Question

The problem refers to the bonds of The Apollo Corporation, all of which have a call feature. The call feature allows Apollo to pay off bonds anytime after the first 15 years, but requires that bondholders be compensated with an extra year's interest at the coupon rate if such a payoff is exercised.

Apollo's Alpha bond was issued 10 years ago for 30 years with a face value of $1000. Interest rates were very high at the time, and the bond's coupon rate is 20%. The interest rate is now 12.5%. Assume bond coupons are paid semiannually.

1. At what price should an Alpha bond sell? Round the answer to the nearest cent.
2. At what price would it sell without the call feature? Round the answer to the nearest cent.

Answer 1

(a) Computation of selling price of bond

Maturity Value = $1,200 [$1,000 Face Value + $200 one-year Coupon payment]

Semi-annual Coupon Amount = $100 [$1,000 x 20% x ½]

Semi-annual Yield to Maturity = 6.25% [12.5% x ½]

Maturity Period = 10 Years [(15 Years – 10 Years) x 2]

Price of the Bond = Present Value of the Coupon Payments + Present Value of the Maturity Value

= $100[PVFA 6.25%,10 ] + $1,200[PVF 6.25%,10]

= [$100 x 7.2737] + [$1,200 x 0.5454]

= $727.37 + $654.47

= $1,381.84

Hence, the selling price of bond is $1,381.84

(b) Computation of price of bond without the call feature

Face Value = $1,000

Semi-annual Coupon Amount = $100 [$1,000 x 20% x ½]

Semi-annual Yield to Maturity = 6.25% [12.5% x ½]

Maturity Period = 40 Years [(30 Years – 10 Years) x 2]

Price of the Bond = Present Value of the Coupon Payments + Present Value of the Face Value

= $100[PVFA 6.25%,40] + $1,000[PVF 6.25%,40]

= [$100 x 14.5843] + [$1,000 x 0.0885]

= $1,458.43 + $88.48

= $1,546.91

Hence, the price of bond without the call feature is $1,546.91 .