You are negotiating to make a 7-year loan of $25,000 to Breck Inc. To repay you,

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. $4,733.15 d. $5,218.30 e. $4,969.81 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. $4,733.15 d. $5,218.30 e. $4,969.81

Explanation / Answer

Determine the Present Value of the 7 annual cash payments. They must total $25,000.

First get the PV of the amounts due in the first 3 yrs, at 8% - $2,315 + 4,287 + 5,954 = 12,556. That leaves 12,444, which is the PV of the 4 equal payments due in Yr 4 - 7.

Next get the PV of 12,444 at T3, which is 15,676. Solve for the Annuity amount, at 8%, over 4 yrs, whose PV is 15,676. That is 4,733, or X in your problem

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