Final answer:
The present value of a $10 million loan paying 8% annual interest can be calculated by discounting the future interest payments and principal repayment using the formula PV = CF / (1 + r)^n at a rate of 8.5%. The computations should include the present value for each yearly interest payment and the principal repaid in the third year, all discounted at the 8.5% rate.
Step-by-step explanation:
The question asks for the present value of a three-year, $10 million loan that pays annual interest at a rate of 8%, with the principal amount due at the end of the third year. To calculate the present value of the loan when it is sold at an 8.5 percent discount rate, we must find the present value of the future interest payments as well as the present value of the principal amount to be repaid at the end of the third year. The process involves finding the present discounted value of each payment the bank is expecting to receive.
In the case of the loan, the bank receives interest payments of $800,000 each year (8% of $10 million) for the first two years and an $800,000 interest payment plus the $10 million principal in the third year. Utilizing the present value formula, we discount each of these cash flows at the 8.5% discount rate. To compute the present value, we'll use the formula PV = CF / (1 + r)^n, where CF is the future cash flow, r is the discount rate, and n is the year number.
Here's how to calculate the present value:
- Year 1 interest payment present value: PV = $800,000 / (1 + 0.085)^1
- Year 2 interest payment present value: PV = $800,000 / (1 + 0.085)^2
- Year 3 total payment present value: PV = $10,800,000 / (1 + 0.085)^3
We would sum up all these present values to find the total present value the bank should receive for the loan.