# fm16 5 - ROE goes up when most other companies’ ROEs...

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. Answers and Solutions: 16 - 5 16-8 a. Expected ROE for Firm C: ROE C = (0.1)(-5.0%) + (0.2)(5.0%) + (0.4)(15.0%) + (0.2)(25.0%) + (0.1)(35.0%) = 15.0%. Note: The distribution of ROE C is symmetrical. Thus, the answer to this problem could have been obtained by simple inspection. Standard deviation of ROE for Firm C (for convenience, we express returns in percentage form rather than in decimal form): %. 0 . 11 120 40 20 0 20 40 ) 20 ( 1 . 0 ) 10 ( 2 . 0 ) 0 ( 4 . 0 ) 10 ( 2 . 0 ) 20 ( 1 . 0 ) 0 . 15 0 . 35 ( 1 . 0 ) 0 . 15 0 . 25 ( 2 . 0 ) 0 . 15 0 . 15 ( 4 . 0 ) 0 . 15 0 . 5 ( 2 . 0 ) 0 . 15 0 . 5 ( 1 . 0 2 2 2 2 2 2 2 2 2 2 C = = + + + + = + + + + = + + + + = σ b. According to the standard deviations of ROE, Firm A is the least risky, while C is the most risky. However, this analysis does not take into account portfolio effects--if C’s
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Unformatted text preview: ROE goes up when most other companies’ ROEs decline (that is, its beta is negative), its apparent riskiness would be reduced. c. Firm A’s σ ROE = σ BEP = 5.5%. Therefore, Firm A uses no financial leverage and has no financial risk. Firm B and Firm C have σ ROE > σ BEP , and hence both use leverage. Firm C uses the most leverage because it has the highest σ ROE- σ BEP = measure of financial risk. However, Firm C’s stockholders also have the highest expected ROE....
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