Question

a. Several years ago, Castles in the Sand Inc. issued bonds at face value of $1,000 at a yield to maturity of 6%. Now, with 6 years left until the maturity of the bonds, the company has run into hard times and the yield to maturity on the bonds has increased to 11%. What is the price of the bond now? (Assume semiannual coupon payments.)

b. Suppose that investors believe that Castles can make good on the promised coupon payments but that the company will go bankrupt when the bond matures and the principal comes due. The expectation is that investors will receive only 85% of face value at maturity. If they buy the bond today, what yield to maturity do they expect to receive?

Answer 1

(a) Since the bond is issued at face value and YTM is 6% the interest rate is 6%. Let x be the current market price.

Interest on bonds = 1000*6% = $ 60 annually

YTM = Interest +( Discount or premium/ Years left)

( Face value + Market value)/2

0.11 = 60 + ( 1000- x /6) => x = 774.44

(1000+x)/2

Current price of bond is $774.44

(b) Since expected realised amount is 85% it is $850.

YTM = 60 + (850-774.44) / 6 => YTM = 8.93%

( 850+774.44)/ 2

Expected YTM is 8.93%