Question

An investor has two bonds in his portfolio that have a face value of $1,000 and pay a 10% annual coupon. Bond L matures in 15 years, while Bond S matures in 1 year. a. What will the value of each bond be if the going interest rate is 5%, 8%, and 12%? Assume that only one more interest payment is to be made on Bond S at its maturity and that 15 more payments are to be made on Bond L. b. Why does the longer-term bond’s price vary more than the price of the shorter-term bond when interest rates change?

Answer 1

Answer:

Bond S

When interest rate 5%

Coupon plus Principal/1+interest rate

Coupon = 100

1100/1.05=1047.6

When interest rate 8%

1100/1.08=1018.5

When interest rate 12%

1100/1.12=982.41

Bond L

This bond has 15 payments which means it will be very difficult to solve it manually and we have to do it on a financial calculator

Put

FV=1000

N=15

I= 5 or 8 or 12

PMT= 100

PV=?

When interest rate

5% PV= 1518.9

8% PV=1171

12% PV=863.3

The reason interest rate varies the price of longer term bonds more is because all the payments of the bond is discounted by the interest rate and the longer the bonds life the more number of payments and the more time they will be discounted which means long term bonds are very sensitive to interest rate changes or have a higher duration

Explanation:

Answer 2

a) The value of each bond with going interest rates like 5%, 8%, and 12% is as follows:

                                     Bond L            Bond S

Prices at market rate:

5%                           $1,518.98        $1,047.62

8%                              $1,171.19        $1,018.52

12%                            $863.78           $982.14

How are the prices of bonds determined?

The prices of bonds are determined by computing the present values of the cash flows till maturity.

The present value can be computed using the present formula table, formula, or an online finance calculator as below:

b) The longer-term bond's price varies more than the price of the shorter-term bond when interest rates change because long-maturity bonds are more sensitive to rate changes than short-maturity bonds.

Another reason is that longer-term bonds have a longer duration and many more coupon payments than short-term bonds which are closer to their maturity periods and have fewer remaining coupon payments.

In addition, longer-term bonds are exposed to a greater probability of fluctuating interest rates.

Data and Calculations:

                                     Bond L            Bond S

Face value                   $1,000             $1,000

Coupon interest rate       10%                 10%

Maturity period          15 years             1 year

Prices at market rate:

5%                           $1,518.98        $1,047.62

8%                              $1,171.19        $1,018.52

12%                            $863.78           $982.14

For example, the price of the 10% $1,000 bonds at a 5% market rate is given as:

N (# of periods) = 1 year

I/Y (Interest per year) = 5%

PMT (Periodic Payment) = $100

FV (Future Value) = $1,000

Results:

PV = $1,047.62

Sum of all periodic payments = $100 ($100 x 1)

Total Interest $52.38

Thus, the higher variability of longer-term bonds allows investors to hedge the interest rate risks through diversification or derivatives.

Learn more about determining the prices of bonds at https://brainly.com/question/25596583