Final answer:
To calculate the amount the company expects to receive for the sale of the bonds, we need to calculate the present value of the bond's interest payments and principal payment at maturity. The present value of the bond's interest payments can be found using the present value formula, and the present value of the principal payment is simply the face value of the bond. By adding these together, we can find the total present value of the bond.
Step-by-step explanation:
To calculate the present value of the bond, we need to find the present value of each semi-annual interest payment and the present value of the principal payment at maturity.
- First, calculate the semi-annual interest payment by multiplying the bond face value of $400,000 by the annual interest rate of 11% divided by two. This gives us $22,000.
- Next, calculate the present value of each semi-annual interest payment using the formula:
- Present Value = Interest Payment / (1 + Discount Rate)^(Number of Periods)
- In this case, the number of periods is 10 years, which means there are 20 semi-annual periods. The discount rate is 10%. Plug in these values into the formula to calculate the present value of each interest payment:
- Present Value of Interest Payment = $22,000 / (1 + 0.10)^20
- Repeat this calculation for each semi-annual payment and sum them up to find the present value of all the interest payments.
- Finally, calculate the present value of the principal payment at maturity. Since the principal payment is made at the end of the bond's term, it does not need to be discounted. Therefore, the present value of the principal payment is simply the face value of the bond, which is $400,000.
- Add the present value of the interest payments and the present value of the principal payment to find the total present value of the bond, which is the amount the company expects to receive for the sale of these bonds.