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Stocks: Measuring expectations

Nov 3, 2001

The most mysterious thing especially with the software stocks has been their price. The price of a security can be broadly divided into two elements viz. the intrinsic value of the stock and the speculative element. But from the point of view of making a long-term investment, and not punting, it is the intrinsic value that ultimately matters. Arriving at the intrinsic value is, however, of little help as many times the stocks are nowhere near their correct valuations and in recent times speculative element in stock price has increased considerably. The idea of this report is to help you evaluate whether market assumptions that go into pricing of the stock are realistic or not. The attempt is not to put a correct price to the stock.The price of a stock is fundamentally based on two components. The future cash flow from expected dividends and the expected capital gains on the stock.

(P1-P0)As expected return (r) = D1/P0 + -------- P0Where, D1 = Divided expected P1= Price at end of year oneP0= Current market price D1 + P1Rearranging we get, P0 = --------- 1 + r

P1 would again depend on the next years expected dividend and the stock price at the end of year two so on and so forth.

D1 D2 D3 D4 Dn + PnP0= ---- + ------ + ----- + ----- + ........ ----------- (1+r) (1+r)2 (1+r)3 (1+r)4 (1+r)n

Thus, the current stock price is nothing but the present value of the dividends and the future market price at a terminal date. To arrive at a stock price we need to know the future price, the expected rate of return and the expected dividend.

Estimating the required rate of return
The key variable here is r, the expected return. The value of r, i.e. expected return will vary according to the risk perception regarding the company in question. More the risk more the return will be expected.

To determine expected return the risk profile of the individual stock is to be measured. The benchmark against which risk for an individual stock is measured is the equities market as a whole represented by indices like DIJA (Dow Jones Industrial Average), BSE Sensex and NSE Nifty. By plotting the returns of a particular stock against the index, the sensitivity of a stock to that particular market can be measured. This measure is known as the Beta or sensitivity of the stock to the market. If the beta is less than one then the stock is less prone to factors affecting the market as a whole. If the beta is more than one the stock price is very sensitive to events in the market.

The expected return can be calculated using the capital asset pricing model (CAPM). According, to the CAPM, the expected risk premium on a stock is the market risk multiplied by beta or the sensitivity. Thus, we can conclude higher the value of beta higher the sensitivity and higher the expected risk.

Expected risk premium (Rp) = beta * (Rm - Rf)Where, Rm = Return on markets Rf = Risk free rate of return

Once we have estimated the risk premium, all we need to do is add the risk free rate of return to the risk premium to get the expected return on the stock. As the risky investment will provide for returns at least equal to risk free investments and additional returns, which are proportional to the risk profile of the investment.

Thus, expected return r = Rf + Rp

For the risk free returns Government security yields can be used. Thus, for Infosys the expected rate of return was 21.1%.

CompanyRisk free
return ( r )
As per company's FY01 balance sheet.
*Yeild on Government securities dated 2021

Estimating the terminal price
It has been observed that over longer period of time the dividend component of a stock price is far greater than the present value of the future price. Thus, for simplicity's sake we will assume that the stock price is a function of the dividends only and neglect the terminal price.

The stock price therefore is the present value of dividends paid out by the company. Assuming constant dividends for simplicity the stock price is now the present value of a perpetuity discounted at r or the expected rate of return.

Thus, D P0 = --- r

If g is the assumed growth for of the dividend over a course of time, the value of the stock price changes to

DP0 = ---- r-g

Rearranging the previous equation would give us a very interesting interpretation of the expected rate of return.

Thus, r = D + g -- P0

The expected return therefore is a combination of the dividend yield and expected growth. We often use terms like growth and income stocks. The stocks, which derive a greater component of their price from dividend yield, are income stocks. While stocks that largely owe their price to growth expectations are growth stocks.

Infosys is expected to pay Rs 15 in dividends this year. At the current market price of Rs 2,956, this works out to be 0.5%. Thus, remaining 20% return is expected from the growth in the business. On the other hand HLL is expected to give a dividend of Rs 4.5 in FY02. The company's cost of equity works out to be 19.7%. Consequently, the implicit growth rate is 17.6%.

To estimate the expected growth rate in a stock price we have to delve a bit deeper. Assume that the company does not see any growth in the future and pays out all its earnings as dividends. In such a case DPS (dividend per share) = EPS (earnings per share).

Thus, DPS r = -------- P0Rearranging we get DPS EPSP0 = ----- = ------- r r

Infosys is expected to earn an EPS of Rs 124 in FY02. Therefore, the price of the stock assuming no growth and cost of equity as 21.0% would be Rs 589. Of the current market price Rs 2,956, Rs 589 is on assumption that the company will continue to have a constant EPS (no growth) of Rs 124 for a considerable period of time in the future.

Thus, Rs 2,368 in the price is due to the present value of the growth. The company pays dividend of Rs 15 and therefore the money ploughed back into the business is Rs 109. With a return on equity of 36.4% this investment is expected to generate Rs 40. Assuming that the investment generates Rs 40 every year

(40) NPV = -109 + ------ = Rs 80 0.21

Returns on growth oppurtunity
Div for FY02E (Rs) 15
Money ploughed back 109
Cash in flow from investment of Rs 108 40
NPV of this investment 80
Thus the price due to growth, NPV PO = ----- r - g 802,368 = ------- 0.21- g

Solving for g we get a growth rate of 17.3% embedded into the stock price. Of course this growth rate is for a considerable period of time. However, any deviation in growth rates from this estimated (towards the downside) in the near future would adversely impact the stock price. According to Gartner, markets for IT services are expected to grow at a CAGR (compounded annual growth rate) of 16%, from a size of US$ 749 bn in FY01 to US$ 1,174 bn in 2004.

In Satyam's case assuming a cost of capital to 24.9%, and an estimated EPS of Rs 52 for FY02 the price considering no growth comes to around Rs 208. However, the stock is trading at Rs 146, as on a consolidated basis it is making losses.

Before concluding we would like to make a point, i.e. companies like Infosys have shown a supernormal growth rates of 100%, which is not sustainable over a long period of time. Eventually, the growth rates fall in line with the growth in GDP and therefore, a growth rate for perpetuity is the growth rate of the global GDP. This is a single digit growth figure, which is below 5%. The decision that has to be made now is will Infosys be able to grow at 17% for the foreseeable future? And will Dr. Reddy be able to grow at 12% for a considerable period of time? This will help you determine the price of the stock is realistic or not.

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