For the past four years, I have been building business cases to justify the sale and implementation of software. Often, I would include an Internal Rate of Return (IRR) calculation. Over the past few weeks, I have been researching why using IRR as a growth rate will often achieve a result much higher than Compound Average Growth Rate (CAGR) for the same project. I have concluded this is because IRR assumes the cashflows in each period measured are reinvested in subsequent projects that grow at the Internal Rate of Return.
In the past, I simply accepted the standard principles
regarding IRR taught in grad school:
- IRR is the rate at which a given set of cash flows are discounted in order to set the Net Present Value (NPV) of the investment to zero.
- The resulting rate is compared to the organization’s Weighted Average Cost of Capital (WACC) or a higher “hurdle rate”.
- If the IRR rate is higher than the WACC/hurdle rate the associated investment is expected to make money for the organization.
I don’t disagree with these principles. However, I couldn’t shake the feeling that IRR had a relation to the CAGR of a given project. I therefore set out to answer whether IRR assumes that the resulting cash flows from the investment are reinvested at a rate equal to IRR?
I assumed this had already been written about and began to read countless blog articles and scholarly journals on the topic. During my research, I found many conflicting opinions. For example, a detailed, well-written, often cited bog at propertymetrics.com concluded that IRR “is a discounting calculation and makes no assumptions about what to do with periodic cash flows received along the way”. It was a convincing article, but I still had a nagging feeling and kept looking. I never found an article that argued for or against the math behind reinvestment. Just articles that either supported or denied the notion. I therefore began to tinker with the math to try and answer my question. I believe I succeeded in proving, with reasonable accuracy, that IRR does assume reinvestment of cash flows. The return rate produced by IRR is aligned with the cash flows plus reinvestment. This is shown by following the process below:
1. On a set of NPV positive cash flows, with initial investment, calculate the Internal Rate of Return.
- Determining IRR is an iterative process of finding the rate that sets the cash flows to values that, when added together, result in the additive inverse of the initial investment, thus setting the NPV to zero.
N = The total
number of periods (i.e., months or years) being measured.
4. Grow the initial investment at each rate. The CAGR ending value will be equal to the IRR ending value plus the initial investment. (In about 13% of cases the two totals will be off by, approximately, less than one billionth of a percent)
The benefit of IRR is in showing the full potential of an
investment. Investments with strong returns in the early periods of the
investment will result in much higher IRR results. The theory that IRR is the
actual return rate is not practical, but it does show the investments full
potential and is helpful when comparing projects. Moreover, since IRR can be a
bit irrational, a more pragmatic tool is MIRR which allows you to set the rate at
which the cash flows are reinvested.
Notes:
This article makes the following assumptions.
- The money used for the initial investment is not borrowed, and the invested asset’s value is equal to the amount of the original investment.
- Click here for an article on levered vs unlevered IRR.
- Cash flows that result in a positive NPV were used.
- Non-normal cashflows, which have multiple real roots, are not in play.
In my next post I will include the spreadsheet progressions
for each of the four steps listed in the section above.


