# How do you compute long term returns from investments?

### Author: Jins Victor

Ideally, Long term returns from investments have to be computed using compound interest formula. That’s because of the longer time frame involved in these investments.

**Basics: **

The formula for compound return is as follows:

FV = P ( 1+ r) n |

- Where , FV is the future value
- P is the money invested
- r is the rate of return
- n is the number of years for which the amount is deposited.

**Situation1.**

You invest Rs 50,000 today and it grows to Rs 100,000 in five years. The five-year return is 100 per cent; but what is its annual return?

To calculate this, you need the formula on compound interest. Using Rs 50,000 as principal, Rs 100,000 as future value and five as the number of years, let’s find out the annual rate.

- FV = P (1+r) n
- Therefore, r = (FV/P) 1/n – 1
- Here, the first step is to calculate 1/n = 1/5 = 0.20
- Now, r = (50000/ 100000) .2 0 -1
- r = 2 .20 -1
- 2 .20 = 1.1487
- 1.1487- 1 = 0.1487

Therefore r as a percentage would be (0.1487 * 100 ) = 14.87 % . This 14.87 % is the compound return, and is the only relevant return when you analyse an investment.

If you divide the 100 percent by the number of years, you get the answer as 20%.This is the simple return.

The 100 per cent is referred to as holding period return. The holding period return keep on changing with the period of holding.

That brings us to the reason behind suggesting compound interest formula for computing long term return.

You can also use the rule 72 discussed elsewhere and arrive at the approximate rate of return since in this question, the investment has doubled in 5 years.

**Situation 2.**

Suppose you want to make an estimate of future rate of return of a stock. One way of doing so, 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 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 ( 100 * 110%) in the first year

Rs 132 (110 * 120% ) in the second year

Rs 151.80 ( 132 * 115% ) in the third year

Rs 106.26 (151.80 * 70%) in the forth year (the company grew at -30%)

Rs 127.51 (106.26 * 120%) in the final year.

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.

As you can see, although the simple average growth rate was the same for both the companies , applying compound interest formula gave more clarity as to which was the better performer. Rs 100 growing to Rs 127.51 is not the same as Rs 100 growing to Rs 133.58.

So, compounded annual growth is considered the right measure of long term return;