Question

Several years ago, Castles in the sand Inc. issued bonds at face value of 1,000 at a yield to maturity of 8.6%. Now, with 7 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 15%. What is the price of the bond now? (Assume semi-annual coupon payments)

Suppose that investors believe that Castles can make good on the promise coupon payments but that the company will go bankrupt when the bond matures and the principle comes due. The expectation is that investors will receive only 80% of face value at maturity. If they buy the bond today, what yield to maturity do they expect to receive?

Answer 1

Solution:

Balance maturity = 7 years, 14 semiannual periods

Face value of bond = $1,000

Current YTM = 15% annual, 7.50% semi annual

Coupon rate = YTM at the time issue = 8.60%

Current price of bond = ($1000*8.6%*6/12) * cumulative PV factor at 7.50% for 14 period + $1,000 * PV factor at 7.50% for 14th period

= $43 * 8.48915 + $1,000*0.363313 = $728.35

Hence current price of bond is $728.35

Expected receiving at maturity = $1000*80% = $800

At YTM, PV of cash flows will be equal to current price of bond.

Lets calculate PV of cash flows at 12% YTM:

= $43*cumulative PV factor at 6% for 14 period + $800*PV factor at 6% for 14th period

= $43*9.294984 + $800*0.442301 = $753.53

PV of cash flows at 13% YTM:

= $43*cumulative PV factor at 6.50% for 14 period + $800*PV factor at 6.50% for 14th period

= $43*9.013842 + $800*0.4141 = $718.88

Semi annual YTM = 6% + ($753.53 - $728.35) / ($753.53 - $718.88) * 0.5

= 6.36%

Annual expected YTM = 6.36*2 = 12.72%