Question

A company has an 8% bond that has a face value of $1,000 and matures in 30 years. Assume that coupon payments are made semi-annually. The bonds are callable after 15 years at 108% of par value. What is the value of the bond if rates drop immediately to 6%?a. $1,277b. $2,192c. $1,452d. $1,229e. $602

Answer 1

a) 1,277 dollars

Step-by-step explanation:

We have to solve for the present value of the coupon payment and maturity art the end of the bond life discounted at 6% annual rate:

Coupon payment

`C * (1-(1+r)^(-time) )/(rate) = PV\\`

Coupon payment: 1,000 x 8% / 2 = 40

time 30 years x 2 = 60

market rate = 6% / 2 = 0.03

`40 * (1-(1+0.03)^(-60) )/(0.03) = PV\\`

PV $1,107.0225

Maturity

`(Maturity)/((1 + rate)^(time) ) = PV`

Maturity 1,000.00

time 60.00

rate 0.03

`(1000)/((1 + 0.03)^(60) ) = PV`

PV 169.73

PV coupon $1,107.0225

PV maturity $ 169.7331

Total $1,276.7556