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Appendix A – The Modified Internal Rate of Return

• The MIRR is used on projects with non-conventional cash flows

• The cash flows are modified first and then the IRR is calculated using the modified cash flows

• There are three MIRR methods that are used:• The Discounting Approach• The Reinvestment Approach• The Combination Approach

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9-2

MIRR Method #1The Discounting Approach

• All negative cash flows are discounted back to the present at the required return and added to the initial cost.

• From the previous non-conventional cash flow example, we had a required return of 15% and:

Year 0 -$90,000

Year 1 $132,000

Year 2 $100,000

Year 3 -$150,000

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MIRR Example - Continued

• Using Method #1, the cash flow at year 3 would be discounted back to year 0 at 15%

• The cash flows would look like this: Year 0: -$90,000 - $150,000/(1.153)

= -$188,627.43 Year 1: $132,000 Year 2: $100,000 Year 3: $0• MIRR using Method #1 is 15.77%

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9-4

MIRR Method #2The Reinvestment Approach

• All cash flows (positive and negative) except the first are compounded out to the end of the project’s life and then the IRR is calculated

• The cash flows would look like this:

Year 0: -$90,000

Year 1: $0

Year 2: $0

Year 3: $-$150,000 + $100,000(1.15) + $132,000(1.152)

• MIRR using Method #2 is 15.75%

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MIRR Method #3The Combination Approach

• All negative cash flows are discounted back to the present and all positive cash flows are compounded out to the end of the project’s life

• The cash flows would look like this:Year 0: -$90,000 - $150,000/(1.153)

= -$188,627.43Year 1: $0Year 2: $0Year 3: $100,000(1.15) + $132,000(1.152)

= $289,570• MIRR using Method #2 is 15.36%

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MIRR vs. IRR

• MIRR can handle non-conventional cash flows, where as the IRR can’t

• But there are problems with MIRR:• There are three methods, and three different MIRRs.

Which MIRR is correct? The differences could be larger on a more complex project

• MIRR is a rate of return on a modified set of cash flows, not the project’s actual cash flows

• Since the MIRR depends on an externally supplied discount rate, the result is not truly an “internal” rate of return

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