Chapter15
•Cost of Capital
McGraw-Hill/Irwin
Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.
Chapter 15 – Index of Sample
Problems
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Slide # 02 - 07
Slide # 08 - 09
Slide # 10 - 15
Slide # 16 - 19
Slide # 20 - 23
Slide # 24 - 27
Cost of equity
Cost of preferred
Cost of debt
Portfolio weights
Weighted average cost of capital (WACC)
Flotation costs
Required return, appropriate
discount rate, cost of capital
• Net Present Value
• Security Market Line
(SML)
RE R f E ( RM R f )
• The cost of capital dependents primarily on
the use of the funds, not the source.
Cost of equity
• Dividend growth model
RE
D1
g
P0
• SML
RE R f E ( RM R f )
2: Cost of equity
Isabelle Thomas and Son, Inc. just paid the annual dividend on
their common stock in the amount of $1.20 per share. The
company expects to maintain a constant 3% rate of growth in their
dividend payments. Currently, the stock is selling for $20.40 a
share.
What is the cost of equity for Isabelle Thomas and Son, Inc.?
3: Cost of equity
D1
RE
g
P0
D 0 (1 g )
g
P0
$1.20 (1 .03)
.03
$20.40
.0606 .03
.0906
9.06%
4: Cost of equity
The Curtis Plane Co. has paid $1.10, $.90, $.83 and $.75 in annual
dividends over the past four years, starting with the latest year
first. This year the company is paying a dividend of $1.22 a share.
What is the average growth rate of the dividends?
5: Cost of equity
$1.22
($1.22 - $1.10) $1.10 = .10909
$1.10
($1.10 - $.90) $.90 = .22222
$ .90
($.90 - $.83) $.83 = .08434
$ .83
($.83 - $.75) $.75 = .10667
$ .75
--- --Total .52232
Average growth rate
.52232
.13058 13.06%
4
6: Cost of equity
The stock of Neal & Co. has a beta of 1.40. The risk-free rate of
return is 3.5% and the risk premium is 8%.
What is the expected rate of return on Neal & Co. stock?
7: Cost of equity
R E R f E (R m R f )
.035 1.4 .08
.035 .112
.147
14.7%
Cost of Preferred stock
• Fixed dividend payment
D
RP
P0
8: Cost of preferred
The 7% preferred stock of Anderson, Inc. is selling for $72.92.
What is the cost of preferred stock?
9: Cost of preferred
D
R P
P0
.07 $100
$72.92
$7.00
$72.92
.0960
9.60%
Cost of debt
• The yield of issuing bond
10: Cost of debt
The bonds of TA, Inc. have a face value of $1,000 per bond, mature
in 13 years, and pay 8% interest annually. These bonds currently
sell for $969.08.
What is the pre-tax cost of debt?
11: Cost of debt
Enter
Solve for
13
N
I/Y
8.4
969.08
PV
80
PMT
1,000
FV
12: Cost of debt
Four years ago, JE, Inc. issued twenty-year bonds that have a face
value of $1,000 per bond and pay interest semi-annually. These
bonds currently sell for $1,012.30 and have a 9% coupon.
What is the pre-tax cost of debt?
13: Cost of debt
Enter
(20-4)2
N
Solve for
/2 1,012.30
I/Y
PV
8.85
90/2
PMT
1,000
FV
14: Cost of debt
The pre-tax cost of debt for Morrison and Sons is 8.78%. The tax
rate is 35%.
What is the after-tax cost of debt for Morrison and Sons?
15: Cost of debt
After - tax cost of debt .0878 (1 - .35)
.0878 .65
.05707
5.71%
Weighted Average Cost of Capital
(WACC)
• V=E+D
• TC=corporate tax rate
E
D
WACC RE RD (1 TC )
V
V
E
P
D
WACC RE Rp RD (1 TC )
V
V
V
16: Portfolio weights
Wilson and Ruth, Inc. has 720,000 shares of common stock
outstanding at a market price of $32.10 per share. They also have
50,000 shares of preferred stock outstanding at a price of $45 a
share. The company has 20,000 bonds outstanding that are
currently selling at 98% of face value and mature in 9 years. The
bonds carry a 6% coupon and pay interest annually. The bonds
have a face value of $1,000. The tax rate is 34%.
What are the portfolio weights that should be used in computing
the weighted average cost of capital?
17: Portfolio weights
Common stock
(E)
720,000 $32.10
$23,112,000
51.4%
Preferred stock
(P)
50,000 $45.00
$ 2,250,000
5.0%
20,000 $1,000 .98
$19,600,000
43.6%
$44,962,000
100.0%
Debt
(D)
Totals
(V)
18: Portfolio weights
The Winston James Co. has a debt-equity ratio of .65. The
company has no preferred stock outstanding.
What is the portfolio weight of the debt?
19: Portfolio weights
Debt/equity = .65
Debt = .65
Equity = 1.00
Value = 1.65
Weights
.65 1.65 = .3939 = 39.39%
1.00 1.65 = .6061 = 60.61%
Total = 1.0000 100.00%
20: Weighted average cost of capital
A firm has a debt-equity ratio of .45 and a tax rate of 34%. The cost
of equity is 9.4% and the pre-tax cost of debt is 8%.
What is the weighted average cost of capital?
21: Weighted average cost of capital
Debt
Equity
Value
= .45
= 1.00
= 1.45
.45 1.45 = .31
1.00 1.45 = .69
Total
= 1.00
E
D
R E R D (1 Tc )
V
V
[.69 .094] [.31 .08 (1 .34)]
.06486 .016368
.081228
8.12%
WACC
22: Weighted average cost of capital
Merilee, Inc. maintains a capital structure of 40% equity, 15%
preferred stock and 45% debt. The cost of equity is 12% and the
cost of preferred is 9%. The pre-tax cost of debt is 8%. The tax rate
is 35%.
What is the weighted average cost of capital?
23: Weighted average cost of capital
E
P
D
WACC R E R P R D (1 Tc )
V
V
V
[.40 .12] [.15 .09] [.45 .08 (1 .35)]
.048 .0135 .0234
.0849
8.49%
24: Flotation costs
The Silow Co. maintains weights of 55% equity, 10% preferred
stock and 35% debt. The flotation costs are 8% for equity, 9% for
preferred and 4% for debt.
What is the weighted average flotation cost?
25: Flotation costs
Average flotation cost (.55 .08) (.10 .09) (.35 .04)
.044 .009 .014
.067
6.7%
26: Flotation costs
Your company maintains a debt/equity ratio of .60. The flotation
cost for new equity is 12% and for debt it is 6%. The firm is
considering a new project which will require $5 million in external
funding.
What is the initial cost of the project including the flotation costs?
27: Flotation costs
Debt
Equity
Value
.60 1.60 = .375
1.00 1.60 = .625
Total
= 1.000
= .60
= 1.00
= 1.60
Average flotation cost (.625 .12) (.375 .06)
.075 .0225
.0975
9.75%
$5,000,000
1 - .0975
$5,000,000
.9025
$5,540,166 (rounded to whole dollars)
Cost , including flotation
Chapter15
•End of Chapter 15
McGraw-Hill/Irwin
Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.
