# UKIRR and cost of capital

#### rob250881

Hello,
I'm hoping someone can help me out with an issue I'm having with IRR and the cost of capital. I just can't get my head around it!
If you have future cash flows, do you apply the discount factor based on the cost of capital and use the Discounted Cash Flow amounts for the IRR formula, or do you use the values based on the cash flow based on year 0 values?
As an example

PROJECT 1
Cost of capital 5%
 Year Cash Flow (CF) Discount Factor Discounted Cash Flow (DCF) 0 (3000) 1 (3000) 1 500 0.952 476 2 3000 0.907 2721 3 500 0.864 432 IRR 15.62% 10.11%

So in this example which IRR figure is correct, 15.62% or 10.11%?

#### kirby

VIP Member
If you are assuming that interest rates are ZERO (unreal assumption although came very close to reality at times) then use the 15.62% figure. Otherwise the 10.11% figure makes more sense.

#### kenm

I would like to revisit this old thread, if only for my edification. Please check my comments below.

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The IRR is derived internally from the sum of discounted cash flows (NPV).

So we would never calculate the IRR (10.11%) of the discounted cash flows directly (D69 in the image below) because that would double-discount (!).

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Whether 15.62% is correct depends on the interpretation of the cash flows.

Presumably, year0 -3000 is an initial capital value or investment, and year1 500 and year2 3000 are the "free cash flows" for each year.

If year3 is the ending balance or "terminal value", 15.62% is correct.

It is calculated by =IRR(B6:B9) in B13 in the image below.

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But if year3 is just the "free cash flow" for that year, and we have a cost of capital, but no "terminal value", I believe the IRR is the cost of capital (5%) by definition.

This is demonstrated below.

The year0 PV in B16 is the year0 cash flow (-3000) minus the NPV of the cash flows (B6:B9), which are discounted internally at the cost of capital rate (C3).

Algebraically, we can see that is just minus the NPV of the cash flows starting in year1 (B7:B9).

Then in B17, we calculate the IRR of the cash flows (B6:B9), substituting the year0 PV for the year0 cash flow.

And indeed, that is the same as the cost of capital, within the limitations of the Excel IRR algorithm.

#### Stuart.Lyons

Hello

In the description of the the below video is link to a file with IRR and a load of other investment Appraisal tools in excel

I think though you are getting confused we use the Internal Rate of Return (IRR) calculation to rank various projects by profitability and potential for growth. It works by finding the interest rate that will bring the cash flows to a net present value of 0. The higher the IRR, the more growth potential a project has.

You are effectively comparing the intrust rate attached to different projects and the one with the highest interest rate (that should always be above your cost of capital WACC) you theoretically invest in.

Hope the above helps

#### kenm

I think though you are getting confused
To a degree, I think you are correct insofar as my statement that ``the IRR is the cost of capital (5%) by definition`` was wrong.

I understand the mathematics of the IRR and NPV calculations very well. But I am not as knowledgeable about their application to business financial models -- other than the simple investment model.

My primary point was: 10.11% (sic; actually 10.12% rounded) is never the corrrect IRR, as it was calculated by "rob". I can explain why mathematically, if that is not obvious to anyone.

My second point, for consideration, was or should have been: 15.62% might not be the correct IRR, either. It depends on the interpretation of the cash flows that "rob"provided without explanation.

If we invested 3000 into a company or investment (written as -3000), and the business earns 500, 300 and 500 in subsequent years, and if that is all (i.e. the business has no remaining value), 15.62% is indeed the IRR. And that might be different from the WACC.

But if the business is on-going (or it is has a terminal value), the cash flows provided by "rob" fail to take into account the remaining value of the business. That should be "added" to the 500 earned in the last year. ("Added" by properly signing it as an outflow.)

And in that case, since "rob" did not provide that information, we cannot calculate the IRR.

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You are right that I made the mistake of thinking that we can use the NPV of just those cash flows discounted by the WACC to make up for the lack of critical information (the remaining value of the business). That result is tautological -- and "illogical". Mea culpa!

Thanks for helping me to realize that.

#### Stuart.Lyons

No worries man sounds like you got there on your own anyway, I personally never really use IRR except to illustrate. I think this might have been a product of real interest rates being so low while Ive been working
Most investment decisions I have been involved in we have been looking at Payback and the Money multiplier
I imagine IRR will make a come back now there is a cost to time value of money