Question

Grummon Corporation has issued​ zero-coupon corporate bonds with a​ five-year maturity​ (assume $ 100 face value​ bond). Investors believe there is a 20 %    chance that Grummon will default on these bonds. If Grummon does​ default, investors expect to receive only 50 cents per dollar they are owed. If investors require a 6 % expected return on their investment in these​ bonds, what will be the

a. price of these​ bonds?

b. yield to maturity on these​ bonds? ​Note: Assume annual compounding.

Answer 1

Face value (FV)= 100

chance of default (d) = 0.2 , When defaulted , return  on investment = 50 cents = $0.5

chances of not doing default, = 0.8. Expected rate of return (r) when no default = 6%

n = number of years = 5

Price of these bonds = FV[(1-d)+(d)*0.5 ]/(1+r)^n

=100[(1-0.2)+(0.2*0.5)]/1.06^5

= 67.25

YTM = [(FV/Bond price)^1/n] - 1

= [(100/67.25)^1/5] - 1

= 8.26%