Question

It is the heart of the financial crisis and Lehman brothers are trying to raise money. They issue a zero-coupon bond with a face value of $1000 and a term of 1 year. However, you expect that Lehman will go bankrupt with a probability 75%, in which case you get $0 in one year rather than the full $1000. Only with probability 25% do you receive the full $1000. If Lehman has an opportunity cost of capital of 20%, how much are you willing to pay for the bond? What is the yield-to-maturity of the bond?

Answer 1

Solution:

a)Maturity value=Probability*Cash flow

=0.75*$0+0.25*$1000

=$250

Cost of capita=20% or 0.20

Price of zero coupon bond=Maturity value/(1+cost of capital)^years to maturity

=$250/(1+0.20)^1

=$223.21

b)Yield to maturity of zero coupon bond:

Yield to maturity=(Face Value/Current price)^1/years to maturity-1

=($250/$223.21)^1/1-1

=12%