A 10year government bond with a face value of 1000 pays a c

A 10-year government bond with a face value of $ 1,000 pays a coupon of 8% annually. The compounded interest rate is 9%. a) Calculate the present value of the bond. b) Generate a table showing how the bond’s present value changes for annually compounded interest rates between 1% and 15%. c) What can you deduce about the relationship between the bond price and the yield to maturity (YTM)?

Solution

Cash Flows of Bond Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 8 Year 9 Year 10 8%X1000 8%X1000 8%X1000 8%X1000 8%X1000 8%X1000 8%X1000 8%X1000 8%X1000 8%X1000 1000 Cash Flows 80 80 80 80 80 80 80 80 80 1080 Present Value 80/(1+9%) 80/(1+9%)^2 80/(1+9%)^3 80/(1+9%)^4 80/(1+9%)^5 80/(1+9%)^6 80/(1+9%)^7 80/(1+9%)^8 80/(1+9%)^9 1080/(1+9%)^10 73.394495 67.3 61.8 56.7 52.0 47.7 43.8 40.1 36.8 456.2037 Total 935.82 When r=8% Value of bond = ? 1,000.00 r=10% Value of bond = ? 877.1 When yield increases, value of bond decreases. So they are inversely proportional