Question

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 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.

a) 1) What will the value of the Bond L e if the going interest rate is 4%? Round your answer to the nearest cent. $___.
2) What will the value of the Bond S be if the going interest rate is 4%? Round your answer to the nearest cent. $___.
3) What will the value of the Bond L be if the going interest rate is 10%? Round your answer to the nearest cent. $___.
4) What will the value of the Bond S be if the going interest rate is 10%? Round your answer to the nearest cent. $___.
5) What will the value of the Bond L be if the going interest rate is 11%? Round your answer to the nearest cent.$___.
6) 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?
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

The value of bonds varies depending on the interest rate due to present value calculations. Bond L's value is more sensitive to changes in interest rates compared to Bond S because it has more future payments impacted by the interest rate. The correct explanation for this sensitivity is that long-term bonds have greater interest rate risk.

Step-by-step explanation:

To determine the present value of both bonds, we will use the present value of an annuity formula for Bond L and the present value of a single payment for Bond S. Let's denote the face value of the bonds as F, the annual coupon rate as C, the current market interest rate as r, and the number of years to maturity as t.

The formula for the present value of an annuity (which is applicable to Bond L's periodic coupon payments) is PV = C * [(1 - (1 + r)^(-t)) / r]. The formula for the present value of a single future payment (applicable to Bond S) is PV = F / (1 + r)^t.

Given that F = $1,000, C = F * 6% = $60, we can calculate the values:

1. Value of Bond L with r = 4%: PV = $60 * [(1 - (1 + 0.04)^(-19)) / 0.04] + $1,000 / (1 + 0.04)^19 = $1,086.59
2. Value of Bond S with r = 4%: PV = $1,000 / (1 + 0.04)^1 = $961.54
3. Value of Bond L with r = 10%: PV = $60 * [(1 - (1 + 0.10)^(-19)) / 0.10] + $1,000 / (1 + 0.10)^19 = $527.63
4. Value of Bond S with r = 10%: PV = $1,000 / (1 + 0.10)^1 = $909.09
5. Value of Bond L with r = 11%: PV = $60 * [(1 - (1 + 0.11)^(-19)) / 0.11] + $1,000 / (1 + 0.11)^19 = $493.37
6. Value of Bond S with r = 11%: PV = $1,000 / (1 + 0.11)^1 = $900.90

This is because longer-dated bonds have more remaining coupon payments that will be impacted by a change in discount rates, causing a more significant change in present value.