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A zero-coupon bond has a beta of 0.7 and promises to pay $1000 next year with...

A zero-coupon bond has a beta of 0.7 and promises to pay $1000 next year with a probability of 90%. If the bond defaults, it will pay nothing. One -year Treasury securities are yielding 1.7%, and the equity premium is 5%. What is the promised rate of return on this bond? Round your answer to the nearest tenth of a percent.

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Answer #1

Using CAPM

Expected Return = Rf + Beta* Equity Premium

Expected Return = 1.7% + 0.7*5% = 5.2%

Expected Cash Flow after 1 year = Prob of Payment * Payoff + Prob of default * Payoff = 0.9*1000 + 0.1*0 = $900

Market value of Bond today = Expected Cash Flow after 1 year / (1+expected return) = 900 / 1.052 = $855.51

Promised rate of return = (Promised return - expected return ) / Expected Return = (1000-855.51)/855.51 =16.89%

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