Question

Suppose a bond with no expiration date has a face value of $10,000 and annually pays a fixed amount of interest of $950. In the table provided below, calculate and enter either the interest rate that the bond would yield to a bond buyer at each of the bond prices listed below or the bond price at each of the interest yields shown.

Answer 1

riskier the bond higher the interest

interest yield and bond prices are inversely related

The interest rate of 8% will yield $800 annually for a bond with a face value of $10,000.

At $8000 of bond price, the interest yield is 10%.

At 8.9% of the interest yield, the bond price is $8989.

At $11,000 of bond price, the interest yield is 7.2%.

At 8.9% of the interest yield, the bond price is 12,903.

Answer 2

The present value of a two-year bond with an 8% interest rate is calculated by discounting the future interest payments and principal back to today's value using the specified discount rate. At an 8% discount rate, the present value is $2,908. When the discount rate increases to 11%, the present value decreases to $2,804.09, showing how rising interest rates can lead to lower bond prices.

To calculate the present value of a bond, we use the present value formula which discounts future cash flows back to their value today, considering a certain discount rate. In this case, we have a two-year bond with an annual interest payment, and we want to know its worth at different discount rates.

Firstly, at an 8% discount rate, the formula will discount both the interest payments and the principal. Each $240 interest payment, along with the $3,000 principal due in the second year, needs to be discounted back to present value terms using that 8%:

• Present Value of 1st year's interest: PV = $240 / (1 + 0.08) = $222.22

• Present Value of 2nd year's interest and principal:

PV = ($240 + $3,000) / (1 + 0.08)² = $2,685.78

Adding these up gives us the total present value of the bond at an 8% discount rate:

PV at 8% = $222.22 + $2,685.78 = $2,908

If the discount rate rises to 11%, the present value of the bond will decrease because future cash flows are discounted at a higher rate. Here is the calculation:

• Present Value of 1st year's interest: PV = $240 / (1 + 0.11) = $216.22

• Present Value of 2nd year's interest and principal: PV = ($240 + $3,000) / (1 + 0.11)² = $2,587.87

Thus, the present value of the bond at an 11% discount rate is:

PV at 11% = $216.22 + $2,587.87 = $2,804.09

This demonstrates how changes in the prevailing interest rates affect the present value of a bond. When interest rates go up, bond prices tend to go down to make the yields more attractive to investors.