16-12. (Interest rate risk) Two years ago your corporate treasurer purchased for

Question

16-12. (Interest rate risk) Two years ago your corporate treasurer purchased for the firm a 20-year bond at its par value of $1,000. The coupon rate on this security is 8 percent. Interest payments are made to bondholders once a year. Currently, bonds of this particular risk class are yielding investors 9 percent. A cash shortage has forced you to instruct your treasurer to liquidate the bond.
a. At what price will your bond be sold? Assume annual compounding.

b. What will be the amount of your gain or loss over the original purchase price?

c. What would be the amount of your gain or loss had the treasurer originally purchased a bond with a 4-year rather than a 20-year maturity? (Assume all characteristics of the bonds are identical except their maturity periods.)

d. What do we call this type of risk assumed by your corporate treasurer?

(Keown. Foundations of Finance: The Logic and Practice of Financial Management, 6th Edition. Pearson Learning Solutions p. 513).
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Explanation / Answer

a. At what price will your bond be sold? Assume annual compounding.

Price(P0) = (Coupon payments x 1 - 1 / (1+r)n / r ) + (Maturity Value x 1 / (1+r)n)
                = ($1,000 x 8% x (1 - 1/(1+0.09)18) / 0.09) + ($1,000 x 1 / (1+0.09)18)
                = ($80 x (1 - 0.212)/0.09)
                = $80 x 8.7556 + ($1,000 x 0.212)
                = $700.44 + $212 = $912.44

b. What will be the amount of your gain or loss over the original purchase price?
Loss = $1,000 - $912.44 = $87.56

c. What would be the amount of your gain or loss had the treasurer originally purchased a bond with a 4-year rather than a 20-year maturity? (Assume all characteristics of the bonds are identical except their maturity periods.)

P0 = ($1,000 x 8% x (1 - 1/(1+0.09)2) / 0.09) + ($1,000 x 1 / (1+0.09)2)
    = ($80 x (1- 0.8418) / 0.09 ) + $1,000 x 1.18
    = ($80 x 1.758) + 841.68 = $982.32

Loss = $1,000 - $982.32 = $17.68

d. What do we call this type of risk assumed by your corporate treasurer?

     This type of risk is called Interest rate risk.

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