Executive Summary
The dividends are off the pace
Their value is below their face
So our models we must bend
Towards the valuation end

When the market and face valuation of dividends differ, the valuation models used for valuing shares and selecting investment projects are likely to result in valuation errors.

Where valuations are undertaken across different tax jurisdictions, different valuation models may be required.

Where adjustments are made to discount rates rather than cash flows, this increases the likelihood of error.

All these problems can be resolved by a simple modification of the standard valuation models.

The approach, called the q method, provides a convenient and simple valuation model with almost universal application.
Introduction
Suppose that a company declares a cash dividend of $1, then the face value of the dividend is $1. The market value, which is what that dividend trades for in the market, may, or may not, be the same as the face value. Traditional approaches to valuation, such as the discounted dividend model (see “Using Dividend Discount Models”), usually assume that the market value and the face value of dividends are the same. When this is not the case you hit problems in valuation and in making investment decisions using traditional capital budgeting techniques.
A common approach to valuing a share is to discount the expected selling price of the share and then add the discounted value of the dividends that you expect to receive before you sell. This approach is the foundation of the discounted dividend model used to estimate the value of shares. The expected price is by definition a market value, but the dividends are at face value. If the market and face value of dividends differ, adding share prices and dividends together is like adding apples and oranges and calling the total apples. The foundation of the discounted dividend model is therefore decidedly shaky if the market value and face values differ.
Whether the face and market values of dividends differ is a much debated question among finance academics, but there is plenty of evidence that they do. One reason for the difference is taxation. If the company gives you a dollar of dividends and then the government takes away $0.25 in tax, you might well value that dividend at less than a dollar. As it turns out, capital gains taxes also play a role. If instead of paying you $1 of dividends the company keeps that cash in the company, your shares have more asset backing. Consequently your shares are more valuable and you end up paying more gains tax.
The market value of dividends relative to their face value then depends on the relative taxation of dividends and capital gains. In many jurisdictions dividends have a tax disadvantage. This is because returns in the form of price changes are taxed at concessional capital gains tax rates, whereas dividends are taxed as income. In other jurisdictions dividends are taxadvantaged. For example, in imputation tax systems the shareholders receive a refund of corporate tax along with their dividend.
The problem raised by the divergence between the market and face value of dividends also extends to traditional discounted cash flow techniques for capital budgeting (see p. 1099). This is because the use of these techniques is based on their equivalence to the discounted dividend model, as was shown by the Nobel Prize winners Merton Miller and Franco Modigliani.^{1}
The Solution Is q
One solution to the problem is to make the discounted values for prices and dividends consistent by adjusting the discount rate. For example, the capital asset pricing model or CAPM, a popular model for estimating discount rates, can be extended to allow for differential taxation of dividends and capital gains. The reality, however, is that these aftertax versions of the CAPM have been little used because of the additional complexity that they involve and because of difficulties in implementation. There is a further problem that different models are needed for different tax jurisdictions.
An alternative solution to the problem involves adjusting the cash flow, and it also requires a small change in the definition of the discount rate.^{2} This alternative approach is called the q method. The advantage of the q method is that it is both simple and general in its application. It works whether dividends have a tax disadvantage or a tax advantage (as under an imputation tax system). The approach also allows the face value and market value of interest payments to differ. Thus, whatever tax jurisdiction the valuation is being conducted under, the q method can be used without modification. The method also works just as well if the face and market value of dividends differ for reasons other than taxes.
An attractive feature of the q method is that the main adjustment is to the measurement of cash flows. One advantage of adjusting the cash flow is that the adjustment is clearly visible, and therefore executives are alerted to the assumptions that are being made. In contrast, where adjustments are buried in the discount rate, it is often a case of out of sight, out of mind. Cash flow adjustments, therefore, are less likely to lead to errors.
The key to the q method is to let the market do the work and express everything in market prices. To do this it is first necessary to define the return on equity in terms of the expected growth in share prices, R_{price}. This is done as follows:
R_{price} = (P^{cum}_{t+1} − P^{ex}_{t}) ÷ P^{ex}_{t}
where P^{cum}_{t+1} represents the expected cumdividend share price in the next period (at time t + 1) and P^{ex}_{t} represents the exdividend share price that we observe now (at time t).^{3} When prices are in equilibrium, R_{price} is the return that investors require on their investment in the shares. In determining their required return R_{price}, investors will factor in the effect of any capital gains taxes that they may have to pay.
Next, we decompose the expected cumdividend price into the expected exdividend price next period (P^{ex}_{t}_{+1}) and the market value of dividends. The market value of the dividend is obtained by multiplying the face value of the next period’s expected dividend (DIV_{t}_{+1}) by q. The q factor is the ratio of the market value of dividends to the face value of dividends. The q factor, just like the famous Tobin’s q, measures the ratio of market value to replacement cost. This is because the cost of replacing the cash paid out as a dividend equals the face value of the dividend. Thus, if the market value of dividends is $0.75 per $1.00 of face value, the q factor is 0.75. The resulting decomposition of the expected cumdividend price is:
P^{cum}_{t+1} = P^{ex}_{t+1} + q(DIV_{t+1})
Everything is now expressed in terms of market value. No further adjustments for taxes on dividends or on capital gains are required. This is because the effects of these taxes are fully captured in q and R_{price}. From the two definitions above it is simply a matter of algebra to derive a set of equations for valuation and the cost of capital. We can omit the algebra and go straight to the results.
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