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# Valuing super normal growth

Dec 8, 2001

In the previous article , we had seen how to put a measure to the growth expectations embedded in a stock price. In this article we attempt to price a stock, which is expected to show very steep earnings growth. We came across very simple formulae, for determining the price of a stock. If g is the assumed growth for of the dividend over a course of time, the value of the stock is determined by

D P0 = ---- r-g Where Po= expected price D = Dividend paid out at the end of the year r = Expected returns g = Perpetual growth rate of dividends being paid

However, the problems here are twofold. Firstly, the growth rate is not constant and can vary significantly year to year. For example, Infosys grew by more than 100% in FY01 but the growth for FY01 is expected to be 30%. Secondly, the value of g is more than r and therefore, the formulae cannot handle this calculation.

Thus, the best method to arrive at a price is to estimate expected the dividends for every year for those years in which supernormal growth is expected and then to assume a perpetual growth rate. This is because a steep or supernormal growth cannot last forever. Eventually, the growth figure will fall in line with the GDP growth rate of the major economy in which the business operates. Otherwise eventually the business will become bigger than the economy.

Thus, the value of a stock is the present value of the expected future dividends. To recall

D1 D2 D3 D4 Dn + Pn P0= ---- + ------ + ----- + ----- + ........ ----------- (1+r) (1+r)2 (1+r)3 (1+r)4 (1+r)n

Here, future dividends are estimated based on the growth expectations.

D1 D1(1+g2) D2(1+g2) D3(1+g3) Dn/(r-g) P0= ---- + ----------- + ----------- + ---------- + ... ---------- (1+r) (1+r)2 (1+r)3 (1+r)4 (1+r)n

The dividends after a foreseeable period of time are expected to grow at a constant growth rate perpetually.

Thus, the variable that becomes most critical in the calculation is growth. Estimating growth rates accurately would give an accurate idea about the value of the stock. The growth rates can be assumed by looking at past data, macro economic numbers, industry growth rates, relative market share data and other qualitative aspects.

 Year EPS DPS Payoutratio EPSgrowth DPSgrowth FY94 1.2 1.8 143.4% - FY95 2.0 2.3 111.9% 64.8% 28.6% FY96 3.2 2.5 78.6% 58.2% 11.1% FY97 5.1 2.8 54.0% 60.1% 10.0% FY98 9.1 3.0 32.9% 79.4% 9.1% FY99 20.7 3.8 18.1% 126.8% 25.0% FY00 43.2 4.5 10.4% 108.7% 20.0% FY01 94.2 10.0 10.6% 118.0% 122.2%

Let us take the example of Infosys here. Infy's dividends in the past 8 years have grown at a CAGR of 30.8%. However, this is due to the spike (115% growth) in FY00. The CAGR growth rate from FY94 to FY00 for dividends works out to be 13.5%. This should give a good idea about what kind of growth rates to expect from the company under normal circumstances.

However, considering the fact that Infosys has established a strong brand for itself, the company is expected to beat industry growth rates and continue to grow swiftly till it reaches substantial market penetration. Infosys, in FY01, with revenues of around US\$ 367 m had a 0.1% market share of the US\$ 367 bn services market. IBM that has had revenues of US\$ 14 bn from services in the US (10% market share) is expected to post a growth of about 7.5% in services revenues for FY01.

For the next three years considering that the US economy revives, Infosys the dividends can be expected to grow at a rate of around CAGR 30%. However, for the next five years after that assuming that revenue growth starts to decline the dividend growth could be expected to taper.

Then we have assumed the growth to be in the range of 15% between (FY08 to FY011). Growth after this has been taken to be 10% for the next three years. Finally, the company is expected to grow perpetually at 5% in the future.

 Year EPS(Rs) DPS(Rs) Payoutratio EPSgrowth DPSgrowth Presentvalue (Rs) FY02E 124 15.0 12.1% 31.8% 15 FY03E 175 26.2 15.0% 40.5% 74.5% 23 FY04E 254 44.5 17.5% 45.7% 70.0% 34 FY05E 330 66.1 20.0% 30.0% 48.6% 43 FY06E 413 92.9 22.5% 25.0% 40.6% 53 FY07E 496 123.9 25.0% 20.0% 33.3% 62 FY08E 570 156.8 27.5% 15.0% 26.5% 68 FY09E 656 196.7 30.0% 15.0% 25.5% 74 FY10E 754 245.0 32.5% 15.0% 24.6% 80 FY11E 867 303.4 35.0% 15.0% 23.8% 86 FY12E 954 357.6 37.5% 10.0% 17.9% 88 FY13E 1,049 419.6 40.0% 10.0% 17.3% 90 FY14E 1,154 490.4 42.5% 10.0% 16.9% 92
(Note the expected returns have been assumed to be 15%)

At the end of FY14, the company's dividends are expected to be Rs 490. Assuming the dividends continue to grow perpetually at the rate of 3%, value of the stock based on stable growth in FY14E would be Rs 4, 083. The present value of this works out to be Rs 664. Thus the total value of the stock comes to around Rs 1,472.

However, the stock currently is trading at a price of Rs 4,533 this works out to be a premium of about 208%. There are certain reasons for which the company commands higher valuations, which could be management quality and transparency. Also another factor contributing to he high price of the stock is sentiment. The markets could be expecting a recovery in the technology sector and even stronger growth rates from the company. However, the theoretical calculations could give you an idea about how low the stock price can move. Post September 11, in the free fall the company touched a low of Rs 2,156.

A significant part of the price is derived from the company's stable growth rate in the future. For our calculations we have assumed a very conservative 3%. To justify the current stock price (Rs 4,533) the perpetual growth rate required (consequent to above mentioned growth rates) is 12.9%. The question is what says the company will be able to manage such a fast growth rate? The S&P 500 between 1925 and 1995 has grown at a CAGR of 10%. This growth rate suggests a price of Rs 2,467.

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