Question

An investor has two bonds in his portfolio that have a face value of $1,000 and pay a 7% annual coupon. Bond L matures in 11 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 11 more payments are to be made on Bond L.

What will the value of the Bond L be if the going interest rate is 5%? Round your answer to the nearest cent.
$    

What will the value of the Bond S be if the going interest rate is 5%? Round your answer to the nearest cent.
$    

What will the value of the Bond L be if the going interest rate is 10%? Round your answer to the nearest cent.
$    

What will the value of the Bond S be if the going interest rate is 10%? 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.

Answer 1

Coupon per period = (Coupon rate / No of coupon payments per year) * Face value

Coupon per period = (7% / 1) * $1000

Coupon per period = $70

Let us compute the Bond L price at YTM = 5%

Bond Price = Coupon / (1 + YTM)^period + Face value / (1 + YTM)^period

Bond Price = $70 / (1 + 5%)¹ + $70 / (1 + 5%)² + ...+ $70 / (1 + 5%)¹¹ + $1000 / (1 + 5%)¹¹

Using PVIFA = ((1 - (1 + Interest rate)^{- no of periods}) / interest rate) to value coupons

No of periods = 11 years

Bond Price = $70 * (1 - (1 + 5%)^-11) / (5%) + $1000 / (1 + 5%)¹¹

Bond Price = $1166.13

Let us compute the Bond S price at YTM = 5%

Bond Price = Coupon / (1 + YTM)^period + Face value / (1 + YTM)^period

Bond Price = $70 / (1 + 5%)¹ + $1000 / (1 + 5%)¹

Bond Price = $1019.05

Let us compute the Bond L price at YTM = 10%

Bond Price = Coupon / (1 + YTM)^period + Face value / (1 + YTM)^period

Bond Price = $70 / (1 + 10%)¹ + $70 / (1 + 10%)² + ...+ $70 / (1 + 10%)¹¹ + $1000 / (1 + 10%)¹¹

Using PVIFA = ((1 - (1 + Interest rate)^{- no of periods}) / interest rate) to value coupons

No of periods = 11 years

Bond Price = $70 * (1 - (1 + 10%)^-11) / (10%) + $1000 / (1 + 10%)¹¹

Bond Price = $805.15

Let us compute the Bond S price at YTM = 10%

Bond Price = Coupon / (1 + YTM)^period + Face value / (1 + YTM)^period

Bond Price = $70 / (1 + 10%)¹ +  $1000 / (1 + 10%)¹

Bond Price = $972.73

Let us compute the Bond L price at YTM = 12%

Bond Price = Coupon / (1 + YTM)^period + Face value / (1 + YTM)^period

Bond Price = $70 / (1 + 12%)¹ + $70 / (1 + 12%)² + ...+ $70 / (1 + 12%)¹¹ + $1000 / (1 + 12%)¹¹

Using PVIFA = ((1 - (1 + Interest rate)^{- no of periods}) / interest rate) to value coupons

No of periods = 11 years

Bond Price = $70 * (1 - (1 + 12%)^-11) / (12%) + $1000 / (1 + 12%)¹¹

Bond Price = $703.12

Let us compute the Bond S price at YTM = 12%

Bond Price = Coupon / (1 + YTM)^period + Face value / (1 + YTM)^period

Bond Price = $70 / (1 + 12%)¹ + $1000 / (1 + 12%)¹

Bond Price = $955.36