You bought one of Rocky Mountain Manufacturing Co.’s 9 percent coupon bonds one

Question

You bought one of Rocky Mountain Manufacturing Co.’s 9 percent coupon bonds one year ago for $1,047.30. These bonds make annual payments and mature seven years from now. Suppose that you decide to sell your bonds today, when the required return on the bonds is 8.50 percent.

If the inflation rate was 3.9 percent over the past year, what would be your total real return on investment?

You bought one of Rocky Mountain Manufacturing Co.’s 9 percent coupon bonds one year ago for $1,047.30. These bonds make annual payments and mature seven years from now. Suppose that you decide to sell your bonds today, when the required return on the bonds is 8.50 percent.

Explanation / Answer

Initial Investment=$1,047.30

Let P =price of Bond today=?, c=coupon on Bond=9% 0f 1000=90, y be the current market rate of interest=8.5%=.085 and FV=1000, T be time to maturity=7

P=(90/.085)(1-1/(1.085)7)+1000/(1.085)7

P=460.66621+564.92635=1025.59256=1025.59

Final value of Investment=coupon from Bond + bond value=90+1025.59=1115.59

total nominal return on investment=(Final value of Investment/Initial Investment)-1=(1115.59/1,047.30)-1=0.0652=6.52%

inflation rate =3.9%=.039

total real return on investment=[(1+nominal return on investment)/((1+ inflation rate)]-1=[(1.0652)/((1.039)]-1=.02522 0r 2.52%

or simply subtract inflation rate to get total real return on investment=6.52%-3.9%=2.62%

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