Question

BOND VALUATION An investor has two bonds in his portfolio that have a face value of $1,000 and pay a 10% annual coupon. Bond L matures in 15 years, while Bond S matures in 1 year.

a. What will the value of each bond be if the going interest rate is 5%, 8%, 12%? Assume that only one more interest payment is to be made on Bond S at its maturity and that 15 more payments are to be made on Bond L.

5%    Bond L:

         Bond S:

8%    Bond L:

         Bond S:

12%  Bond L:

         Bond S:

Answer 1

5%

Bond L

K = N

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

k=1

K =15

Bond Price =∑ [(10*1000/100)/(1 + 5/100)^k]     +   1000/(1 + 5/100)^15

k=1

Bond Price = 1518.98

Bond S

K = N

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

k=1

K =1

Bond Price =∑ [(10*1000/100)/(1 + 5/100)^k]     +   1000/(1 + 5/100)^1

k=1

Bond Price = 1047.62

8%

Bond L

K = N

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

k=1

K =15

Bond Price =∑ [(10*1000/100)/(1 + 8/100)^k]     +   1000/(1 + 8/100)^15

k=1

Bond Price = 1171.19

Bond S

K = N

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

k=1

K =1

Bond Price =∑ [(10*1000/100)/(1 + 8/100)^k]     +   1000/(1 + 8/100)^1

k=1

Bond Price = 1018.52

12%

Bond L

K = N

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

k=1

K =15

Bond Price =∑ [(10*1000/100)/(1 + 12/100)^k]     +   1000/(1 + 12/100)^15

k=1

Bond Price = 863.78

Bond S

K = N

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

k=1

K =1

Bond Price =∑ [(10*1000/100)/(1 + 12/100)^k]     +   1000/(1 + 12/100)^1

k=1

Bond Price = 982.14