CHAPTER
11
Problem 1
On January 1, 2005, the total assets of the Dexter
Company were $270 million. The firm’s present capital structure, which follows,
is considered to be optimal. Assume that there is no short-term debt.
Long-term debt $135,000,000
Common equity 135,000,000
Total liabilities and
equity $270,000,000
New bonds will have a 10 percent coupon rate and will
be sold at par. Common stock, currently selling at $60 a share, can be sold to
net the company $54 a share. Stockholders’ required rate of return is estimated
to be 12 percent, consisting of a dividend yield of 4 percent and an expected
growth rate of 8 percent. (The next expected dividend is $2.40, so $2.40/$60 =
4%). Retained earnings are estimated to be $13.5 million. The marginal tax rate
is 40 percent. Assuming that all asset expansion (gross expenditures for fixed
assets plus related working capital) is included in the capital budget, the
dollar amount of the capital budget, ignoring depreciation, is $135 million.
a. To
maintain the present capital structure, how much of the capital budget must
Dexter finance by equity?
b. How
much of the new equity funds needed will be generated internally? Externally?
c.
Calculate the cost of each of the equity components.
Solution
to Problem 1
a. Common equity needed: 0.50($135,000,000) =
$67,500,000.
b. Expected
internally generated equity (retained earnings) is $13.5 million. External equity needed is as follows:
New equity needed $67,500,000
Retained earnings 13,500,000
External equity needed $54,000,000
c. Cost of
equity:
ks =
Cost of retained earnings
= Dividend yield + Growth rate = 12% = 4% + 8% = 12%.
= /P0 + g = $2.40/$60 + 0.08 = 0.04 + 0.12 = 12.0%.
ke =
Cost of new equity
= /NP + g = $2.40/$54.00 + 0.08 = 0.044 + 0.08 = 0.124 = 12.4%.
Problem 2
A company’s 6 percent coupon rate, semiannual payment,
$1,000 par value bond that matures in 30 years sells at a price of $515.16. The
company’s marginal tax rate is 40 percent. What is the firm’s component cost of
debt for purposes of calculating the WACC? (Hint: Base your answer on the
simple rate, not the effective annual rate, EAR .)
Solution
to Problem 2
We
can use the equation given (Equation 7‑3) in Chapter 7 to find the
approximate yield to maturity:
Note
that we use the number of years rather than the number of interest payments in
this computation, because the “approximate YTM” computation does not consider
the time value of money.
Using the calculator, enter these values: N = 60, PV = -515.16, PMT = 30, and FV =
1000, to get I = 6% = periodic rate. The simple rate is 6%(2) = 12%, and the after-tax
component cost of debt is 12%(0.6) = 7.2%.
CHAPTER
12
Multiple
Choice Questions
1.
The optimal capital structure is the one that maximizes
__________, and this will always be lower than the debt/equity ratio that
maximizes __________.
|
a.
|
expected EPS; the firm's stock price
|
|
b.
|
net income, expected EPS
|
|
c.
|
book value of the firm; net income
|
|
d.
|
the firm's stock price; expected EPS CORRECT
|
2.
If a given change in sales results in a larger relative
change in EPS then we can definitely say that the firm has
|
a.
|
a degree of financial leverage greater than one.
|
|
b.
|
a degree of operating leverage less than
one.
|
|
c.
|
a degree of total leverage less than one. CORRECT
|
|
d.
|
a degree of total leverage greater than one.
|
Problem 1
Brown Products is a
new firm just starting operations. The
firm will produce backpacks that will sell for $22.00 each. Fixed costs are $500,000 per year, and
variable costs are $2.00 per unit of production. The company expects to sell 50,000 backpacks
per year, and its marginal tax rate is 40 percent. Brown needs $2 million to build facilities,
obtain working capital, and start operations.
If Brown borrows part of the money, the interest charges will depend on
the amount borrowed as follows:
Percentage
of Debt Interest Rate on Total
Amount Borrowed in Capital Structure
Amount Borrowed
$ 200,000 10% 9.00%
400,000 20 9.50
600,000 30 10.00
800,000 40 15.00
1,000,000 50 19.00
1,200,000 60 26.00
Assume that stock can be sold at a price of $20
per share on the initial offering, regardless of how much debt the company
uses. Then after the company begins
operating, its price will be determined as a multiple of its earnings per
share. The multiple (or the P/E ratio)
will depend upon the capital structure as follows:
Debt/Assets P/E Debt/Assets
P/E
0.0 12.5 40.0 8.0
10.0 12.0 50.0 6.0
20.0 11.5 60.0 5.0
30.0 10.0
What
is Brown’s optimal capital structure, which maximizes stock price, as measured
by the debt/assets ratio?
Solution
to Problem 1
The first step is to calculate EBIT:
Sales in dollars [50,000($22)] $1,100,000
Less: Fixed
costs (500,000)
Variable costs [50,000($2)] (100,000)
EBIT $ 500,000
The
second step is to calculate the EPS at each debt/assets ratio using the
formula:
EPS = .
Recognize (1) that I = Interest
charges = (Dollars of debt)(Interest rate at each D/A ratio), and (2) that
shares outstanding = (Assets – Debt)/Initial price per share = ($2,000,000 –
Debt)/$20.00.
D/A EPS D/A
EPS
0% $3.00 40% $3.80
10 3.21 50 3.72
20 3.47 60 2.82
30 3.77
Finally, the third step is to
calculate the stock price at each debt/assets ratio using the following
formula: Price = (P/E)(EPS).
D/A Price D/A
Price
0% $37.50 40% $30.40
10 38.52 50 22.32
20 39.91 60 14.10
30 37.70
Thus, a debt/assets ratio of 20
percent maximizes stock price. This is
the optimal capital structure.
Problem 2
The Strasburg Company plans to raise a net amount of $270
million to finance new equipment and working capital in early 2011. Two
alternatives are being considered: Common stock can be sold to net $60 per
share, or bonds yielding 12 percent can be issued. The balance sheet and income
statement of the Strasburg Company prior to financing are as follows:
The Strasburg
Company: Balance Sheet as of December
31, 2010
(millions of
dollars)
__________
Current assets $900.00
Net fixed assets 450.00
___________
Total assets $1,350.00
Accounts payable $172.50
Notes payable to bank $255.00
Other current liabilities $255.00
__________
Total current liabilities $652.50
Long-term debt (10%) 300.00
Common Stock, ($3 par) 60.00
Retained earnings 337.50
___________
Total liabilities and equity $1,350.00
The Strasburg Company: Income Statement for year ended December 31, 2010
(millions of dollars)
Sales $2,475.00
Operating costs (2,227.50)
__________
Earnings before interest and taxes $247.50
Interest on short-term debt (15.00)
Interest on long-term debt (30.00)
___________
Earnings before taxes (EBT) $202.50
Taxes (40%) (81.00)
___________
Net income $121.50
The probability distribution for annual sales is as
follows:
Probability Annual Sales (millions of
dollars)
0.30 $2,250
0.40
2,700
0.30 3,150
Assuming that EBIT is equal to 10 percent of sales, calculate
earnings per share under both the debt financing and the stock financing
alternatives at each possible level of sales. Then calculate expected earnings
per share and σEPS under both debt and stock financing. Also calculate the
debt-to-total assets ratio and the times-interest-earned (TIE ) ratio at the expected sales level under each
alternative. The old debt will remain outstanding. Which financing method do
you recommend?
Solution
to Problem 2
Use
of debt ($ millions):
Probability 0.3 0.4 0.3
Sales $2,250.0
$2,700.0 $3,150.0
EBIT (10%)
225.0
270.0
315.0
Interest* (
77.4) (
77.4) (
77.4)
EBT 147.6 192.6
237.6
Taxes (40%)
( 59.0) (
77.0) (
95.0)
Net income $ 88.6 $ 115.6 $ 142.6
Earnings
per share
(20
million shares) $ 4.43 $ 5.78 $ 7.13
*Interest on debt = ($270 x 0.12) + Current interest
expense
=
$32.4 + ($15 + $30) = $77.4
Expected EPS = (0.30)($4.43) + (0.40)($5.78) +
(0.30)($7.13) = $5.78 if debt is used.
Expected Sales =
0.3($2,250) + 0.4($2,700) + 0.3($3,150) = $2,700. At Sales = $2,700, EBIT =
$270.
Debt/Assets
= ($652.50 + $300 + $270)/($1,350 + $270) = 75.5%.
Use of stock (Millions of dollars):
Probability 0.3 0.4 0.3
Sales $2,250.0 $2,700.0
$3,150.0
EBIT 225.0 270.0
315.0
Interest (45.0)
(45.0)
(45.0)
EBT 180.0 225.0
270.0
Taxes (40%) (72.0)
(90.0)
(108.0)
Net income $ 108.0 $ 135.0 $ 162.0
Earnings per share
(24.5 million shares)* $ 4.41 $ 5.51 $ 6.61
*Number of shares = ($270 million/$60) + 20 million
= 4.5
million + 20 million = 24.5 million.
EPSEquity =
(0.30)($4.41) + (0.40)($5.51) + (0.30)($6.61) = $5.51.
Debt/Assets
= ($652.50 + $300)/($1,350 + $270) = 58.8%
Under Debt financing the expected EPS is $5.78, the
standard deviation is $1.05, the CV is 0.18, and the debt ratio increases to
75.5%. (The debt ratio had been 70.6 percent.) Under Equity financing the
expected EPS is $5.51, the standard deviation is $0.85, the CV is 0.15, and the
debt ratio decreases to 58.8 percent. At this interest rate, debt financing
provides a higher expected EPS than equity financing; however, the debt ratio
is significantly higher under the debt financing situation as compared with the
equity financing situation. Because EPS is not significantly greater under debt
financing, but the risk is noticeably greater, equity financing should be
recommended.
