 # Computing ‘growth rates'

| Updated on May 21, 2011  ## Understanding growth rate helps you make informed investment decisions.

Very often, we are advised not to be tempted by short-term out performance/underperformance and instead take a long-term view of our investments. “Longer the Better” is certainly a guiding dictum in investment analysis. This means that the investors need to look at the long-term trend in returns generated by the asset class they choose to invest in, before parking their hard-earned money in them.

But, how do you find out the long-term track record of returns produced by a stock? Here, an investor can make use of either “the simple average method” or the “compound growth rate method” in arriving at the growth rate.

### The Simple Average Growth Rate

Suppose an investor decided to buy the Infosys stock on May 4, 2011. Let us find out how to calculate the simple average growth rate for the Infosys stock from, say, a three-year perspective. First, get the price at which the stock was trading on the very same day in each of the three previous years.

The closing price of Infosys at the National Stock Exchange on a 3 year horizon as follows: May 4, 2008: Rs 1,787.45; May 4, 2009: Rs 1,628.20; May 4, 2010 – Rs 2,666.15; May 4, 2011 – Rs 2,869.75.

Next, arrive at the yearly returns for each of the three years. For instance, for the first year (May 4, 2008 to May 4, 2009) the yearly return is a loss of Rs 159.25. This can be expressed in percentage terms as [1,787.45-1,628.20]/ 1,787.45, which results in a loss of 8.9 per cent Likewise, the yearly returns for 2009-10 comes to 63.75 per cent; for 2010-11, it stands at 7.64 per cent.

That done, you must now compute the average of the yearly returns; The simple total of the yearly notional returns generated by the Infosys stock for the above-mentioned investment horizon of 3 years = [-8.91]+63.75+7.64 = 62.48.

If the sum of the three year returns is divided by 3 years, then we can obtain the simple average growth rate [in terms of notional returns]of Infosys. Here it is [62.48]/3 = 20.83 per cent.

The drawback of this method is that the result is impacted by extreme numbers. In this case, the yearly return of 2009-10 and that of 2008-09 are two extreme numbers, which impact the result on two different directions. Hence the resulting number does not talk about the real average growth rate. This leads to the usage of the compounded annual growth rate method.

### Compounded Annual Growth Rate (CAGR)

This method is based on the time value of money (i.e. value now vs. value a few years later), which states that the value of money keeps declining over the passage of time due to inflation and the opportunity returns lost by not deploying the funds in a productive manner.

So, the CAGR method answers the question “For a present value of Rs 1,787.45 (which the share price as on May 4, 2008), what is the notional rate of return that results in a future value of Rs 2,869.75 (share price as on May 4, 2011) in a three year investment horizon?”

The formula for calculating this is: Future Value = Present Value [1+growth rate] ˆnumber of years. Future value in our example is Rs 2,869.75. Present Value in the case is Rs 1,787.45; number of years = 3; if we apply the given numbers for a “growth rate” on a trial and error basis, we will get growth rate as 17 per cent. At this rate, the present value approaches the future value.

Though this method is little complicated, it gives the annualised growth rate in notional returns after taking into account of the effect of compounding. The three and five year returns that mutual funds give out for every fund, is actually their CAGR.

But the disadvantage of this method is that its result is subject to the bias based on a very high or very low first or last year or both first and last year numbers. In such cases, the investors can make use of the simple average growth rate.

### Implied growth rate

Going a step further, if the investors want to know at what rate of growth a company can grow without mobilising additional equity capital, they then have to employ the implied growth rate. It is computed by multiplying the return on equity (ROE) by the profit retention rate (computed as 1- Dividend Payout Rate).

For Instance, if the ROE of Infosys is 20 per cent and its Dividend Payout Rate is 20 per cent, then its implied growth rate is 0.2*[1-0.2] = 0.16*100 = 16 per cent. It communicates to the investors that if Infosys has to fund its expansion requirements without mobilising additional equity capital, then it has to earn a minimum ROE of 20 per cent and maintain its dividend payout at a maximum of 20 per cent.

Thus, we can conclude that it is essential for an investor to understand the above stated measures of growth in order to take sound and successful investment decisions. Like the teaching in the poem “The Road Not Taken”, past investment decisions after having turned out to be wrong, can never be turned around to be right.

(The writers teach Accounting and Finance courses at IIM-Shillong)

Published on May 21, 2011