Two years ago your corporate treasurer purchased for the firm a 20 year bond at
ID: 2664050 • Letter: T
Question
Two years ago your corporate treasurer purchased for the firm a 20 year bond at its par value of $1000. The coupon rate on this security is 8%. Interest payments are made to the bondholders once a year. Currently, bonds of this particular risk class are yielding investors 9%. 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 you 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 $ 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?
Explanation / Answer
a) sale price = PV of future cash flows = a*r(1-r^n)/(1-r) + 1000*r^n, (where r = DF, a= annual cash flow.) = 1000*0.08*(1/1.09)*(1-(1/1.09)^18)/(1 - 1/1.09) + 1000*(1/1.09)^18 = 912.44 ($) (ANSWER) b) FV of previous flows = 1000*(1.09)^2 -1000*0.08*(1.09+1)= 1020.9 ($) loss = 1020.9 - 912.44 = 108.46 ($) (ANSWER) c) maturity period not defined. d) It is maturity risk.
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