For many years, a particular criticism was levelled at the accounting profession. This referred to the fact that there was no clear relationship between the numbers published in companies’ annual financial statements, and the values placed on those companies by the market.

This is not to say that accountants hadn’t considered the problem and come up with a few ideas. For example, once it was agreed that the market price of a share should reflect the ’present value’ of future cash flows accruing to that share, the Dividend Discount Model was developed. So, if one knew the percentage return required by shareholders, and could forecast one future dividend as well as the rate at which dividends would grow in the future, this information could be used to predict share prices.

Yet others recognised that this model could be applied to the firm as a whole, so that even if a company did not pay dividends, its annual ‘free cash flow’ (FCF) could be taken as a substitute. FCF is the cash profit left over for shareholders (before dividend payments), and if the required rate of return is known, and future FCFs and the rate of growth in those FCFs can be predicted, the market value of equity can be estimated.

All good and well, but this did leave a lot to the predictive powers of the forecaster. And how did one value companies that did not pay dividends, or were making losses and not generating positive FCFs? These were the problems facing accountants in the early 1990s, until in 1995 an academic named James Ohlson from Columbia University proposed a solution.

Ohlson formulated a simple-looking model (based on some complex-looking maths), that built upon the classic work produced by Modigliani and Miller in 1958 and 1961. As such, it incorporated aspects of the dividend discount model and the FCF model, yet went one step further. The model relies exclusively upon financial statement information, and can be expressed as follows:

MVt = Et + BVt-1 + AEt + Vt

Where:

MVt = Cum-dividend market value of the company at end of year t

Et = Earnings for current year t (calculated on a ‘clean surplus’ basis, and taken from the income statement, or the statement of changes in equity [and excluding dividends declared])

BVt-1 = Beginning of year book value of equity for year t (taken from the balance sheet)

AEt = Abnormal Earnings for year t

Vt = Non-accounting, value-relevant effects

There are also certain key assumptions upon which the model is based:

- The clean surplus figure (‘earnings’) represents comprehensive income, i.e. not income from operations, or net income before extraordinary items etc. Comprehensive income, therefore, refers to income for the year from all sources, after interest and tax but before dividend payments.
- Abnormal earnings (AE) refer to those earnings for the year which exceed the shareholders’ expected rate of return, and which are included in current year earnings. For example, if a company has a beginning net book value of R100 million, and a required rate of return on equity of 10%, normal earnings for the year would be R10 million (10% x R100m). However, if earnings for the year were R13m, R10m would be shown as earnings and R3m as abnormal earnings.
- The model includes value-relevant information beyond earnings, book value, and dividends (Vt). Ohlson notes that some value-relevant events may affect future expected earnings as opposed to current earnings. That is to say, accounting measurements may incorporate some value-relevant events, but only after a time delay.
- Dividends reduce (are paid out of) current book value, and do not affect current earnings.
- Dividends displace market value on a rand-for-rand basis, so that dividend payment irrelevancy applies.
- Ohlson’s model is consistent with the logic of the dividend discount model and the FCF valuation model.

This might all be a bit confusing, so we’ll now look at a simple example to illustrate the implications and workings of the model.** **

**How Ohlson’s valuation model works**

Let us assume that the company being examined has normal earnings, i.e. the annual clean surplus is exactly equal to the return required by shareholders (10%), and there are no excess returns. An annual 10% of beginning NBV is paid at the end of the year as a dividend. Market value of R100m is exactly equal to the NBV of the firm at t-1, which is also equal to the present value of all future dividends (as shown below). This implies that there are no non-accounting information issues affecting market value.

The current cum-div market value of the company can now be calculated, using the above-mentioned formula:

MVt = Et + BVt-1 + AEt + Vt

Where:

MVt = Cum-dividend market value of the company at end of year t

Et = Earnings for current year t (calculated on a ‘clean surplus’ basis)

BVt-1 = Beginning of year book value for year t

AEt = Abnormal Earnings for year t

Vt = Non-accounting, value-relevant effects

So: R110m = R10m + R100m + 0 + 0

However, once the dividend is paid, the cum-dividend share price will be reduced by the amount of the dividend (as happens in practice), and the market capitalisation of the company will remain stable at R100m. Prior year NBV will also be reduced by the dividend payment, going from R100m to R90m, but will increase by the R10m clean surplus for the year, taking the NBV back to R100m.

The implications of this calculation are that, for a firm that has stopped growing, the market value of the firm = the NBV of the firm as shown by the balance sheet.

This can also be confirmed by way of the Dividend Discount Model, set out below:

P0 = D1 / (r-g)

Where:

P0 = Current share price (Say, at yt-1)

D1 = Next dividend (Say, at yt)

r = Required rate of return on equity (expressed as a decimal fraction)

g = Annual growth rate (expressed as a decimal fraction)

So, given the above-mentioned total dividend of R10m at Yt, a zero growth rate, and a required rate of return of 10%, the market value of equity at yt-1 would be:

R10m / (0.10 – 0) = R100m

So we can see that, as stated by Ohlson (1995), for a non-growth company the market value of equity is equal to the present value of expected future dividends, as well as to the NBV of equity. It also confirms the principle that dividend payments reduce the NBV, whereas the annual clean surplus increases the NBV. **Implications for investors**

One of the big problems we have is that, while it makes absolute sense that share prices should represent the present value of future cash flows, we don’t know if they actually do so in practice. Because there is no crystal ball to accurately predict future dividends and cash flows, we will never be able to test Ohlson’s theory.

As things stand, to predict market values of equity, Ohlson’s formula uses actual accounting numbers on the right-hand-side of the equation, except for the last item, a number which represents the value of non-accounting, value-relevant information. That one item will capture the difference between the actual market value of a firm, and the value suggested by Ohlson’s other three terms, but no-one has any idea of how to determine a value for Vt.

This is not to say that Ohlson’s insights do not have value. If a company has reached maturity and is no longer growing, then it would be foolish to pay more than the NBV per share. In fact, any share purchase should be preceded by an NBV per share calculation, to establish to what extent the market price exceeds or lags behind this figure. If the share price is higher than the NBV per share, can this be justified by expected higher abnormal returns in future? If not, the price may be unrealistically inflated.

Unfortunately, we do not yet have a satisfactory valuation model that can predict share prices from accounting information. One suspects, somehow, that Ohlson’s model might be as close as we’ll ever get.

**AJ Cillers**

AJ is an academic and a freelance financial journalist who has written for Sharenet for some 15 years. He spent 25 years as an accountant and financial manager in various South African companies before moving into academia. He has a broad range of interests, including all aspects of business and stock market investing. Apart from a bachelor’s degree in Accounting, AJ holds a Master’s degree in Financial Management. He is also a Fellow of the Chartered Institute of Management Accountants.