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

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TomShelby TomShelby · Answer 1 · 2019-12-27T01:15:21+01:00

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

[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]

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

time 30 years x 2 = 60

market rate = 6% / 2 = 0.03

[tex]40 \times \frac{1-(1+0.03)^{-60} }{0.03} = PV\\[/tex]

PV $1,107.0225

Maturity

[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]

Maturity 1,000.00

time 60.00

rate 0.03

[tex]\frac{1000}{(1 + 0.03)^{60} } = PV[/tex]

PV 169.73

PV coupon $1,107.0225

PV maturity $ 169.7331

Total $1,276.7556