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Valuation of ordinary stocks on Ghanaian markets

Valuation of ordinary stocks is perhaps the single most important area of investment analysis that is common on the Stock Exchanges of less developed markets. Generally, analysts apply the so-called Gordon’s growth model as one of the discounted cash flow methods on such exchanges.

This is a natural consequence of simple assumptions that are made. Dividends in this model will increase at a constant growth rate. This model also involves the determination of the growth rate of the dividends. These methods as well as all discounted factor models are limited by the uncertainty in the parameter values used. In the face of these limitations it is the ingenuity of the Analyst that counts.

Selling shares of a company on a stock exchange like the Ghana Stock Exchange (GSE) is a means of transferring risk from entrepreneurs to investors and between investors. On the other hand hedging may be a means of reducing risk. For example a cocoa farmer in Tetteh Quarshie’s hometown may enter into an agreement with a chocolate manufacturer on the price of cocoa to be delivered at a future date. They both hedge their risks. But if the chocolate manufacturer on the basis of this expectation of cocoa beans lists her shares on the GSE she is transferring risk to other investors. But of course she bears some risk too.

Buying an ordinary share therefore transfers some rights to the buyer.

Depending on the terms of issue, the rights may include voting rights at the company’s AGM, the right to dividends and some rights to share in the profits of the company.

Ordinary shares may be attractive for several reasons including their limited liability and possible unlimited returns. In the case of liquidation of a company, shareholders may be liable for the unpaid element of their shares.

Ordinary shares are distinct from shares that serve as an underlying for a certain financial instrument. Popular models include options and futures traded on developed exchanges.

It is generally held that supply and demand drive the price of stocks. A decrease in demand for a stock, i.e. the decrease in investor’s favourable perception of a stock and research of investors and analysts all determine the demand of a stock.

Following the market equilibrium principle, stock prices are then fixed. This makes trading on exchanges an exercise in psychology. This is clear: economics, psychology and philosophy are all considered one branch of study. Faith and emotions of buyers and sellers based on information received determined the supply and demand levels.

On the basis of the simple driving processes of stocks, valuation models have been largely based on the discounted cash flow models without adequate regard to the random elements. It is in this sense that the Black-Scholes-Merton equation (BSM) becomes a valuable tool for Analysts in the valuation of stock prices, pure (ordinary) as well as derivative-based stocks.

This last assertion might raise some questions, e.g. BSM can never be used to valuate pure stock. These concerns are genuine ones. BSM (partial differential equation) is also to be distinguished from the BS formula which valuates European-style call prices.

Let us assume an Analyst defines a stock price process as a function of some variables like temperature of Mampong during the cocoa period, or the dividend paid by the company, or non-constant interest rate or of inflation. These may be treated as random variables that ought to be modelled as such. In the case of the price of cocoa there is a relationship between temperatures and cocoa production. The process followed by temperature is clearly not dependent on some human risk preferences. The market price of risk associated with this variable lends stock pricing to BSM. The argument from using the heat equation is obvious. Therefore, temperatures can be modelled using the heat equation of physics. BSM is a variant of heat equation.

By Paul A. Agbodza.

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