Chapter 13: Capital Structure and Leverage
70.
You work for the CEO of a new company that plans to manufacture and sell a new product, a watch that
has an
embedded TV set and a magnifying glass crystal. The issue now is how to finance the company, with
only equity or
with a mix of debt and equity. Expected operating income is $400,000. Other data for the
firm are shown below.
How much higher or lower will the firm‘s expected ROE be if it uses some debt
rather than all equity, i.e., what is
ROEL − ROEU?
0% Debt, U
60% Debt, L
Oper. income (EBIT)
$400,000
$400,000
Required investment
$2,500,000
$2,500,000
% Debt
0.0%
60.0%
$ of Debt
$0.00
$1,500,000
$ of Common equity
$2,500,000
$1,000,000
Interest rate
NA
10.00%
Tax rate
35%
35%
a. 5.85%
b. 6.14%
c. 6.45%
d. 6.77%
e. 7.11%
% Debt
$ of Debt
$1,500,000
$ of Common equity
$1,000,000
Interest rate
Tax rate
Operating income (EBIT)
Interest
Taxable income
71.
You work for the CEO of a new company that plans to manufacture and sell a new type of laptop computer.
The
issue now is how to finance the company, with only equity or with a mix of debt and equity. Expected
operating
income is $600,000. Other data for the firm are shown below. How much higher or lower will the
firm‘s expected
EPS be if it uses some debt rather than only equity, i.e., what is EPSL − EPSU?
60% Debt, L
Oper. income (EBIT)
$600,000
Required investment
$2,500,000
% Debt
60.0%
$ of Debt
$1,500,000
$ of Common equity
$1,000,000
Shares issued, $10/share
100,000
Interest rate
10.00%
Tax rate
35%
a. $1.00
b. $1.11
c. $1.23
d. $1.37
e. $1.50
Required investment
% Debt
$ of Debt
$ of Common equity
Shares issued at $10/share
Interest rate
Tax rate
Operating income (EBIT)
$600,000
Interest
0
Taxable income
$450,000
V
F
72.
Confu Inc. expects to have the following data during the coming year. What is the firm‘s expected ROE?
Capital
$200,000
Interest rate
8%
Debt/Capital, book value
65%
Tax rate
40%
EBIT
$25,000
a. 12.51%
b. 13.14%
c. 13.80%
d. 14.49%
e. 15.21%
73.
Senate Inc. is considering two alternative methods for producing playing cards. Method 1 involves using a
machine
with a fixed cost (mainly depreciation) of $12,000 and variable costs of $1.00 per deck of cards.
Method 2 would use
a less expensive machine with a fixed cost of only $5,000, but it would require a
variable cost of $1.50 per deck. The
sales price per deck would be the same under each method. At what
unit output level would the two methods
provide the same operating income (EBIT)?
a. 12,600
b. 14,000
c. 15,400
d. 16,940
e. 18,634
74.
A group of venture investors is considering putting money into Lemma Books, which wants to produce a
new reader
for electronic books. The variable cost per unit is estimated at $250, the sales price would be
set at twice the
VC/unit, or $500, and fixed costs are estimated at $750,000. The investors will put up the
funds if the project is likely
to have an operating income of $500,000 or more. What sales volume would
be required in order to meet the
minimum profit goal? (Hint: Use the break-even formula, but include the
required profit in the numerator.)
a. 4,513
b. 4,750
c. 5,000
d. 5,250
e. 5,513
75.
El Capitan Foods has a capital structure of 40% debt and 60% equity, its tax rate is 35%, and its beta
(leveraged) is 1.25. Based on the Hamada equation, what would the firm‘s beta be if it used no debt, i.e.,
what is its unlevered beta,
bU?
a. 0.71
b. 0.75
c. 0.79
d. 0.83
e. 0.87
76.
Gator Fabrics Inc. currently has zero debt (i.e., wd = 0). It is a zero growth company, and additional firm
data are
shown below. Now the company is considering using some debt, moving to the new capital
structure indicated
below. The money raised would be used to repurchase stock at the current price. It is
estimated that the increase in
risk resulting from the additional leverage would cause the required rate of
return on equity to rise somewhat, as
indicated below. If this plan were carried out, by how much would
the WACC change, i.e., what is WACCOld −
WACCNew?
wd 55% Orig. cost of equity, rs 10.0%
wc 45% New cost of equity = rs 11.0%
Interest rate new = rd 7.0% Tax rate 40%
a. 2.74%
b. 3.01%
c. 3.32%
d. 3.65%
e. 4.01%
77.
As a consultant to First Responder Inc., you have obtained the following data (dollars in millions). The
company
plans to pay out all of its earnings as dividends, hence g = 0. Also, no net new investment in
operating capital is
needed because growth is zero. The CFO believes that a move from zero debt to 20.0%
debt would cause the cost
of equity to increase from 10.0% to 12.0%, and the interest rate on the new debt
would be 8.0%. What would the
firm’s total market value be if it makes this change? Hints: Find the FCF,
which is equal to NOPAT = EBIT(1 − T)
because no new operating capital is needed, and then divide by
(WACC − g).
Oper. income (EBIT) $800 Tax rate 40.0%
New cost of equity (rs) 12.00% New wd 20.0%
Interest rate (rd) 8.00%
a. $2,982
b. $3,314
c. $3,682
d. $4,091
e. $4,545
78.
You plan to invest in one of two home delivery pizza companies, High and Low, that were recently
founded and are
about to commence operations. They are identical except for their use of debt (wd) and the
interest rates on their
debt—High uses more debt and thus must pay a higher interest rate. Based on the
data given below, how much
higher or lower will High’s expected EPS be versus that of Low, i.e., what is
EPSHigh − EPSLow?
Applicable to Both Firms Firm High’s Data Firm Low‘s Data
Capital
$3,000,000
wd
70%
wd
20%
EBIT
$500,000
Shares
90,000
Shares
240,000
Tax rate
35%
Int. rate
12%
Int. rate
10%
a. $0.49
b. $0.54
c. $0.60
d. $0.66
e. $0.73
79.
Firms HD and LD are identical except for their use of debt and the interest rates they pay HD has more
debt and
thus must pay a higher interest rate. Based on the data given below, how much higher or lower
will HD’s ROE be
versus that of LD, i.e., what is ROEHD − ROELD?
Applicable to Both Firms Firm HD’s Data Firm LD’s Data
Capital
$3,000,000
wd
70%
wd
20%
EBIT
$500,000
Int. rate
12%
Int. rate
10%
Tax rate
35%
a. 5.41%
b. 5.69%
c. 5.99%
d. 6.29%
e. 6.61%
80.
Firm A is very aggressive in its use of debt to leverage up its earnings for common stockholders, whereas
Firm NA
is not aggressive and uses no debt. The two firms’ operations are identical they have the same
total investor-supplied capital, sales, operating costs, and EBIT. Thus, they differ only in their use of
financial leverage (wd).
Based on the following data, how much higher or lower is A’s ROE than that of
NA, i.e., what is ROEA − ROENA?
Applicable to Both Firms Firm A’s Data Firm NA’s Data
Capital
$150,000
wd
50%
wd
0%
EBIT
$40,000
Int. rate
12%
Int. rate
10%
Tax rate
35%
a. 8.60%
b. 9.06%
c. 9.53%
d. 10.01%
e. 10.51%
81.
Your firm’s debt ratio is only 5.00%, but the new CFO thinks that more debt should be employed. She
wants to sell
bonds and use the proceeds to buy back and retire common shares so the percentage of
common equity in the
capital structure (wc) = 1 − wd. Other things held constant, and based on the data
below, if the firm increases the
percentage of debt in its capital structure (wd) to 60.0%, by how much
would the ROE change, i.e., what is
ROENew − ROEOld?
Operating Data Other Data
Capital $150,000 Old wd 5%
ROIC = EBIT(1 − T)/Capital 13.00% Old interest rate 10%
Tax rate 35% New wd 60%
New interest rate 12%
a. 6.73%
b. 7.09%
c. 7.46%
d. 7.83%
e. 8.22%
82.
You have been hired by a new firm that is just being started. The CFO wants to finance with 60% debt, but
the
president thinks it would be better to hold the percentage of debt in the capital structure (wd) to only
10%. Other
things held constant, and based on the data below, if the firm uses more debt, by how much
would the ROE change,
i.e., what is ROENew − ROEOld?
Operating Data Other Data
Capital $4,000 Higher wd 60%
ROIC = EBIT(1 − T)/Capital 13.00% Higher interest rate 13%
Tax rate 35% Lower wd 10%
Lower interest rate 9%
a. 5.44%
b. 5.73%
c. 6.03%
d. 6.33%
e. 6.65%
83.
Your girlfriend plans to start a new company to make a new type of cat litter. Her father will finance the
operation,
but she will have to pay him back. You are helping her, and the issue now is how to finance the
company, with
equity only or with a mix of debt and equity. The price per unit will be $10.00 regardless of
how the firm is financed.
The expected fixed and variable operating costs, along with other information, are
shown below. How much higher
or lower will the firm‘s expected EPS be if it uses some debt rather than
only equity, i.e., what is EPSL − EPSU?
0% Debt, U
60% Debt,
Expected unit sales
225,000
225,000
Price per unit
$10.00
$10.00
Fixed costs
$1,000,000
$1,000,000
Variable cost/unit
$3.50
$3.50
Required investment
$2,500,000
$2,500,000
Shares issued at $10/share
250,000
100,000
% Debt
0.00%
60.00%
Debt, $
$0
$1,500,000
Equity, $
$2,500,000
$1,000,000
Interest rate
NA
10.00%
Tax rate
35.00%
35.00%
a. $0.54
b. $0.60
c. $0.67
d. $0.75
e. $0.83
84.
Southeast U’s campus book store sells course packs for $15.00 each, the variable cost per pack is $11.00,
fixed
costs for this operation are $300,000, and annual sales are 100,000 packs. The unit variable cost
consists of a $4.00
royalty payment, VR, per pack to professors plus other variable costs of VO = $7.00.
The royalty payment is
negotiable. The book store‘s directors believe that the store should earn a profit
margin of 10% on sales, and they
want the store’s managers to pay a royalty rate that will produce that
profit margin. What royalty per pack would
permit the store to earn a 10% profit margin on course packs,
other things held constant?
a. $2.55
b. $2.84
c. $3.15
d. $3.50
e. $3.85
85.
Dye Industries currently uses no debt, but its new CFO is considering changing the capital structure to
40.0% debt
(wd) by issuing bonds and using the proceeds to repurchase and retire common shares so the
percentage of common
equity in the capital structure (wc) = 1 − wd. Given the data shown below, by how
much would this recapitalization
change the firm‘s cost of equity, i.e., what is rL − rU?
Risk-free rate, rRF
6.00%
Tax rate, T
40%
Market risk premium, RPM
4.00%
Current wd
0%
Current beta, bU
1.15
Target wd
40%
a. 1.66%
b. 1.84%
c. 2.02%
d. 2.23%
e. 2.45%
Target D/E = wd/(1 − wd)
86.
Dyson Inc. currently finances with 20.0% debt (i.e., wd = 20%), but its new CFO is considering changing
the capital
structure so wd = 60.0% by issuing additional bonds and using the proceeds to repurchase and
retire common shares
so the percentage of common equity in the capital structure (wc) = 1 − wd. Given the
data shown below, by how
much would this recapitalization change the firm‘s cost of equity? (Hint: You
must unlever the current beta and then
use the unlevered beta to solve the problem.)
Risk-free rate, rRF
5.00%
Tax rate, T
40%
Market risk premium, RPM
6.00%
Current wd
20%
Current beta, bL1
1.15
Target wd
60%
a. 4.05%
b. 4.50%
c. 4.95%
d. 5.45%
e. 5.99%
87.
Monroe Inc. is an all-equity firm with 500,000 shares outstanding. It has $2,000,000 of EBIT, and EBIT is
expected
to remain constant in the future. The company pays out all of its earnings, so earnings per share
(EPS) equal
dividends per shares (DPS), and its tax rate is 40%. The company is considering issuing
$5,000,000 of 9.00% bonds
and using the proceeds to repurchase stock. The risk-free rate is 4.5%, the
market risk premium is 5.0%, and the
firm’s beta is currently 0.90. However, the CFO believes the beta
would rise to 1.10 if the recapitalization occurs.
Assuming the shares could be repurchased at the price that
existed prior to the recapitalization, what would the price
per share be following the recapitalization?
(Hint: P0 = EPS/rs because EPS = DPS.)
a. $28.27
b. $29.76
c. $31.25
d. $32.81
e. $34.45
Expected unit sales
Price per phone
$250.00
Fixed operating costs
Variable operating cost/unit
Required investment
% Debt
Debt, $
Equity, $
Interest rate
Fixed costs
Variable costs
Operating income
Interest
0
Taxable income
88.
You were hired as the CFO of a new company that was founded by three professors at your university.
The
company plans to manufacture and sell a new product, a cell phone that can be worn like a wrist
watch. The issue
now is how to finance the company, with equity only or with a mix of debt and equity.
The price per phone will be $250.00 regardless of how the firm is financed. The expected fixed and
variable operating costs, along with other
data, are shown below. How much higher or lower will the
firm’s expected ROE be if it uses 60% debt rather than
only equity, i.e., what is ROEL − ROEU?
0% Debt, U
60% Debt,
Expected unit sales (Q)
28,500
28,500
Price per phone (P)
$250.00
$250.00
Fixed costs (F)
$1,000,000
$1,000,000
Variable cost/unit (V)
$200.00
$200.00
Required investment
$2,500,000
$2,500,000
% Debt
0.00%
60.00%
Debt, $
$0
$1,500,000
Equity, $
$2,500,000
$1,000,000
Interest rate
NA
10.00%
Tax rate
35.00%
35.00%
a. 5.68%
b. 5.94%
c. 6.22%
d. 6.52%
e. 6.83%