Question

An investor has two bonds in his portfolio that have a face value of $1,000 and pay a 9% annual coupon. Bond L matures in 10 years, while Bond S matures in 1 year.

a. What will the value of the Bond L be if the going interest rate is 6%, 7%, and 10%? Assume that only one more interest payment is to be made on Bond S at its maturity and that 10 more payments are to be made on Bond L. Round your answers to the nearest cent. Answer for 6%, 7%, and 10% for both Bond L and Bond S.

b. Why does the longer-term bond’s price vary more than the price of the shorter-term bond when interest rates change?

1. The change in price due to a change in the required rate of return decreases as a bond's maturity increases.
2. Long-term bonds have lower interest rate risk than do short-term bonds.
3. Long-term bonds have lower reinvestment rate risk than do short-term bonds.
4. The change in price due to a change in the required rate of return increases as a bond's maturity decreases.
5. Long-term bonds have greater interest rate risk than do short-term bonds.

Answer 1

a)

Bond L

No of periods = 10 years

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

Coupon per period = (9% / 1) * $1000

Coupon per period = $90

Let us compute the Bond L price at YTM = 6%

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

Bond Price = $90 / (1 + 6%)¹ + $90 / (1 + 6%)² + ...+ $90 / (1 + 6%)¹⁰ + $1000 / (1 + 6%)¹⁰

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

Bond Price = $90 * (1 - (1 + 6%)^-10) / (6%) + $1000 / (1 + 6%)¹⁰

Bond Price = $1220.80

Let us compute the Bond L price at YTM = 7%

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

Bond Price = $90 / (1 + 7%)¹ + $90 / (1 + 7%)² + ...+ $90 / (1 + 7%)¹⁰ + $1000 / (1 + 7%)¹⁰

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

Bond Price = $90 * (1 - (1 + 7%)^-10) / (7%) + $1000 / (1 + 7%)¹⁰

Bond Price = $1140.47

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

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

Bond Price = $90 / (1 + 10%)¹ + $90 / (1 + 10%)² + ...+ $90 / (1 + 10%)¹⁰ + $1000 / (1 + 10%)¹⁰

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

Bond Price = $90 * (1 - (1 + 10%)^-10) / (10%) + $1000 / (1 + 10%)¹⁰

Bond Price = $938.55

Bond S

No of periods = 1 year

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

Coupon per period = (9% / 1) * $1000

Coupon per period = $90

Let us compute the Bond S price at YTM = 6%

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

Bond Price = $90 / (1 + 6%)¹ + $1000 / (1 + 6%)¹

Bond Price = $1028.30

Let us compute the Bond S price at YTM = 7%

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

Bond Price = $90 / (1 + 7%)¹ +  $1000 / (1 + 7%)¹

Bond Price = $1018.69

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

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

Bond Price = $90 / (1 + 10%)¹ + $1000 / (1 + 10%)¹

Bond Price = $990.91

b)

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