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How Much are These Shares Worth? – Models of Stock Valuation

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The debate rages all over Eastern and Central Europe, in countries in transition as well as in Western Europe. It raged in Britain during the 80s.

Is privatization really the robbery in disguise of state assets by a select few, cronies of the political regime? Margaret Thatcher was accused of it – and so were privatizers in developing countries. What price should state-owned companies have fetched? This question is not as simple and straightforward as it sounds.

There is a stock pricing mechanism known as the Stock Exchange. Willing buyers and willing sellers meet there to freely negotiate deals of stock purchases and sales. New information, macro-economic and micro-economic, determines the value of companies.

Greenspan testifies in the Senate, economic figures are released – and the rumour mill starts working: interest rates might go up. The stock market reacts with frenzily – it crashes. Why?

A top executive is asked how profitable will his firm be this quarter. He winks, he grins – this is interpreted by Wall Street to mean that profits will go up. The share price surges: no one wants to sell it, everyone want to buy it. The result: a sharp rise in its price. Why?

Moreover: the share price of a company of an identical size, similar financial ratios (and in the same industry) barely budges. Why not?

We say that the stocks of the two companies have different elasticity (their prices move up and down differently), probably the result of different sensitivities to changes in interest rates and in earnings estimates. But this is just to rename the problem. The question remains: Why do the shares of similar companies react differently?

Economy is a branch of psychology and wherever and whenever humans are involved, answers don’t come easy. A few models have been developed and are in wide use but it is difficult to say that any of them has real predictive or even explanatory powers. Some of these models are “technical” in nature: they ignore the fundamentals of the company. Such models assume that all the relevant information is already incorporated in the price of the stock and that changes in expectations, hopes, fears and attitudes will be reflected in the prices immediately. Others are fundamental: these models rely on the company’s performance and assets. The former models are applicable mostly to companies whose shares are traded publicly, in stock exchanges. They are not very useful in trying to attach a value to the stock of a private firm. The latter type (fundamental) models can be applied more broadly.

The value of a stock (a bond, a firm, real estate, or any asset) is the sum of the income (cash flow) that a reasonable investor would expect to get in the future, discounted at the appropriate rate. The discounting reflects the fact that money received in the future has lower (discounted) purchasing power than money received now. Moreover, we can invest money received now and get interest on it (which should normally equal the discount). Put differently: the discount reflects the loss in purchasing power of money deferred or the interest lost by not being able to invest the money right away. This is the time value of money.

Another problem is the uncertainty of future payments, or the risk that we will never receive them. The longer the payment period, the higher the risk, of course. A model exists which links time, the value of the stock, the cash flows expected in the future and the discount (interest) rates.

The rate that we use to discount future cash flows is the prevailing interest rate. This is partly true in stable, predictable and certain economies. But the discount rate depends on the inflation rate in the country where the firm is located (or, if a multinational, in all the countries where it operates), on the projected supply of and demand for its shares and on the aforementioned risk of non-payment. In certain places, additional factors must be taken into account (for example: country risk or foreign exchange risks).

The supply of a stock and, to a lesser extent, the demand for it determine its distribution (how many shareowners are there) and, as a result, its liquidity. Liquidity means how freely can one buy and sell it and at which quantities sought or sold do prices become rigid.

Example: if a controlling stake is sold – the buyer normally pays a “control premium”. Another example: in thin markets it is easier to manipulate the price of a stock by artificially increasing the demand or decreasing the supply (“cornering” the market).

In a liquid market (no problems to buy and to sell), the discount rate is comprised of two elements: one is the risk-free rate (normally, the interest payable on government bonds), the other being the risk-related rate (the rate which reflects the risk related to the specific stock).

But what is this risk-related rate?

The most widely used model to evaluate specific risks is the Capital Asset Pricing Model (CAPM).

According to it, the discount rate is the risk-free rate plus a coefficient (called beta) multiplied by a risk premium general to all stocks (in the USA it was calculated to be 5.5%). Beta is a measure of the volatility of the return of the stock relative to that of the return of the market. A stock’s Beta can be obtained by calculating the coefficient of the regression line between the weekly returns of the stock and those of the stock market during a selected period of time.

Unfortunately, different betas can be calculated by selecting different parameters (for instance, the length of the period on which the calculation is performed). Another problem is that betas change with every new datum. Professionals resort to sensitivity tests which neutralize the changes that betas undergo with time.

Still, with all its shortcomings and disputed assumptions, the CAPM should be used to determine the discount rate. But to use the discount rate we must have future cash flows to discount.

The only relatively certain cash flows are dividends paid to the shareholders. So, Dividend Discount Models (DDM) were developed.

Other models relate to the projected growth of the company (which is supposed to increase the payable dividends and to cause the stock to appreciate in value).

Still, DDM’s require, as input, the ultimate value of the stock and growth models are only suitable for mature firms with a stable, low dividend growth. Two-stage models are more powerful because they combine both emphases, on dividends and on growth. This is because of the life-cycle of firms. At first, they tend to have a high and unstable dividend growth rate (the DDM tackles this adequately). As the firm matures, it is expected to have a lower and stable growth rate, suitable for the treatment of Growth Models.

But how many years of future income (from dividends) should we use in our calculations? If a firm is profitable now, is there any guarantee that it will continue to be so in the next year, or the next decade? If it does continue to be profitable – who can guarantee that its dividend policy will not change and that the same rate of dividends will continue to be distributed?

The number of periods (normally, years) selected for the calculation is called the “price to earnings (P/E) multiple”. The multiple denotes by how much we multiply the (after tax) earnings of the firm to obtain its value. It depends on the industry (growth or dying), the country (stable or geopolitically perilous), on the ownership structure (family or public), on the management in place (committed or mobile), on the product (new or old technology) and a myriad of other factors. It is almost impossible to objectively quantify or formulate this process of analysis and decision making. In telecommunications, the range of numbers used for valuing stocks of a private firm is between 7 and 10, for instance. If the company is in the public domain, the number can shoot up to 20 times net earnings.

While some companies pay dividends (some even borrow to do so), others do not. So in stock valuation, dividends are not the only future incomes you would expect to get. Capital gains (profits which are the result of the appreciation in the value of the stock) also count. This is the result of expectations regarding the firm’s free cash flow, in particular the free cash flow that goes to the shareholders.

There is no agreement as to what constitutes free cash flow. In general, it is the cash which a firm has after sufficiently investing in its development, research and (predetermined) growth. Cash Flow Statements have become a standard accounting requirement in the 80s (starting with the USA). Because “free” cash flow can be easily extracted from these reports, stock valuation based on free cash flow became increasingly popular and feasible. Cash flow statements are considered independent of the idiosyncratic parameters of different international environments and therefore applicable to multinationals or to national, export-orientated firms.

The free cash flow of a firm that is debt-financed solely by its shareholders belongs solely to them. Free cash flow to equity (FCFE) is:

FCFE = Operating Cash Flow MINUS Cash needed for meeting growth targets

Where:

Operating Cash Flow = Net Income (NI) PLUS Depreciation and Amortization

Cash needed for meeting growth targets = Capital Expenditures + Change in Working Capital

Working Capital = Total Current Assets – Total Current Liabilities

Change in Working Capital = One Year’s Working Capital MINUS Previous Year’s Working Capital

The complete formula is:

FCFE = Net Income PLUS

Depreciation and Amortization MINUS

Capital Expenditures PLUS

Change in Working Capital

A leveraged firm that borrowed money from other sources (even from preferred stock holders) exhibits a different free cash flow to equity. Its CFCE must be adjusted to reflect the preferred dividends and principal repayments of debt (MINUS sign) and the proceeds from new debt and preferred stocks (PLUS sign). If its borrowings are sufficient to pay the dividends to the holders of preference shares and to service its debt – its debt to capital ratio is sound.

The FCFE of a leveraged firm is:

FCFE = Net Income PLUS

Depreciation and Amortization MINUS

Principal Repayment of Debt MINUS

Preferred Dividends PLUS

Proceeds from New Debt and Preferred MINUS

Capital Expenditures MINUS

Changes in Working Capital

A sound debt ratio means:

FCFE = Net Income MINUS

(1 – Debt Ratio)*(Capital Expenditures MINUS

Depreciation and Amortization PLUS

Change in Working Capital)

Sam Vaknin ( http://samvak.tripod.com ) is the author of Malignant
Self Love – Narcissism Revisited and After the Rain – How the West
Lost the East. He served as a columnist for Central Europe Review,
PopMatters, Bellaonline, and eBookWeb, a United Press International
(UPI) Senior Business Correspondent, and the editor of mental health
and Central East Europe categories in The Open Directory and
Suite101.

Until recently, he served as the Economic Advisor to the Government
of Macedonia.

Visit Sam’s Web site at http://samvak.tripod.com

How Much are These Shares Worth? – Models of Stock Valuation
About Sam Vaknin
Sam Vaknin ( http://samvak.tripod.com ) is the author of Malignant Self Love - Narcissism Revisited and After the Rain - How the West Lost the East. He served as a columnist for Central Europe Review, PopMatters, Bellaonline, and eBookWeb, a United Press International (UPI) Senior Business Correspondent, and the editor of mental health and Central East Europe categories in The Open Directory and Suite101.

Until recently, he served as the Economic Advisor to the Government of Macedonia.

Visit Sam's Web site at http://samvak.tripod.com WebProNews Writer
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  • Guest michael

    what is the worth of  20 shares of Dun&bradstreet stock purchased in 1965 in today market the simbol is DNB

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