Question

Problem 7-5

Bond valuation

An investor has two bonds in his portfolio that both have a face value of $1,000 and pay a 6% 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.

a. 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 9%? Round your answer to the nearest cent. $ What will the value of the Bond S be if the going interest rate is 9%? Round your answer to the nearest cent. $

What will the value of the Bond L be if the going interest rate is 11%? Round your answer to the nearest cent. $

What will the value of the Bond S be if the going interest rate is 11%? Round your answer to the nearest cent. $

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

I. The change in price due to a change in the required rate of return increases as a bond's maturity decreases.

II. Long-term bonds have greater interest rate risk then do short-term bonds.

III. The change in price due to a change in the required rate of return decreases as a bond's maturity increases.

IV. Long-term bonds have lower interest rate risk then do short-term bonds.

V. Long-term bonds have lower reinvestment rate risk then do short-term bonds.

Answer 1

Answer a.

Bond L:

Face Value = $1,000
Annual Coupon = 6%*$1,000 = $60
Time to Maturity = 11 years

If Market Interest Rate is 4%:

Price of Bond = $60 * PVIFA(4%, 11) + $1,000 * PVIF(4%, 11)
Price of Bond = $60 * (1 - (1/1.04)^11) / 0.04 + $1,000 / 1.04^11
Price of Bond = $1,175.21

If Market Interest Rate is 9%:

Price of Bond = $60 * PVIFA(9%, 11) + $1,000 * PVIF(9%, 11)
Price of Bond = $60 * (1 - (1/1.09)^11) / 0.09 + $1,000 / 1.09^11
Price of Bond = $795.84

If Market Interest Rate is 11%:

Price of Bond = $60 * PVIFA(11%, 11) + $1,000 * PVIF(11%, 11)
Price of Bond = $60 * (1 - (1/1.11)^11) / 0.11 + $1,000 / 1.11^11
Price of Bond = $689.67

Bond S:

Face Value = $1,000
Annual Coupon = 6%*$1,000 = $60
Time to Maturity = 1 year

If Market Interest Rate is 4%:

Price of Bond = $60 * PVIFA(4%, 1) + $1,000 * PVIF(4%, 1)
Price of Bond = $60 / 1.04 + $1,000 / 1.04
Price of Bond = $1,019.23

If Market Interest Rate is 9%:

Price of Bond = $60 * PVIFA(9%, 1) + $1,000 * PVIF(9%, 1)
Price of Bond = $60 / 1.09 + $1,000 / 1.09
Price of Bond = $972.48

If Market Interest Rate is 11%:

Price of Bond = $60 * PVIFA(11%, 1) + $1,000 * PVIF(11%, 1)
Price of Bond = $60 / 1.11 + $1,000 / 1.11
Price of Bond = $954.95

Answer B.

Long-term bonds have greater interest rate risk then do short-term bonds.