Consider two bonds, a 3-year bond paying an annual coupon of 7%, and a 20-year b
ID: 1171639 • Letter: C
Question
Consider two bonds, a 3-year bond paying an annual coupon of 7%, and a 20-year bond, also with an annual coupon or 7%. Both increases to 11%. bonds currently sell at par value. Now suppose that interest rates rise and the yield to maturity ofthe two bond a. What is the new price of the 3-year bond? (Round your answer to 2 decimal places.) Price of the 3-year bond b. What is the new price of the 20-year bond? (Round your answer to 2 decimal places.) Price of the 20-year bond c. Do longer or shorter maturity bonds appear to be more sensitive to changes In Interest rates? O Longer O ShorterExplanation / Answer
ANSWER = 1 Step 1 : Calculation of Annual Coupon Payments Par value of the bond issued is = $ 1,000 Annual Coupon % 7% Annual Coupon Amount $ 70 Step 2: Calculate number of years to Maturity Number of years to maturity = 3 years Step 3 : Yield to Maturity = 11%, So discount rate = 11% PVF = 1 / Discount rate = 1/ 1.11 Result of above will again divide by 1.11 , repeat this till last period Option 1= Life of the bond is 10 years CALCULATION OF CURRENT MARKET PRICE OF THE BOND OR PURCHASE PRICE Years Interest Amount PVF @ 11% PresentValue 1 Interest $ 70 0.9009 $ 63.06 2 Interest $ 70 0.8116 $ 56.81 3 Interest $ 70 0.7312 $ 51.18 3 Bond Value $ 1,000 0.7312 $ 731.19 Total $ 902.25 Current price of the Bond = $ 902.25 ANSWER = 2 Step 1 : Calculation of Annual Coupon Payments Par value of the bond issued is = $ 1,000 Annual Coupon % 7% Annual Coupon Amount $ 70 Step 2: Calculate number of years to Maturity Number of years to maturity = 20 years Step 3 : Yield to Maturity = 11%, So discount rate = 11% PVF = 1 / Discount rate = 1/ 1.11 Result of above will again divide by 1.11 , repeat this till last period Option 1= Life of the bond is 20 years CALCULATION OF CURRENT MARKET PRICE OF THE BOND OR PURCHASE PRICE Years Interest Amount PVF @ 11% PresentValue 1 Interest $ 70 0.9009 $ 63.06 2 Interest $ 70 0.8116 $ 56.81 3 Interest $ 70 0.7312 $ 51.18 4 Interest $ 70 0.6587 $ 46.11 5 Interest $ 70 0.5935 $ 41.54 6 Interest $ 70 0.5346 $ 37.42 7 Interest $ 70 0.4817 $ 33.72 8 Interest $ 70 0.4339 $ 30.37 9 Interest $ 70 0.3909 $ 27.36 10 Interest $ 70 0.3522 $ 24.65 11 Interest $ 70 0.3173 $ 22.21 12 Interest $ 70 0.2858 $ 20.01 13 Interest $ 70 0.2575 $ 18.03 14 Interest $ 70 0.2320 $ 16.24 15 Interest $ 70 0.2090 $ 14.63 16 Interest $ 70 0.1883 $ 13.18 17 Interest $ 70 0.1696 $ 11.87 18 Interest $ 70 0.1528 $ 10.70 19 Interest $ 70 0.1377 $ 9.64 20 Interest $ 70 0.1240 $ 8.68 20 Bond Value $ 1,000 0.1240 $ 124.03 Total $ 681.47 Current price of the Bond = $ 681.47 Answer =3) Shorter maturity of bonds are more sensitive to change in interest rates. Answer = Shorter.