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Internal Rate of Return & Modified Internal Rate of ReturnPWC Course Notes P53

Mark Fielding- Pritchard

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Advantages and Disadvantages of the IRR

Advantages

% so people feel they understand it

Rate of return

Relatively easy to calculate

Widely accepted

No need to pick a discount rate

Disadvantages

% so 20% of $1 is better than 15% of $1m

How to benchmark

Multiple IRRs

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We have a potential coal mining project in Scotland. There will be an initial investment in purchase of land, licenses, equipment. We can harvest coal from the

surface so the NPV quickly becomes positive. Once exhausted we must dig down to the next seam which requires expenditure so the NPV becomes negative, once

mining resumes we receive sales and he NPV becomes positive

Net Present ValuesYear 1 -20Year 2 2.5Year 3 -6Year 4 4.5Year 5 12

Internal Rate of Return

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Year 1 Year 2 Year 3 Year 4 Year 5

-25

-20

-15

-10

-5

0

5

10

15

-20

2.5

-6

4.5

12

Mining Project

Time

Net

Pre

sent

Valu

e

Internal Rate of Return

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Modified IRR Used to counter the fact that we get multiple IRRs

Year Net after tax cash flow $

0 -20

1 7

2 -3

3 12

4 10

Company uses discount rate of 10%Note that for exam purposes we are looking here at cash flows, not NPV

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MIRR

Year Net after tax cash flow $

Inflow Outflow

0 -20 20

1 7 7x(1+0.1)³ = 9.32

2 -3 3x = 2.48

3 12 12x1.1= 13.2

4 4 4

Total 26.52 22.48

What we are doing is smoothing the cash flows so that we don’t get multiple IRRS. We make 2 assumptions- All expenses (negative numbers) occur at time 0- All income (positives) occur at time 4- Discount rate 10%

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MIRR

Therefore at IRR the NPV of the outflows = NPV of inflows22.48 T0 = 26.52 at T4 , so22.48 = 26.52 where k is the discount rate (so the IRR)= 1.18K= 4.22%So if MIRR is > cost of finance or threshold then we accept the project