Problem 7-5 An investor has two bonds in his portfolio that both have a face val
ID: 2647039 • Letter: P
Question
Problem 7-5
An investor has two bonds in his portfolio that both have a face value of $1,000 and pay a 8% annual coupon. Bond L matures in 19 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 19 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 12%? Round your answer to the nearest cent.
$
What will the value of the Bond S be if the going interest rate is 12%? Round your answer to the nearest cent.
$
Explanation / Answer
(1) Computation of value of bond L.We have,
Face value of Bond = $ 1,000
Coupon Amount = $ 1,000 x 8 % = $ 80
Rate of interest = 4 %
Number of years = 19 years.
Value of Bond = Coupon rate x PVIFA(4%, 19 YEARS) + Face value x PVIF( 4% , 19 YEARS)
Value of Bond = 80 x 13.134 + 1,000 X 0.475 = 1,050.715 + 475 = $ 1,526
Hence, The value of bond L is $ 1,526.
(2) Computation of value of the Bond S be if the going interest rate is 4%.We have,
Face value of Bond = $ 1,000
Coupon Amount = $ 1,000 x 8 % = $ 80
Rate of interest = 4 %
Number of years = 1 years.
Value of Bond = Coupon rate x PVIFA(4%, 1 YEARS) + Face value x PVIF( 4% , 1 YEARS)
Value of Bond = 80 x 0.962 + 1,000 X 0.962 = 76.96+ 962 = $ 1,038.96
Hence, The value of bond S is $ 1,038.96.
(3) Computation of the value of the Bond L be if the going interest rate is 8%.We have,
Face value of Bond = $ 1,000
Coupon Amount = $ 1,000 x 8 % = $ 80
Rate of interest = 8 %
Number of years = 19 years.
Value of Bond = Coupon rate x PVIFA(8%, 19 YEARS) + Face value x PVIF( 8% , 19 YEARS)
Value of Bond = 80 x 7.366 + 1,000 X 0.116 = 589 + 116 = $ 705.
Hence, The value of bond L is $ 705.
(4) Computation of value of the Bond S be if the going interest rate is 8%.We have,
Face value of Bond = $ 1,000
Coupon Amount = $ 1,000 x 8 % = $ 80
Rate of interest = 8 %
Number of years = 1 years.
Value of Bond = Coupon rate x PVIFA(8%, 1 YEARS) + Face value x PVIF( 8% , 1 YEARS)
Value of Bond = 80 x 0.926 + 1,000 X 0.926 = 74.08+ 926 = $ 1,000.08
Hence, The value of bond S is $ 1,000.08
(5) Computation of the value of the Bond L be if the going interest rate is 12%.We have,
Face value of Bond = $ 1,000
Coupon Amount = $ 1,000 x 8 % = $ 80
Rate of interest = 12%
Number of years = 19 years.
Value of Bond = Coupon rate x PVIFA(12%, 19 YEARS) + Face value x PVIF( 12% , 19 YEARS)
Value of Bond = 80 x 7.365+ 1,000 X 0.116 = 589+ 116 = $ 705
Hence, The value of bond L is $ 705.
(6) Computation of value of the Bond S be if the going interest rate is 12%.We have,
Face value of Bond = $ 1,000
Coupon Amount = $ 1,000 x 8 % = $ 80
Rate of interest = 12 %
Number of years = 1 years.
Value of Bond = Coupon rate x PVIFA(12%, 1 YEARS) + Face value x PVIF( 12% , 1 YEARS)
Value of Bond = 80 x 0.962 + 1,000 X 0.962 = 76.96+ 962 = $ 1,038.96
Hence, The value of bond S is $ 1,038.96.