You invest Rs 10,000 today in X Ltd, and it grows to Rs 20,000 in five years. Yes, the investment has doubled in five years; yes, the five-year return is 100 per cent; but what is its annual return? Is it 20 per cent per annum? You invest Rs 10,000 today in Y Ltd, and it grows to Rs 40,000 in ten years’ time. Yes, the investment has quadrupled in 10 years; yes the ten-year return is 300 per cent; but what is its annual return? Is it 30 per cent per annum?
When an investment in X Ltd doubles in five years, it would, if reinvested at the same rate, double again in the next five years. Hence Rs 10,000 invested in X Ltd will become Rs 40,000 in 10 years. Therefore, both, the investment in X Ltd and that in Y Ltd, give identical returns whereas we had earlier thought that the first gave 20 per cent and the second, 30 per cent.
Go back to the school formula on compound interest to get the right rate. Using Rs 10,000 as principal, Rs 20,000 as amount, and five as years, we get the rate as 14 per cent in the case of X Ltd. Using Rs 10,000 as principal, Rs 40,000 as amount, and 10 as years, we get 14 per cent in Y Ltd, as well.
This 14 per cent is the compound return, and is the only relevant return when you analyse an investment. The 20 per cent and the 30 per cent are called simple return. They are misleading and should not form part of an analysis. The 100 per cent and the 300 per cent are referred to as holding period return. They too are misleading because they grow with time.
That brings us to the first moral of computing return. Simple return is wrong; holding period return is misleading; go by compound rate of return only.
Suppose you want to make an estimate of future rate of return of a stock. One way of doing so, in the absence of the crystal ball, is to look at the past rate of return as an indicator of the future. Here’s how the return is computed in this case.
Consider a stock, A Ltd, whose return during each of the last five years has been 10 per cent, 20 per cent, 15 per cent, minus 30 per cent and 20 per cent per annum. Hence its simple average, also known as Arithmetic Mean, is 7 per cent per annum. Consider another stock, B Ltd, whose return during the last five years has been 10 per cent, 15 per cent, 20 per cent, 10 per cent and minus 20 per cent. Its simple average return too is 7 per cent per annum. So should we say that they are identical performers? Surprisingly, the answer is ‘No’. Here’s why.
If the stock price of A Ltd began at Rs 100, it would have grown to Rs 110, Rs 132, Rs 151.8, Rs 106.26 and Rs 127.51 at the end of each of the five years. Rs 100 growing to Rs 127.51 is a compounded rate (CARG) of 4.98 per cent using the compound interest rate formula. Similarly Y Ltd, which began at Rs 100 at the beginning of the first year, would have sequentially grown to Rs 110, Rs 126.5, Rs 151.8, Rs 166.98 and Rs 133.54 at the end of each of the five years. Rs 100 growing to Rs 133.58 is a compounded rate of 5.96 per cent.
Clearly, Rs 100 growing to Rs 127.51 is not the same as Rs 100 growing to Rs 133.58. Yet CARG, also called geometric mean, suggests exactly that. We already know that the 7 per cent return called Arithmetic Mean is incorrect. So what should we consider? While the geometric mean is considered the right measure of return, the arithmetic mean is used for purposes of projecting the expected return on a stock. The logic runs thus: The geometric mean is relevant only to the investor who buys, goes to sleep for five years and wakes up five years later — long term investors. As most investors are not of that kind, the arithmetic mean is relevant. For instance, in the case of Stock A, an investor has the opportunity to make 10 per cent, 20 per cent, 15 per cent, -30 per cent and 20 per cent. Hence the expected return is 7 per cent.
That brings us to the second moral of return. In making an estimate of future return, arithmetic mean, rather than the more sophisticated geometric mean, is adopted.
Actually, computing returns is not complicated, especially if you use spreadsheets. Once you have laid out the cash flow, you can calculate the compounded rate of return using a tool called internal rate of return (IRR) in the spreadsheet. Let’s take an example.
Bought 100 shares in January 2004 Rs 150
Dividend per share in each year end Rs 12, Rs 15, Rs 10 and Rs 8 per share
Rights offer 1:2 in December 05 at Rs 100
Bonus 1:1 in December 06
Market price 2007 end Rs 125
The cash flows appear as under during the period from January 2004 to December 2007 (Table)
The IRR works out to 27 per cent.
There is, however, a major catch here. Without getting into the details, let me tell you that the above computation assumes that the in-between cash flows that you received, namely the dividends, are also reinvested at 27 per cent. If those cash flows are actually reinvested at a lower rate, the IRR is overstated. That brings us to the third moral of return. Return is always the IRR. But you have to use it with care, especially when it is high. That’s because the computation assumes reinvestment at IRR.
With so many rates — simple interest, compound interest, holding period, arithmetic mean, geometric mean, IRR — floating around, it is important to know what each stands for, how to compute them, where they are useful and when they are misleading.
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