Two firms exist that are identical in all respects except for the risk of their
ID: 2782576 • Letter: T
Question
Two firms exist that are identical in all respects except for the risk of their assets. Both firms have assets worth $1,000,000, and have issued zero coupon bonds with a face value of $500,000. The standard deviation of the return on these firm 1’s assets is 30%, and the standard deviation of the return on firm 2’s assets is 50%. Assume that both firms will be liquidated one year from today and that the rate of interest is 5%.
A. What is the fair market value for the bonds issued by firm 1? What is the dollar value of its limited liability put option? What is the yield to maturity on its bonds?
Explanation / Answer
A.
Fair market value of the bond = $500,000/(1+5%) = $476190.48
Yield to Maturity = (Face Value / Current Price of Bond) ^ (1 / Years to Maturity) - 1 = ($500,000/$476190.48)^(1/1) - 1 = 0.05 = 5%
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