Question

Investors are evaluating two 6-year bonds at time t in an emerging financial crisis setting where
there is a strong likelihood of default. Assume the following values for the expected probability
of default (z) of the two bonds, issued respectively by companies A and B.

t+1 t+2 t+3 t+4 t+5 t+6
A 0.1 0.2 0.3 0.3 0.4 0.3
B 0 0.2 0.6 0.7 0.3 0.25

a. Assume both bonds are 6-year, 8% coupon, $1000 face value coupon bonds, each selling for
$1000. Calculate the yields on the two bonds. Which is higher?

b. Now assume a setting where all future interest rates are exogenously fixed at 6%; the prices
of the bond are now to be determined. What are the prices of bond A and B? Which is
higher?

c. With respect to (b) above, and taking both present value streams together, does there exist
some value for i that would make the price of Bond A equal to the price of Bond B?

Answer 1

a. we solve using the formula for the full yield of coupon bonds

$r=\frac{\frac{N-P}{n}+C}{\frac{N+P}{2}}=\frac{\frac{1000-1000}{6}+80}{\frac{1000+1000}{2}}=0.08$

the probability of default is a decrease in the yield, so reduce the resulting yield by this probability

$0.08-0.08\times0.3=0.056$

$0.08-0.08\times0.25=0.06$

the greater the probability of default, the lower the yield

B is higher

b. we will also find the price from the formula of the full yield of coupon bonds

$0.06=\frac{\frac{1000-P}{6}+80}{\frac{1000+P}{2}}$

P=800

P(B)=800

c.

it can be any interest rate if the bonds are equal in all other parameters: price, maturity, par value, coupon rate and probability of default, etc.