Capital Structure and Leverage - Solutions9

Capital Structure and Leverage - Solutions9 - 46. Assume...

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Old Exam Questions - Capital Structure and Leverage - Solutions Page 45 of 59 Pages 46. Assume that Firm A is an all-equity firm with total assets of $1,000 and the following distribution of EBIT for the coming year: Economy Firm A (Unlevered) Bad Average Good Probability 30% 40% 30% EBIT $150.00 $180.00 $210.00 Interest $0.00 $0.00 $0.00 EBT $150.00 $180.00 $210.00 Taxes (40%) -$60.00 -$72.00 -$84.00 Net Income $90.00 $108.00 $126.00 BEP 15.00% 18.00% 21.00% ROA 9.00% 10.80% 12.60% ROE 9.00% 10.80% 12.60% As you can calculate, the variance of the ROE distribution is 0.01944 percent (standard deviation of 1.394274 percent). Now assume that the firm plans to issue $300 of debt, at an interest rate of 8 percent, and use the proceeds to repurchase equity (you may ignore potential impacts on price and assume that the firm will then have $700 of equity). As you will be able to calculate, the variance of the resulting ROE distribution will be 0.0396735 percent (0.0396735% = 0.000396735). Given this information, and using the concept of Z-scores, determine the probability that the actual observed ROE will be less than 10.0 percent. A. 5.29% * B. 4.55% C. 5.66% D. 4.92% E. 6.03% The new distribution will look like the following: Economy Firm A (Levered) Bad Average Good Probability 30% 40% 30% EBIT $150.00 $180.00 $210.00 Interest -$24.00 -$24.00 -$24.00 EBT $126.00 $156.00 $186.00 Taxes (40%) -$50.40 -$62.40 -$74.40 Net Income $75.60 $93.60 $111.60 BEP 15.00% 18.00% 21.00% ROA 7.56% 9.36% 11.16% ROE 10.80% 13.37% 15.94%
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Old Exam Questions - Capital Structure and Leverage - Solutions Page 46 of 59 Pages Expected ROE = (10.8%)(.30) + (13.37%)(.40) + (15.94%)(.30) Expected ROE = 3.24% + 5.35% + 4.78% = 13.37% Alternatively, since the values for ROE and the probabilities are symmetrical around the middle value, we know that the expected ROE must be 13.37%. σ 2 ROE = (.108 - .1337) 2 (.30) + (.1337 - .1337) 2 (.40) + (.1594 - .1337) 2 (.30) σ 2 ROE = 0.000198367 + 0.00 + 0.000198367 = 0.000396735 σ ROE = (0.000396735) 1/2 = 0.0199182 Z = (.10 - .1337) / .0199182 = -1.69 Z(-1.69) = Z(1.69) = .4545 = 45.45% Probability of Less than 10.0% = 50.00% - 45.45% = 4.55%
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This note was uploaded on 07/13/2011 for the course FIN 4414 taught by Professor Staff during the Spring '08 term at University of Florida.

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Capital Structure and Leverage - Solutions9 - 46. Assume...

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