Question

Dooley, Inc., has outstanding $100 million bonds that pay an annual coupon rate of interest of 11 percent. Par value of each bond is $1,000. The bonds are scheduled to mature in 10 years. Because of Dooley’s increased risk, investors now require a 13 percent rate of return on bonds of similar quality. The bonds are callable at 110 percent of par at the end of 5 years.

1. What price would the bonds sell for assuming investors do not expect them to be called?
2. What price would the bonds sell for assuming investors expected them to be called at the end of 5 years?

Answer 1

Using the present value formula to calulate the bond price:

P = c/(1+i) + c/(1+i)² + ........... + c/(1+i)ⁿ + f/(1+i)ⁿ where c is the coupon payment ; i is the interest rate f is the par value and n is number of payments

P = 110/(1+0.11) + 110/(1+0.11)² + 110/(1+0.11)³ + .............. + 1110/(1+0.11)¹⁰ = $647.815399

The bonds would sell for $647.815399 assuming investors do not expect them to be called

Price of a callable bond can be computed using the following formula:

P = (c/m) * f * [1 - (1+ r/m)^(-n*m)] / (r/m) + c/ [1+ (r/m)]^(n*m)

where P: callable bond price; c: coupon rate; m: number of coupon payments per year; f: face value of bond; r: market interest rate for an equivalent bond of similar risk; n: numbers of years till call date and c: call price

P = (0.11/1) * 1000 * [1 - (1+0.13/1)^(-5*1)] / (0.13/1) + 1100/ [1 + (0.13/1)]^(5*1) = $983.922599

The bonds would sell for $386.946373 assuming investors expected them to be called at the end of 5 years