You are negotiating to make a 7-year loan of $37,500 to Breck Inc.To repay you,Breck will pay $2,500 at the end of Year 1,$5,000 at the end of Year 2,and $7,500 at the end of Year 3,plus a fixed but currently unspecified cash flow,X,at the end of each year from Year 4 through Year 7.Breck is essentially riskless,so you are confident the payments will be made.You regard 8% as an appropriate rate of return on a low risk but illiquid 7-year loan.What cash flow must the investment provide at the end of each of the final 4 years,that is,what is X?

Question

Quizplus · Accepted Answer

The correct answer is A.The present value of the cash flows at the end of Years 1, 2, and 3 is $15,000. The present value of the cash flows at the end of Years 4 through 7 is $X * 4 / (1 + 0.08)^3 = $X * 3.605. The total present value of the cash flows is $15,000 + $X * 3.605. This must be equal to the present value of the loan, which is $37,500 / (1 + 0.08)^7 = $22,526.32. Therefore, $X * 3.605 = $22,526.32 - $15,000 = $7,526.32, and X = $7,526.32 / 3.605 = $9,487.32.

You Are Negotiating to Make a 7-Year Loan of $37,500