You are negotiating to make a 6-year loan of $40,000 to Breck Inc. To repay you, Breck will pay $5,000 at the end of Year 1, $10,000 at the end of Year 2, and $15,000 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 6. 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 6-year loan. What cash flow must the investment provide at the end of each of the final 3years, that is, what is X?

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Asked Jun 9, 2019
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You are negotiating to make a 6-year loan of $40,000 to Breck Inc. To repay you, Breck will pay $5,000 at the end of Year 1, $10,000 at the end of Year 2, and $15,000 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 6. 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 6-year loan. What cash flow must the investment provide at the end of each of the final 3years, that is, what is X?

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Expert Answer

Step 1

In order to profit from lending, one has to ensure that the PV of loan payments must be greater than or equal to the  loan amount at required rate of return ie Net present value (NPV) is equal to (or greater than)  0. NPV can be calculated by hand using the formula shown below where n is the number of periods.

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Cashflow in period1 NPV= (1+rate of return)(1+rate of return)2 ' (1+rate of return)3 Cashflow in period 2 Cashflow in period 3 Cashflow in period n Loan amount (1+rate of return)"

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Step 2

Inserting values in given formula and setting NPV = 0, we get $7278.1428.

This is the minimu...

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$5000 $10000 $15000 $x $x NPV= + (+8%) (+8%) ' (1+8%)3 (1+8%)4 ° (1+8%)5 ' (1+8%)6 $40000 NPV $25110.50145 + $2.045782677 X - $40000 Setting NPV0, we get $40000- $25110.50145 = $2.045782677 X x $7278.142844

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