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

Answer:

a) 1,277 dollars

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

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$  

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

time 30 years x 2 = 60

market rate = 6% / 2 = 0.03

$40 \times \frac{1-(1+0.03)^{-60} }{0.03} = PV$  

PV $1,107.0225  

Maturity

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity   1,000.00  

time   60.00  

rate  0.03

$\frac{1000}{(1 + 0.03)^{60} } = PV$  

PV   169.73  

 

PV coupon  $1,107.0225  

PV maturity  $   169.7331    

Total          $1,276.7556