Bond X is a premium bond making annual payments. The bond pays an 8 percent coup
ID: 2669206 • Letter: B
Question
Bond X is a premium bond making annual payments. The bond pays an 8 percent coupon, has a YTM of 6 percent, and has 13 years to maturity. Bond Y is a discount bond making annual payments. This bond pays a 6 percent coupon, has an 8 percent YTM, and also has 13 years to maturity. If interest rates remain unchanged, what do you expect the price of these bonds to be one year from now? In three years? In eight years? In 12 years? In 13 years? What's going on here? Illustrate your answers by graphing bond prices versus time to maturity. *Hint: You are finding present valuesThis can be done excel, actually I would prefer it to be on excel if you can do it.
Explanation / Answer
According to the given information for Bond-A: Face value of the bond = $1,000 Coupon rate = 8% YTM = 6% Years to maturity = 13 According to the given information for Bond-B: Face value of the bond = $1,000 Coupon rate = 6% YTM = 8% Years to maturity = 13 Calculating the present value of the bond for Bond-A using excel sheet: Annual coupon payment for Bond-A = $1000 * 8% = $80 Step1: Go to excel and Click "insert" to insert the function Step2: Select the "PV" function as we are finding the present value of the bond in this case. Step3: Enter the values as Rate = 6%; Nper = 13; PMT = -80; FV = -1000 Step4: Click "OK" to get the desired value. The value comes to " $1,177.05" Therefore, the present value of Bond-A is $1,177.05 Calculating the present value of the bond for Bond-B using excel sheet: Annual coupon payment for Bond-B = $1000 * 6% = $60 Step1: Go to excel and Click "insert" to insert the function Step2: Select the "PV" function as we are finding the present value of the bond in this case. Step3: Enter the values as Rate = 8%; Nper = 13; PMT = -60; FV = -1000 Step4: Click "OK" to get the desired value. The value comes to " $841.92" Therefore, the present value of Bond-B is $842 Calculating the price of the bonds one year from now? For Bond-A: Step1: Go to excel and Click "insert" to insert the function Step2: Select the "PV" function as we are finding the present value of the bond in this case. Step3: Enter the values as Rate = 6%; Nper = 1; PMT = -80; FV = -1000 Step4: Click "OK" to get the desired value. The value comes to " $1,018.87" Therefore, the present value of Bond-A is $1,019 For Bond-B: Step1: Go to excel and Click "insert" to insert the function Step2: Select the "PV" function as we are finding the present value of the bond in this case. Step3: Enter the values as Rate = 8%; Nper = 1; PMT = -60; FV = -1000 Step4: Click "OK" to get the desired value. The value comes to " $981.48" Therefore, the present value of Bond-B is $981 Calculating the price of the bond 3 years from now? For Bond-A: Step1: Go to excel and Click "insert" to insert the function Step2: Select the "PV" function as we are finding the present value of the bond in this case. Step3: Enter the values as Rate = 6%; Nper = 3; PMT = -80; FV = -1000 Step4: Click "OK" to get the desired value. The value comes to " $1,053.46" Therefore, the present value of Bond-A is $1,053 For Bond-B: Step1: Go to excel and Click "insert" to insert the function Step2: Select the "PV" function as we are finding the present value of the bond in this case. Step3: Enter the values as Rate = 8%; Nper = 3; PMT = -60; FV = -1000 Step4: Click "OK" to get the desired value. The value comes to " $948.46" Therefore, the present value of Bond-B is $948 Calculating the price of the bond 8yrs from now? Step1: Go to excel and Click "insert" to insert the function Step2: Select the "PV" function as we are finding the present value of the bond in this case. Step3: Enter the values as Rate = 6%; Nper = 8; PMT = -80; FV = -1000 Step4: Click "OK" to get the desired value. The value comes to " $1,124" Therefore, the present value of Bond-A is $1,124 For Bond-B: Step1: Go to excel and Click "insert" to insert the function Step2: Select the "PV" function as we are finding the present value of the bond in this case. Step3: Enter the values as Rate = 8%; Nper = 8; PMT = -60; FV = -1000 Step4: Click "OK" to get the desired value. The value comes to " $885" Therefore, the present value of Bond-B is $885 Therefore, the value of bond-A for 1,3,8 and 13yrs is as follows: $1,019 , $1,053 , $1,124, $1,177 Therefore, the value of bond-B for 1,3,8 and 13yrs will be as follows: $981, 948, $885 and $842 As the number of years are increasing the value of bond-A is increasing and the value of bond-B is decreasing. The bond-B is reacting inversely that is as the years to maturity increasing the present value of the bond is decreasing. The difference in the present values of Bonds-A and Bond-B is because of the diferent coupon rates and the yields. For Bond-A, the coupon rate is greater than the yield which results in the higher bond price and for Bond-B, the coupon rate is less than the yield which results in the lower bond price with the increase in the number of years.