Consider three bonds with 6.40% coupon rates, all making annual coupon payments
ID: 2816271 • Letter: C
Question
Consider three bonds with 6.40% coupon rates, all making annual coupon payments and all selling at face value. The short-term bond has a maturity of 4 years, the intermediate-term bond has a maturity of 8 years, and the long-term bond has a maturity of 30 years. a. what will be the price of the 4-year bond if its yield increases to 7.40%? (Do not round intermediate calculations. Round your answers to 2 decimal places.) 12.5 points Bond price 03:33:46 eBook Print References b, what will be the price of the 8-year bond if its yield increases to 7.40%? (Do not round intermediate calculations. Round your answers to 2 decimal places.) Bond price c. what will be the price of the 30-year bond if its yield increases to 7.40%? (Do not round intermediate calculations. Round your answers to 2 decimal places.) Bond priceExplanation / Answer
a. Price of 4 year bond if the yield increases to 7.40% Price of bond = sum of present values of future cashflows Present Value = Future value/ ((1+r)^t) where r is the yield to maturity that is 7.40% and t is the time period Coupon rate 0.064 Face value 1000 Annual coupon payment 64 Yield to maturity 0.074 Year 1 2 3 4 Future cash flow 64 64 64 1064 Present value 59.59 55.48 51.66 799.70 Sum of present values 966.43 Bond price $966.43 b. Price of 8 year bond if the yield increases to 7.40% Price of bond = sum of present values of future cashflows Present Value = Future value/ ((1+r)^t) where r is the yield to maturity that is 7.40% and t is the time period Coupon rate 0.064 Face value 1000 Annual coupon payment 64 Yield to maturity 0.074 Year 1 2 3 4 5 6 7 8 Future cash flow 64 64 64 64 64 64 64 1064 Present value 59.59 55.48 51.66 48.10 44.79 41.70 38.83 601.05 Sum of present values 941.20 Bond price $941.20 c. Price of 30 year bond if the yield increases to 7.40% Price of bond = sum of present values of future cashflows Present Value = Future value/ ((1+r)^t) where r is the yield to maturity that is 7.40% and t is the time period Coupon rate 0.064 Face value 1000 Annual coupon payment 64 Yield to maturity 0.074 Year 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Future cash flow 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 1064 Present value 59.59 55.48 51.66 48.10 44.79 41.70 38.83 36.15 33.66 31.34 29.18 27.17 25.30 23.56 21.93 20.42 19.02 17.71 16.49 15.35 14.29 13.31 12.39 11.54 10.74 10.00 9.31 8.67 8.07 124.97 Sum of present values 880.74 Bond price $880.74