Problem 3 Suppose the interest rate is 10 ... [FREE SOLUTION]

Chapter 15: Problem 3

Suppose the interest rate is 10 percent. What is the value of a coupon bond that pays $\$ 80$ per year for each of the next five years and then makes a principal repayment of $\$ 1000$ in the sixth year? Repeat for an interest rate of 15 percent.

Short Answer

Expert verified

The value of the coupon bond at a 10% interest rate is the sum of present values computed at step 3. And the value of the coupon bond at a 15% interest rate is the sum of present values computed at step 4. These bond values will differ because different interest rates have been used.

Step by step solution

Calculate Present Value of Yearly Payments (10% Interest)

Firstly, calculate the present value of each of the $80 payments at 10% interest rate. The present value formula is: \[PV = \frac{FV}{(1 + r)^n}\] Where, PV is the present value, FV is the future value, r is the interest rate, and n is the number of years. In this case, FV = \$80, r = 10% or 0.10, and n = 1 to 5. Do these computations for each year.

Calculate Present Value of Principal Repayment (10% Interest)

Next, calculate the present value of the final principal repayment of $1000 in the sixth year at a 10% interest rate using the same present value formula with FV = \$1000, r = 0.10, and n = 6.

Sum all Present Values (10% Interest)

Add up the present values from steps 1 and 2. This will give the total present value of the bond at a 10% interest rate.

Repeat Steps 1 to 3 for 15% Interest

Repeat all the previous steps, but this time with an interest rate of 15% or 0.15. That means to compute again the present value of each of the $80 payments and $1000 principal repayment at a 15% interest rate, and sum up all these present values.