An engineer approaching retirement thinks that the market interest rate will dec

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

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