## On Mark Leonard’s IRR Thought Experiment

*The Private Investment Brief is published eight times per year to a subscriber base of university endowments, family offices, high-net-worth individuals, and fund managers. Contact info@privateinvestmentbrief.com for a sample issue. Follow us on Twitter at @ThePIBnyc.*

It was my great honor to interview Mark Leonard of Constellation Software last fall at the Santangel’s Investor Forum. I learned many things, chief among them that if you ever find yourself disagreeing with him, chances are you are wrong. That said, I’m about to (gingerly) do just that.

The disagreement arises from this thought experiment that Mr. Leonard posed in his 2015 letter to Constellation shareholders:

*“Assume attractive return opportunities are scarce and that you are an excellent forecaster. For the same price you can purchase a high profit declining revenue business or a lower profit growing business, both of which you forecast to generate the same attractive after tax IRR. Which would you rather buy?”*

Which he proceeded to answer as follows:

*“It’s easy to go down the pro and con rabbit hole of the false dichotomy. The answer we’ve settled on (though the debate still rages), is that you make both kinds of investments. The scarcity of attractive return opportunities trumps all other criteria. We care about IRR, irrespective of whether it is associated with high or low organic growth.”*

I cannot disagree with Mr. Leonard’s answer, but I must point out that he cheated a bit by posing a question that demanded we choose one or the other business, only to reveal that there is no need to choose at all. I can’t decide if that counts as being too nice or too mean.

But let’s try to answer the question on its own terms: Given the assumptions, and forced to choose—which business do you buy? This brings me to the disagreement, because I believe there is a clear answer, with no rabbit holes or raging debates required: you should buy the growing business.

To explain why, let me first observe that the internal rate of return (IRR) is not the same thing as the compounded annual rate of return (CAGR). It’s CAGR that long-term investors care about most, because it is the means to answering the question “How much money will I end up with at the end?” which is the name of the game for most of us. There is one scenario in which an investment’s IRR and its CAGR are the same, and that is if the rate of return on the cash flows generated by the investment and reinvested is itself equal to the IRR, and then the cash flows generated by all of those investments are in turn reinvested at the IRR, and so on, Russian doll-style, until the end of the investment period. In real life, of course, this almost never happens, nor do you know in advance what the rate of return on future cash flows yet to be generated and yet to be invested will be. But IRR is still useful for comparing various investment options in the here and now.

Second observation: IRR can be decomposed roughly as follows:

IRR (%) = initial yield (%) + growth rate of distributions (%)

This equation becomes precisely true as a company distributes cash out to infinity, but it’s roughly true enough for the practical purposes of those rare investors, Mr. Leonard included, who truly do buy for keeps. Note that the equation implies that an investment with a high initial yield and a low growth rate can generate the identical IRR as an investment with a low initial yield and a high growth rate.

Which is precisely the scenario Mr. Leonard’s thought experiment asks us to consider. We’re offered two different businesses with identical IRRs—one achieved by means of a high initial yield and a low (in fact negative) growth rate, and the other by means of a low initial yield and a high growth rate. Again, which business do we choose?

Suppose business A has a 20 percent initial yield and a negative 4 percent growth rate. Using Microsoft Excel’s XIRR function and running the movie for 50 years gives an IRR of 15.99 percent, which is roughly the (20 percent + -4 percent) we’d expect from the equation above.

Now suppose business B has a 6.45 percent initial yield and a 10 percent growth rate. Using the same 50-year time frame, we get the same 15.99 percent IRR, which is roughly what the equation predicts as well, with the difference likely due to some eccentricity in how Excel calculates annualized returns.

So far so good, but we still have to choose a business and we don’t yet have a reason to prefer one over the other. But let’s now go back to our first observation, the one about IRR not being the same thing as CAGR. Let’s assume that given a choice, we would prefer the investment that would somehow lead to “more money at the end”—in other words, that would produce the higher CAGR. The way to get from an investment’s IRR to its CAGR is to make some guess about the rate of return we will earn on the cash flows generated by the investment and reinvested. That is, to make a guess about the CAGR of each of the 50 “mini-investments” we’ll make with the dividends paid by each main investment, and then to sum the final values of each mini-investment.

The big question now is: What guess do we make?

We could assume the mini-investments will earn the same 15.99 percent CAGR as the IRR of the main investment, in which case we would be indifferent between business A and business B, according to the internal logic of the IRR calculation. Things could shake out exactly that way, but they almost certainly won’t.

We could assume the CAGR on reinvested cash flows will be higher than 15.99 percent, but that raises a question: if we’re so confident we can earn more than 15.99 percent on our money starting in one year’s time, why are we slumming among investments with a mere 15.99 percent IRR?

We’re left with the more conservative and logical assumption: that we’ll earn a lower-than-the-IRR rate of return on reinvested cash flows. It may well be a more likely assumption as well, because as you grow your capital base in a world of scarce opportunities, the opportunities tend to get scarcer. So let us assume we’ll earn say 12 percent on the reinvested dividends of each of business A and B. Are we still indifferent?

The answer is no. When you make that assumption and run the numbers, higher-growing business B ends up producing a higher CAGR, 13.5 percent vs. 12.5 percent. That might not seem like a lot, but it amounts to a 53 percent larger pot of money at the end. I think this result corresponds with intuition too, because a business that saddles you with a lot of cash up front and a little later places you at the mercy of your ability to reinvest that cash long-term more than a business that saddles you with less cash today and much much more later. In a sense—and sometimes in literal fact—the high-growing investment does the reinvesting for you.

I take pains to point out that this little exercise is not an endorsement of growth investing. The thought experiment assumes we have excellent forecasting skills, and in the real world most of us don’t, and the further out we’re asked to forecast, the worse we tend to do. So despite everything I just said, put me down as favoring, all else equal, the bird in the hand of initial yield over the growth-rate birds in the bush.

But you have to play a thought experiment as it lays. And under the assumptions stated, I’d take the high-growth business.

*The Private Investment Brief is published eight times per year to a subscriber base of university endowments, family offices, high-net-worth individuals, and fund managers. Contact info@privateinvestmentbrief.com for a sample issue. Follow us on Twitter at @ThePIBnyc.*