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In: Finance

DYI Construction Co. is considering a new inventory system that will cost $750,000. The system is...

DYI Construction Co. is considering a new inventory system that will cost $750,000. The system is expected to generate positive cash flows over the next four years in the amounts of $350,000 in year one, $325,000 in year two, $150,000 in year three, and $180,000 in year four. DYI's required rate of return is 11%. What is the modified internal rate of return of this project?

Solutions

Expert Solution

As per Modified Internal Rate of Return the Present Value of Cash outflows will be equal to the Present Value of Terminal Value of Cash inflows.

FV = Future Value

PV = Present Value

K = 11% or 0.11

Terminal Value = FV1 +  FV2 +  FV3 +  FV4

= PV( 1+K)n +PV2( 1+K)n2 + PV3( 1+K)n3 + PV4( 1+K)n4

= $350,000 (1+0.11)3 +  $325,000 (1+0.11)2 + $150,000 (1+0.11)1+ $180,000(1+0.11)0

=  $350,000 (1.11)3 + $325,000 (1.11)2 + $150,000(1.11)1 + $180,000(1.11)0

= $350,000 * 1.367631 +  $325,000 * 1.2321 + $150,000 * 1.11 + $180,000 * 1

= $478,670.85 + 400,432.5 + 166,500 + 180,000

= $1,225,603.35

This is the future value of Terminal Value and not the Present Value. Present Value of Terminal Value of Cash inflows is calculated in the next step.

Present Value of Cash outflows = $750,000

Modified Internal Rate of Return = Present Value of Cash outflows = Present Value of Terminal Value of Cash inflows.

$750,000 = $1,225,603.35 / (1 + r)n

Firstly we need to understand why - $1,225,603.35 / (1 + r)n

This is because Present Value = Future Value ( 1+r)n

Here r is MIRR or Modified Internal Rate of Return

$750,000 = $1,225,603.35 / (1 + r)4

(1 + r)4 = $1,225,603.35 / $750,000

(1 + r)4 = 1.634

(1 + r) = 1.131

[Note : How did we get 1.131. Take Square root of 1.634 twice to get 1.131]

r = 1.131 - 1

r = 0.131

or r = 13.1%

Therefore modified internal rate of return of this project is 13.1%


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