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27.12.2007 09:23
Chapter 9. Solution to end-of-chapter spreadsheet problem Here is condensed balance sheet for Skye Computer Company (in thousands of dollars): CONDENSED BALANCE SHEET FOR SKYE COMPUTER COMPANY % Capital Structure % incl. curr. liab. % excl. current liab. Current assets Net fixed assets Total assets
2002 $2.000 $3.000 $5.000
Current liabilities Long-term debt Preferred stock Common stock Retained earnings Total common equity Total L & E
$900 $1.200 $250 $1.300 $1.350 $2.650 $5.000
18,0% 24,0% 5,0%
29,3% 6,1%
53,0% 100,0%
64,6% 100,0%
Skye Computer's earnings per share of common stock last year was $3.20; the stock sells for $55, and last year’s dividend was $2.10. A flotation cost of 10% would be required to issue new common stock. Skye’s preferred stock pays a dividend of $3.30 dividend per share, and new preferred could be sold at a price to net the company $30 per share. Security analysts are projecting that the common dividend will grow at a rate of 9% a year. The firm can also issue additional long- term debt at an interest rate (or before-tax cost) of 10%, and it marginal tax rate is 35%. The market risk premium is 5%, the risk free rate is 6%, and Skye’s beta is 1.516. In its cost of capital calculations, the company considers only long- term capital, hence it disregards current liabilities for this purpose. a. Calculate the cost of each capital component, i.e., the after-tax cost of debt, the cost of preferred stock, the cost of equity from retained earnings, and the cost of newly issued common stock. Use the DCF method. INPUT DATA EPS P0 Ppf Dpf D0 g B-T kd Skye's beta Market risk premium, kM - kRF Risk free rate, kRF
$3,20 $50,00 $30,00 $3,30 $2,10 9% 10% 1,516 5,0% 6,0%
Tax rate Flotation cost for common
35% 10%
Cost of debt B-T kd 10%
x
(1-T) 65%
=
A-T kd 6,50%
56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117
A Cost of preferred stock Dpf $3,30
/
B
C
Ppf $30,00
D
=
E
F
kpf 11,00%
Cost of common equity from retained earnings D1 $2,29
/
P0 $50,00
+
g 9%
=
ks 13,58%
g 9%
=
ke 14,09%
Cost of common equity from new common stock D0 * (1+g) $2,29
/
P0*(1-F) $45,00
+
b. Now calculate the cost of common equity from retained earnings using the CAPM method. ke ke
=
kRF
=
6,0%
+
b * MRP = 7,58%
=
13,58%
IMPORTANT NOTE: HERE THE CAPM AND THE DCF METHODS PRODUCE EXACTLY THE SAME ESTIMATED COST OF RETAINED EARNINGS. THAT OCCURRED BECAUSE WE USED A BETA IN THE PROBLEM THAT FORCED THE SAME RESULT. ORDINARILY, THE TWO METHODS WILL PRODUCE SOMEWHAT DIFFERENT RESULTS. c. What is the cost of new common stock, based on the CAPM? (Hint: Find the difference between k e and ks as determined by the DCF method, and add that differential to the CAPM value for ks. ke
=
ks 13,58%
+ +
Differential 0,51%
=
14,09%
Again, we would not normally find the CAPM and DCF methods to yield identical results.
d. If Skye Computer continues to use the same capital structure, what is the WACC assuming (1) uses only retained earnings for equity and (2) assuming that it expands so rapidly that it must issue new common stock? WACC using retained earnings wd wpf ws
29,3% 6,1% 64,6% 100,0% wd * A-T kd + 1,90%
wpf * kpf + 0,67%
Note that we used the capital structure based on long-term capital as calculated above.
ws * ks 8,78%
=
WACC 11,35%
ws * ke 9,10%
=
WACC 11,68%
WACC using new common stock wd wpf ws
29,3% 6,1% 64,6% 100,0% wd * A-T kd + 1,90%
wpf * kpf + 0,67%
Skye's WACC will be 11.35% so long as it finances with debt, preferred stock, and common equity raised as retained earnings. If it expands so rapidly that it uses up all of its retained earnings and must issue new common stock with a cost of 14.09%, then its WACC will increase to 11.68%
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