**Internal rates of return conflate rewards for risk with returns for patience. That is why they are often misleading indicators of the profitability of alternative investments**.

Students of corporate finance are taught the dangers of judging projects by their internal rate of return. The problem is that the attractiveness of a project depends not just on its rate of return, but on the amount of capital invested in it. You might reasonably prefer a 30 per cent rate of return on a £1,000 investment to a 40 per cent rate of return on a £10 investment. Ludovic Phalippou, a Dutch economist, has described how this problem makes the use of internal rates of return by proponents of alternative investments more misleading than helpful for investors.

Would you rather turn £100 into £140 over one year, a 40 per cent internal rate of return, or the same hundred pounds into £300 over four years, a 30 per cent internal rate of return? The longer-term investment is a better buy unless you believe the world is full of other opportunities to invest at a return of 40 per cent. That is why students of corporate finance are told that in appraising investment projects they ought to have in their minds a measure of the opportunity cost of the funds required for an investment project – the cost of capital.

The measurement of private equity returns is complex because the drawdown of funds, and the returns to investors, are both generally gradual processes. Rates of return on different investments vary widely, and the internal rate of return on an overall investment is not the average internal rate of return of the underlying projects.

You invest £100 in a fund, and your money is divided equally between two companies. Suppose it is quickly obvious that one is a winner (worth £90) and the other a dud (worth, say, £30). The private equity house has indeed added value – the portfolio is worth 20 per cent more than its cost. Now suppose the underlying value of both companies increases by 10 per cent a year. The IRR from selling the winner immediately and retaining the dud for five years is over 35 per cent. But if the manager sells the dud right away and keeps the winner, the IRR falls to 15 per cent. Mr Phalippou shows that a strategy of taking profits and running losses is common practice among private equity managers. Not surprising – but whatever the reason, or the fund manager’s judgment, the IRR is a poor guide to the investor.

It gets worse. Suppose there is a bonanza, and the early realisations return more than the investor’s initial funds. Then there may be many solutions to the calculation of an internal rate of return. Some may be what mathematicians, with nice irony, call imaginary numbers.

Then it is necessary to factor in the effect of delayed drawdown of committed funds. Suppose the private equity manager with a £1,000 fund makes sequential investments of £100 each. He sells one each year to finance the next. If each returns £120, the investor earns a steady 20 per cent return on a £100 investment. But what is the risk-adjusted return? The capital at risk in the transaction is not £100, but the £1,000 that was committed – and on which the fees may also be based. Many investors in private equity were alerted to that reality rather sharply in the recent credit crunch. All rate of return measures suffer the flaw that they conflate rewards to risk with rewards to patient waiting – two quite distinct things.

The reason internal rate of return calculations remain popular, despite their overwhelming disadvantages, is that they do not require you to specify the cost of capital or alternative rate of return. But – as I described in my book, *The Long and the Short of It* – having a realistic target rate of return in your mind is an indispensable tool for the sophisticated investor. One reason is to enable you to look through calculations of projected internal rates of return. Ask how much cash you might earn, relative to the cash that you can expect to earn in other things. Measure this return against the risks associated with the investment. Review the past performance of investment managers in the same manner.

And, by the way, take all projections with a pinch of salt. But you knew that.