Suppose you bought a 10-year bond, which pays $50 at the end of each of the 10 c

Question

Suppose you bought a 10-year bond, which pays $50 at the end of each of the 10 consecutive years and, after the tenth year, additional pays you $1000. You just collected your seventh annual payment on the bond.

a) Suppose that you decide to sell the bond now, assuming that the interest rate is 5% and this is expected to continue for the indefinite future. How much can you expect to sell the bond for?

b) Suppose the interest rate has changed to 10%. Now how much can you expect to sell the bond for?

Explanation / Answer

Term to maturity = 10 - 7 = 3

Selling price = Present value (PV) of bond interests for next 3 years + PV of $1,000 paid after 3 years

(a) Interest rate = 5%

Selling price ($) = 50 x PVIFA(5%, 3) + 1,000 x PVIF(5%, 3)

= 50 x 2.7232 + 1,000 x 0.8638 = 136.16 + 863.8 = 999.96 ~ 1,000

Quick Note: When bond interest rate = Market interest rate, Selling price = Face value [Bond interest rate = $50 / $1,000 = 5%]

(b) Interest rate = 10%

Selling price ($) = 50 x PVIFA(10%, 3) + 1,000 x PVIF(10%, 3)

= 50 x 2.4869 + 1,000 x 0.7513 = 124.35 + 751.3 = 875.65

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