Question

The Coleman-Smith Corporation has an outstanding bond that matures in exactly 10 years. The bonds have an annual coupon of 5%. The current market interest rate is 8%.

A: Assume the bonds have a face value of 1,000. What should be the bond's price?

B:

Now assume that the last 4 coupons were stripped from the bond and sold off separately. What would be the value of the remaining bond?

(As a technical matter, you should assume that the yield curve is flat. If you don't know why this is important, don't worry about it.)

Answer 1

A)

Using a financial calculator

FV = 1000

PMT = 50 (5% coupon rate)

I/Y = 8% (Market interest rate)

N = 10

cpt PV, we get PV = 798.7

Hence, bond price = $798.7

B)

The value of the remaining bond would be PV of 8-year bond coupons with same coupon rate and market interest rate + the PV face value of the bond maturing after 10 years

PV of coupons (Using a financial calculator)

FV = 0

PMT = 50 (5% coupon rate)

I/Y = 8% (Market interest rate)

N = 8

cpt PV, we get PV = 287.33

PV of 1000 face-value payable after 10 years = 1000/(1.08^10) = 463.19

Bond value (after stripping the mentioned coupons) = 463.19 +287.33 = $750.52