**RELATIVE VALUATION MODELS**

When a firm has grown to a size that the ‘rule of thumb’ approaches are no longer appropriate then some form of market based pricing methodology must be used. The principle here is to find some common variable within companies which appear to be consistently priced by the capital market. As expected, there are a large number of such variables including annual earnings, sales turnover, book value, fixed asset value, and net worth. The variable to be used depends on the type of the company. The three most commonly used in practice are:

- Price Earnings (P/E) multiples
- Market to net worth (Tobin’s Q)
- Market to book (M/B) value ratios

**102.2.1 Price Earnings Multiples**

The price earnings ratio is calculated as the ratio of the price per share divided by the underlying earnings per share. Normally a company publishes its earning per share under a number of different bases: basic earnings per shares which is simply the published earnings divided by the numbers of shares in issue. If the company has a number of share options in issue to its employees and directors then it will also produce a ‘diluted’ earnings per share calculated on the basis that all options are taken up.

Different variants of the PE ratio can be used by analysts. Some prefer to use a historical PE using the average of quoted figures over the last 12 months. This historical or ‘trailing’ PE ratio is claimed to remove price ‘noise’ (the random fluctuation) from the share price. Other analysts prefer a ‘leading’ PE ratio being the estimate from forecasts of the next twelve months earnings figures.

The magnitude of the PE ratio indicates the degree of volatility attaching to the firm’s earnings stream. A low ratio suggests a low value is being placed on the earnings stream and hence (other things being equal) the higher its volatility and vice versa.

**The Challenges to using PE methods**

The challenges to using the PE method are as follows:

**First**it is reliant upon an accounting estimate of earnings. As we outlined earlier, the accounting model makes a number of assumptions about the temporal matching of cash flows to time periods which even though firms may be acting quite consistently in their application of the Generally Accepted Accounting Principles (GAAP) can result in quite different outcomes across and between industries.**Second**, is that the model avoids the valuation issue in that it is transferring the problem of valuation to the market in assuming that a benchmark PE say for the market as a whole, or a industrial segment, however constructed, represents an appropriate price for earnings either across the market or across the industry.**Third**, it assumes that the market does in fact value earnings rather than some other aspect of the companies financial output such as dividends, or growth in earnings or indeed risk and the market is an efficient market.

**102.2.2 Market to net worth (Tobin’s Q)**

This particular ratio has an impeccable academic pedigree. It was first proposed by the ** Nobel Prize winning economist James Tobin in 1969** and since that time has developed a small but influential following. Its principle advantage as a metric is that it would appear to allow us to determine whether a market is over or undervalued although its use at the individual stock level is more questionable.

Tobin defined Q as the ratio of total capital value (equity plus debt) to the replacement (or reproduction cost) of all capital market assets. The long run equilibrium for this ratio is one. Taking this ratio to the firm level:

Following Modligliani and Miller’s proposition 1 that total market capitalisation is the sum of the value of equity and the value of debt then an ‘equity version of Q can be defined as:

When viewed this way all that Tobin’s Q is saying is that the rate of return the firm generates on the replacement cost of its net assets is equal to the rate of return required by equity investors. To see this let us assume that the market value of the firm’s equity is the capitalised value of the economic earnings of the business (E):

However, the economic profit of the business is the replacement cost of the firm’s net assets (C

_{R}) multiplied by the rate of return on that invested capital (r

_{RC}):

As a result Q becomes:

If Q = 1, then this ratio simply asserts that at long run equilibrium the rate of return on invested capital must equal the firm’s cost of capital (i.e., the required rate of return on equity) or, to put it another way, the rate of return on new capital invested in firms (the internal rate of return on the capital invested) is equal to the rate of return on existing capital traded in the market (the required rate of return on equity). We have met this concept already in that in the long run the net present value of internal investment is driven down to zero i.e., the point at which the internal rate of return on the firm’s investments equals the firm’s cost of capital. This is an important (if rather unsurprising result) for reasons we return to when we discuss the problems of estimating the growth rate of the firm.

To what extent can Tobin’s Q and the implied relationship between equity value and a firm’s net worth be used for prediction purposes?

**have conducted studies into the properties of their equity version of Q. They demonstrate that over time, and at the level of the market Q exhibits strong mean reversion. This is what we would expect if at the market level the internal rate of return on invested capital was markedly different from the prevailing market required rates of return. Firms that earned greater than the market rate would attract investors and hence their equity prices would rise, and firms earning a lower than market rate would find their share price falling.**

*Smithers and Wright (2000)*There is some evidence that Q is also a superior leading indicator for share price changes than either the P/E ratio (where earnings is the fundamental lead indicator) or dividend yield (where dividends are the fundamental lead indicators). In causality tests Smithers and Wright report that net worth (the fundamental in the Q ratio) has only a 1.4per cent probability of no predictive power, whilst dividends and earnings have 43.8 per cent and 88.6 per cent probability respectively. They also found that net worth only really works as a predictor when used as a ratio with equity value rather than on its own.

**In practice,**the application of Tobin’s Q invariably relies upon the use of accounting information as a proxy for replacement cost. This leads to the more measurable market to book ratio.

**102.2.3 Market to book (M/B) value ratios**

The market to book ratio is a pragmatic interpretation of Tobin’s Q. This ratio assumes that there is a consistent relationship between market value and the net book value of the firm, or to put it another way that the market prices one Unit (pound, dollar, shilling, dinar, riyal,dirham) of book value in one firm, the same as in another.

**Summary and Conclusion**

Like with all other valuation methods, this method is suited to particular situations and has fundamental assumptions, which need to hold true, which would due to market inefficiencies not always hold true. Therefore it is an indicative value subject to negotiation. It should be noted that the concept can be applied to valuation of non-quoted companies too.