Question

A firm can be worth $90 or $310 with equal probability. The firmʹs debt consists of a zero -coupon bond with a face value of $180 that matures at the end of one year. Assume risk neutrality and a cost of capital of 11%. What will the bondholders pay for this debt? 143 200 162 180

Answer 1

Zero Coupon Bonds are those bonds on which investors are not paid any interest but are entitled only to
repayment of principal sum on the maturity period .

Value of Zero Coupon Bond =

where, Face Value = 180

n = Year to Maturity (1 Year)

Yield = Cost of Capital (11%)

= 180/(1+.11)^1

= 162

Therefore, the bondholders will pay $162 for this debt.

Note

$90 or $310 with equal probability has been provided for the value of firm. If the same would have been given for the price of bond, then it would have been considered for determining the value of bond. No Information for equity has been given.

If the above probability has to be considered for value of bond, Maturity value will be (90*0.50 + 310*0.50) = $ 200.

Value of Zero Coupon Bond will be then computed as =

= 200/(1+.11)^1

= 180

Therefore, the bondholders will pay $180 for this debt.