Question

The term structure of interest rates is flat at 9.5 %, but rates could change immediately to 11.5 % or 7.5 % with probability of 0.72 and 0.28 , respectively, and stay at that level forever. You purchase a callable bond with 14 years to maturity and 9.5 % coupon paid annually. The callable bond can be called at $ 130 with a call protection period of 0 years.

Answer 1

Period remaining till maturity = 14 years
Coupon amount = 100*9.5% = 9.5 paid annually
­

Alternative 1 : Interest Rate changes to 11.5%

Value of Bond = Present Value of Coupons + PV of Principal Amount
                        = [PVAF (11.5%,14) * 9.5] + [PVIF (11.5%,14) * 100]
                         = (6.8013 * 9.5) + (0.2178 * 100)
                        = 64.61 + 21.78
                         = 86.39

Present Value Factor have been calculated as = (1/1+r)n

Where

r= Required rate of Return (Discount rate)
n= No of Periods

PVAF (11.5%,14) is calculated by adding the PV Factor of 11.5% for 14 years

Alternative 2 : Interest Rate changes to 7.5%

Value of Bond = Present Value of Coupons + PV of Principal Amount
                        = [PVAF (7.5%,14) * 9.5] + [PVIF (7.5%,14) * 100]
                         = (8.4892 * 9.5) + (0.3633 * 100)
                        = 80.65 + 36.33
                         = 116.98

Present Value Factor have been calculated as = (1/1+r)n

Where

r= Required rate of Return (Discount rate)
n= No of Periods

PVAF (7.5%,14) is calculated by adding the PV Factor of 7.5% for 14 years

This is a callable bond. But despite the interest rate falling the callable price is $130 which is more than the value of bond as calculated above. Therefore the bond will not be called.

Value of Bond = (Value of bond given Alternate 1 * Probability of Alternate 1) + (Value of bond given Alternate 2 * Probability of Alternate 2)

                      = (86.39 * 0.72) + (116.98 * 0.28)
                      = 62.20 + 32.75
                      = 94.95