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

Total cashflows = $12,555+2.629x

x = $9,488.40

Explanation:

The computation of cash flow must the investment provide at the end of each of the final 4 years, that is, and X is shown below:-

Year     Cashflow       Present value at 8%        Discounted cashflow

1             $2,500                   0.926                              2,315

2             $5,000                  0.857                               4,285

3             $7,500                   0.794                               5,955

4              x                          0.735                               0.735x

5              x                          0.681                               0.681x

6               x                         0.63                                 0.630x

7               x                         0.583                                0.583x

Total cashflows                                                $12,555+2.629x

Therefore,

$12,555 + 2.629x = $37500

2.629x = $37500 - $12555

x = $24945 ÷ 2.629

x = $24945 ÷ 2.629

x = $9,488.40

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