An engineer approaching retirement thinks that the market interest rate will dec
ID: 1098278 • Letter: A
Question
An engineer approaching retirement thinks that the market interest rate will decrease before then and therefore plans to invest in corporate bonds. Specifically, the plan is to buy a $50,000 bond that matures 20 years from now and has a 12% coupon rate payable quarterly. How much should the engineer be able to sell the bond for 5 years from now, if the market rate is 8% per year compounded quarterly. During the 5 years before selling the bond, the engineer invests the quarterly dividend payments received in a venture yielding a 12% interest per year compounded quarterly. How much would the engineer have altogether, after selling the bond?Explanation / Answer
Since, all the rates are compounded quarterly the time period used shall be in quarters.
The quarterly interest paid by bond is 50,000*12%*3/12 = $1500
We want to know the price remaining with 15 years to maturity or 15*4 = 60 quarters.
The market rate is 8% per year compounded quarterly. Thus, effective quarterly rate is 8/4 = 2%
Price of Bond = P.V. of future payments
= 1500*PVA(2%,60) + 50000*PV(2%,60)
= $67380.44
The rate of dividend investment is 12% per year compounded quarterly. Thus, effective quarterly rate is 12/4 = 3%
The accumulated value of dividend received for 5 years (5*4 = 20 quarters) is:
1500*FVA(3%,20)
= 1500*26.8704
= $40305.56
Thus, total amount after selling the bond and accumulating the value of interest paid is :
$67380.44 + $40305.56
$107686