Question

An investor has two bonds in his portfolio that have a face value of $1,000 and pay a 12% annual coupon. Bond L matures in 16 years, while Bond S matures in 1 year. Assume that only one more interest payment is to be made on Bond S at its maturity and that 16 more payments are to be made on Bond L. What will the value of the Bond L be if the going interest rate is 4%? Round your answer to the nearest cent. $ What will the value of the Bond S be if the going interest rate is 4%? Round your answer to the nearest cent. $ What will the value of the Bond L be if the going interest rate is 8%? Round your answer to the nearest cent. $ What will the value of the Bond S be if the going interest rate is 8%? Round your answer to the nearest cent. $ What will the value of the Bond L be if the going interest rate is 13%? Round your answer to the nearest cent. $ What will the value of the Bond S be if the going interest rate is 13%? Round your answer to the nearest cent. $ Why does the longer-term bond’s price vary more than the price of the shorter-term bond when interest rates change? The change in price due to a change in the required rate of return increases as a bond's maturity decreases. Long-term bonds have greater interest rate risk than do short-term bonds. The change in price due to a change in the required rate of return decreases as a bond's maturity increases. Long-term bonds have lower interest rate risk than do short-term bonds. Long-term bonds have lower reinvestment rate risk than do short-term bonds.

Answer 1

Bond L

K = N

Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =1

Bond Price =∑ [(12*1000/100)/(1 + 4/100)^k]     +   1000/(1 + 4/100)^1

k=1

Bond Price = 1076.92

Bond S

K = N

Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =16

Bond Price =∑ [(12*1000/100)/(1 + 4/100)^k]     +   1000/(1 + 4/100)^16

k=1

Bond Price = 1932.18

Bond L

K = N

Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =1

Bond Price =∑ [(12*1000/100)/(1 + 8/100)^k]     +   1000/(1 + 8/100)^1

k=1

Bond Price = 1037.04

Bond S

K = N

Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =16

Bond Price =∑ [(12*1000/100)/(1 + 8/100)^k]     +   1000/(1 + 8/100)^16

k=1

Bond Price = 1354.05

Bond L

K = N

Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =1

Bond Price =∑ [(12*1000/100)/(1 + 13/100)^k]     +   1000/(1 + 13/100)^1

k=1

Bond Price = 991.15

Bond S

K = N

Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =16

Bond Price =∑ [(12*1000/100)/(1 + 13/100)^k]     +   1000/(1 + 13/100)^16

k=1

Bond Price = 933.96

Long-term bonds have greater interest rate risk than do short-term bonds