax rate of 20% on income from
dividends and capital gains, what is the value of the interest tax shield from the new debt?
A tax shield= tax rate* D= 25 million
B t* = 1 - (1 - tc)(1 - te) /(1 - ti)= 1-(1-25%)(1-20%)/(1-37%)=4.76%
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15-26.
Colt Systems will have EBIT this coming year of $15 million. It will also spend $6 million on total
capital expenditures and increases in net working capital, and have $3 million in depreciation
expenses. Colt is currently an all-equity firm with a corporate tax rate of 21% and a cost of capital of
10%.
a.
If Colt is expected to grow by 8.5% per year, what is the market value of its equity today?
b. If the interest rate on its debt is 8%, how much can Colt borrow now and still have nonnegative
net income this coming year?
c.
Is there a tax incentive for Colt to choose a debt-to-value ratio that exceeds 50%? Explain.
A. Cash flow= net income + depreciation- capital expenditure- increases in NWC=8.85 million
PV= 8.85/(10%-8%)= 442.5 million
B. (EBIT-Interest)*(1-tax rate)＞0
Interest ＜ 15million
Debt max= 15million/8%= 187.5 million
C. When debt to value ≥50%
Debt ＞ 187.5 million, will give out negative net income this coming year. Colt should not choose a
D/V ration that exceeds 50%.
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