Transcript Chapter 9 – Index of Sample Problems
Chapter
15
•
Cost of Capital
McGraw-Hill/Irwin Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.
Chapter 15 – Index of Sample Problems • • • • • •
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)
R E R f
E
(
R M
R f
)
•
The cost of capital dependents primarily on the use of the funds, not the source.
Cost of equity
•
Dividend growth model
R E
D
1
P
0
g
•
SML
R E R f
E
(
R M
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 R E D 1 g P 0 D 0 ( 1 g ) g P 0 $ 1 .
20 ( 1 .
03 ) .
$ 20 .
40 0606 .
03 .
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?
$1.22
$1.10
$ .90
$ .83
$ .75
5: Cost of equity ($1.22 - $1.10) $1.10 = .10909
($1.10 - $.90) $.90 = .22222
($.90 - $.83) $.83 = .08434
($.83 - $.75) $.75 = .10667
--- -- Total .52232
Average growth rate .52232
4 .
13058 13 .
06 %
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 .
035 1 .
4 .
08 .
035 .
112 R f ) .
147 14 .
7 %
Cost of Preferred stock
•
Fixed dividend payment
R P
D P
0
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 R P D P 0 .
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 13
969.08
N I/Y 80 1,000 PV PMT FV Solve for 8.4
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 /2
1,012.30
N I/Y 90/2 1,000 PV PMT FV Solve for 8.85
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
WACC E E V D V R D WACC V E E P R p V V D R D T C
)
T C
)
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) Preferred stock (P) Debt (D) Totals (V) 720,000 50,000 $32.10
$45.00
$23,112,000 $ 2,250,000 $44,962,000 51.4% 5.0% 20,000 $1,000 .98
$19,600,000 43.6% 100.0%
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 1.00 1.65 = .3939 = 39.39% 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 1.00 1.45 = .31
1.45 = .69
Total = 1.00
WACC [.
E V 69 R E .
094 ] D V [.
R 31 D ( 1 .
08 T c ( 1 ) .
34 )] .
06486 .
016368 .
081228 8 .
12 %
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 WACC E R V [.
40 E .
12 ] P R V [.
15 P D V .
09 ] R D [.
45 ( 1 .
08 T c ( 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
= 1.00
= 1.60
.60 1.60 = .375
1.00 1.60 = .625
Total = 1.000
Average flotation cost (.625
.12) (.375
.06) .075
.0225
.0975
9.75% Cost , including flotation $5,000,000 1 .0975
$ 5 , 000 , 000 .
9025 $ 5 , 540 , 166 (rounded to whole dollars)
Chapter
15
•
End of Chapter 15
McGraw-Hill/Irwin Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.