Question

In: Finance

You purchased an annual interest coupon bond one year ago with 6 years remaining to maturity at the time of purchase.

You purchased an annual interest coupon bond one year ago with 6 years remaining to maturity at the time of purchase. The coupon interest rate is 10% and par value is $1,000. At the time you purchased the bond, the yield to maturity was 8%. If you sold the bond after receiving the first interest payment and the bond's yield to maturity had changed to 7%, your annual total rate of return on holding the bond for that year would have been a. 7.00%. b. 8.00%. c. 9.95%. d. 11.95%. e. none of the above

Solutions

Expert Solution

Annual coupon = 10% of 1000 = $100

Now after 1st year no. of years left = 6-1 = 5 years. Let us now determine the price at which you sold the bond. The price will be = present value of 5 coupon payments of $100 each + present value of maturity value of $1,000. The applicable discount rate = current YTM = 7%.

Thus value of the bond = PV (7%, 5, 100, 1000) = $1,123.01

Now price at which the bond was bought = PV (8%, 6, 100, 1000) = $1,092.46

Annual rate of return from holding the bond = (annual coupon + price at which bond was sold - price at which bond was bought)/price at which bond was bought

= (100 + 1123.01 - 1092.46)/1092.46

= 11.95%

Thus the answer is option "d" i.e. 11.95%


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