The Garraty company has two bond issues outstanding. Both bonds pa $100 annual interest plus $1,000 at maturity. Bond L has a maturity of 15 years and Bond S a maturity of 1 year. A). What will be the value of each of these bonds when the going rate of inters is (1) 5 percent, (2) 8 percent and (3) 12 percent? Assume that there is only one more interest payment to be made on Bond S.

B) Why does the longer term (15 year) bond fluctuate more when interest rates change than does the shorter term bond (1 year).

5% 1,047.62 1,518.98
8% 1,018.52 1,171.19
12% 982.14 863.78

(A.)1. 5%: Bond L: Input N = 15, I/YR = 5, PMT = 100, FV = 1000, PV = ?, PV = $1,518.98.

Bond S: Change N = 1, PV = ? PV = $1,047.62.

2. 8%: Bond L: From Bond S inputs, change N = 15 and I/YR = 8, PV = ?, PV = $1,171.19.
Bond S: Change N = 1, PV = ? PV = $1,018.52.

3. 12%: Bond L: From Bond S inputs, change N = 15 and I/YR = 12, PV = ? PV = $863.78.
Bond S: Change N = 1, PV = ? PV = $982.14.

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A) Here are the values of Bond L and Bond S at different interest rates:

At 5% interest:
- Bond L: $1,047.62
- Bond S: $1,518.98

At 8% interest:
- Bond L: $1,018.52
- Bond S: $1,171.19

At 12% interest:
- Bond L: $982.14
- Bond S: $863.78

B) The longer-term bond fluctuates more when interest rates change than the shorter-term bond because it has a higher duration. Duration is a measure of how sensitive a bond's price is to changes in interest rates. The longer the duration, the more the bond's price will change in response to interest rate fluctuations. Bond L, with a maturity of 15 years, has a longer time period over which it will be affected by changes in interest rates, leading to greater price fluctuations. On the other hand, Bond S, with a maturity of only 1 year, has a much shorter duration and is less affected by interest rate changes. So, Bond L will have larger price swings compared to Bond S.

A) The values of the bonds for different interest rates are as follows:

1) At 5 percent interest rate:
- Bond L: $1,047.62
- Bond S: $1,518.98

2) At 8 percent interest rate:
- Bond L: $1,018.52
- Bond S: $1,171.19

3) At 12 percent interest rate:
- Bond L: $982.14
- Bond S: $863.78

B) The longer-term bond (15-year) fluctuates more when interest rates change compared to the shorter-term bond (1-year) because it has a longer maturity period. The value of a bond is influenced by the present value of its future cash flows. When interest rates rise, the present value of future cash flows decreases, resulting in a decline in the bond's value. Conversely, when interest rates decrease, the present value of future cash flows increases, leading to an increase in the bond's value.

Since the longer-term bond has more future cash flows (with 15 interest payments and a larger principal payment at maturity), its value is more sensitive to changes in interest rates. This is because a change in interest rates has a greater impact on the present value of multiple future cash flows compared to a single future cash flow of a shorter-term bond. Hence, the longer-term bond fluctuates more.

To calculate the value of each bond at different interest rates, you can use the present value formula, which calculates the present value of future cash flows.

The formula for calculating the present value of a bond is:
PV = (C / (1 + r)^n) + (F / (1 + r)^n)

Where:
PV = Present value
C = Annual interest payment
r = Interest rate
n = Number of years until maturity
F = Face value (the amount received at maturity)

Now let's calculate the values of Bond L and Bond S at different interest rates:

For Bond L:
1) When the interest rate is 5%:
PV = (100 / (1 + 0.05)^15) + (1000 / (1 + 0.05)^15)
= (100 / 1.938) + (1000 / 1.938)
= 51.57 + 516.23
= $567.80

2) When the interest rate is 8%:
PV = (100 / (1 + 0.08)^15) + (1000 / (1 + 0.08)^15)
= (100 / 2.980) + (1000 / 2.980)
= 33.56 + 335.57
= $369.13

3) When the interest rate is 12%:
PV = (100 / (1 + 0.12)^15) + (1000 / (1 + 0.12)^15)
= (100 / 5.535) + (1000 / 5.535)
= 18.06 + 180.59
= $198.65

For Bond S:
1) When the interest rate is 5%:
Bond S only has one more interest payment remaining, so we only need to calculate the present value of that payment.
PV = 100 / (1 + 0.05)
= 100 / 1.05
= $95.24

2) When the interest rate is 8%:
PV = 100 / (1 + 0.08)
= 100 / 1.08
= $92.59

3) When the interest rate is 12%:
PV = 100 / (1 + 0.12)
= 100 / 1.12
= $89.29

B) The longer-term bond (Bond L) fluctuates more than the shorter-term bond (Bond S) when interest rates change because it has a higher sensitivity to changes in interest rates. Due to the longer time until maturity, Bond L's cash flows (interest payments and face value) are discounted over a longer period, making it more sensitive to changes in discount rates. Therefore, even a small change in interest rates has a larger impact on the present value of those cash flows, leading to greater price fluctuations for Bond L compared to Bond S.