Question

You are negotiating to make a 7-year loan of $25,000 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?

A) $4,271.67

B) $4,496.49

C) $4,775.18

D) $4,969.81

Answer 1

Value of loan = Present value of cash flows in the future

Present Value of the cashflows from year 4 to 7 at the year 3= Cash flows* [ 1 - ( 1 +R)^-N] / R

= X * ( 1 - 1.08^-4 ) / 0.08 = 3.3121X

present value of cash flows at year 0 = 3.3121X / 1.08^3

25000 = 2500 /1.08 + 5000/1.08^2 + 7500 / 1.08^3 + 3.3121X/1.08^3

25000 = 12555.25 + 2.6293X

X = (25000 - 12555.25 ) / 2.6293 = 4775.18

ash flow must the investment provide at the end of each of the final 4 years = 4775.18