# Internal Rate of Return: A Simple, Non-Mathematical Explanation

### Thomas C. Klein, Wilson Sonsini Goodrich & Rosati

How do venture investors compare investments in portfolio companies when the amounts invested, the timing of those investments, the returns, and the timing of those returns are all different? The tool venture investors use to compare the rates of return on each investment on an "apples-to-apples" basis is the internal rate of return (also known as the compound annual growth rate or CAGR).

A typical venture investment involves several investments into a portfolio company at various stages of the company's development. From an investment perspective, those investments are considered negative cash flow; that is, cash going out from the venture fund. Of course, the cash goes out from the venture fund at different times. Investing \$100 today is more expensive to the venture fund than investing \$100 in a Series C Preferred Stock round three years from today because the venture fund would only have to put aside, say, \$80 today to grow into the \$100 needed in three years for the Series C Preferred Stock investment. This \$80 is known as the discounted value or the value in "today's dollars" of the \$100 investment that would be made in three years. Accordingly, any "apple-to-apples" comparison of investments would have to compare investments based on today's dollars.

Similarly, when the portfolio company is successful, cash is returned to the venture fund. This is positive cash flow for the venture fund. Obviously, it would be better for the venture fund to receive the positive cash flow earlier rather than later for the same reason the venture fund would prefer to have the negative cash flow later rather than earlier. Receiving dollars today is more valuable than receiving the same number of dollars in the future, because if the fund receives the dollars today, it can invest those funds and earn a return on them. Accordingly, an "apples-to-apples" comparison of investments would have to compare investments not just on when the dollars are invested and how much those dollars are, but also on when the returning cash is received and how much it is. Thus, if a venture fund is to compare an investment into one portfolio company versus another, it will want to compare those investments based on outflows of cash in today's dollars and inflows of cash in today's dollars.

If a venture fund projected its investments into a portfolio company, and projected how much it would receive when the portfolio company would get purchased or go public, and also took into consideration when it made the investments and when it would receive the returns, then the venture fund could determine what rate of return it earned in today's dollars. Thus, this calculation would reflect all of the investments and all of the returns in today's dollars, and show the venture fund what rate of return it would earn in that investment. This rate of return calculation is called the internal rate of return, also known as the compound annual growth rate.

Accordingly, the venture fund analyst takes the above information and solves for the rate of return, rather than knowing the rate of return and solving for value in today's dollars of the investment. Thus, the cash outflows and inflows, in today's dollars, determine the rate of return. With this in mind, it is easy to see that in order to calculate the internal rate of return, all that the analyst needs to know or assume is the amount of money to be invested and when (and it might be lumpy; that is, different amounts invested at different times), and the amount of money assumed to be returned and when (and this too may be lumpy).

Timing Is Something...but not Everything

Accordingly, the timing of the fund's investments and the timing of the receipt of the returns of cash are crucial determinants of whether the investment should be made. If the fund invests a lot today and a small amount later, then the fund will have its money in the company at risk longer and therefore will not have the opportunity to use those funds to earn a return elsewhere. It is not the same to the venture fund if it makes its entire investment in the company right away instead of staging its investments over time. Therefore, even if the total investment amount would be equal and the final payments back to the venture fund would be equal in each case, the timing of the investments would be important in determining whether the investment was a good one or not compared to other investments available to the fund.

Timing is also important with regard to the ultimate funds received when the investment is liquidated. The venture fund would definitely prefer to receive its returns earlier rather than later, and depending on the circumstances, the fund would accept a smaller return if it is received earlier. Thus, the internal rate of return informs the venture investor that the smaller the early round investments and the earlier the returns are generated (assuming the early returns are equal in amount to the later returns), the better the internal rate of return. That is fairly intuitive.

For example an investment of \$100 that returns \$100 in earnings plus the \$100 capital invested in one year is a much better investment than if the returns are received in fifty years. The question is how much better of an investment is it - and the internal rate of return can answer that question.

The Internal Rate of Return: Putting Dollars and Timing Together

The internal rate of return informs an investor of the rate of return of the investments made based on how much was invested, when it was invested, how much was returned, and when the return was received. Thus, if several investments are made at different times, like venture fund investments in a portfolio company at the time of different rounds of financing, the internal rate of return informs the fund managers of the rate of return for the total of the investments based upon when those investments were made and when the returns were, or are expected to be, received. It even works if the returns are spread over time as well. Therefore, for complicated staged or lumpy investments, or for those that return periodic payments or returns (like a bond), calculating the internal rate of return can allow a venture fund to compare that investment to other similar staged or lumpy investments to see which one actually offers the highest compound annual growth rate, the internal rate of return.

For example, if a venture fund makes an investment in a portfolio company's Series A financing today, makes an additional investment in the company's Series B financing one year later, makes a final investment in the company's Series C financing 20 months after that, and the company is expected to be sold or go public at three years from the Series C investment, the investor can compare that investment to others in the venture fund's portfolio by using the internal rate of return.

Rather than just compute the difference between the final sale proceeds of the investments and the sum of the amounts invested, which would be the total profit, and then divide the profit by the total amount invested (which would provide a total percentage return), the internal rate of return uses time to determine the rate of return needed for the investments to equal returns generated. That is why the internal rate of return is sometimes referred to as the compound annual growth rate - the rate at which lumpy investments grow to equal the final returns.

So What?

The power of the internal rate of return is that it allows an investor to compare different investments, because the internal rates of return incorporate timing - when the investments are to be made and when the returns are expected to be received. That is, the magic of the internal rate of return is that it allows an investor to compare the rate of return on different investments in today's dollars. Taking the example above about a \$100 investment returning \$100 plus the capital invested in either one year or fifty years, the only difference was when the returns were received. In both cases, the total percentage return is 100% (\$100 profit on \$100 invested), but the internal rates of return are much different. For the investment returning all capital and profit in one year, the internal rate of return is 100%; for the investment returning capital and profit in fifty years, the internal rate of return is 1.4%.