DDM Basics

Equity Valuation 9 min readModule 1 of 3Save

What you'll learn

LOS 18.a
Compare dividends, free cash flow, and residual income as inputs to discounted cash flow models and identify investment situations for which each measure is suitable.
LOS 18.b
Calculate and interpret the value of a common stock using the dividend discount model (DDM) for single and multiple holding periods.

In stock valuation models, there are three predominant definitions of future cash flows: dividends, free cash flow, and residual income.

Dividends. Dividend discount models (DDMs) define cash flow as the dividends to be received by the shareholders. The primary advantage of using dividends as the definition of cash flow is that it is theoretically justified.

The shareholder’s investment today is worth the present value of the future cash flows he expects to receive, and ultimately he will be repaid for his investment in the form of dividends. Even if the investor sells the stock at any time prior to the liquidation of the company, before all the dividends are paid, he will receive from the buyer of the shares the present value of the expected future dividends.

An additional advantage of dividends as a measure of cash flow is that dividends are less volatile than other measures (earnings or free cash flow), and therefore the value estimates derived from dividend discount models are less volatile and reflect the long- term earning potential of the company.

The primary disadvantage of dividends as a cash flow measure is that it is difficult to implement for firms that don’t currently pay dividends. It is possible to estimate expected future dividends by forecasting the point in the future when the firm is expected to begin paying dividends. The problem with this approach in practice is the uncertainty associated with forecasting the fundamental variables that influence stock price (earnings, dividend payout rate, growth rate, and required return) so far into the future.

A second disadvantage of measuring cash flow with dividends is that it takes the perspective of an investor who owns a minority stake in the firm and cannot control the dividend policy. If the dividend policy dictated by the controlling interests bears a meaningful relationship to the firm’s underlying profitability, then dividends are appropriate. However, if the dividend policy is not related to the firm’s ability to create value, then dividends are not an appropriate measure of expected future cash flow to shareholders.

Dividends are appropriate as a measure of cash flow in the following cases:

The company has a history of dividend payments.
The dividend policy is clear and related to the earnings of the firm.
The perspective is that of a minority shareholder.

Firms in the mature stage of the industry life cycle are most likely to meet the first two criteria.

Worked example: Identifying the appropriate valuation model

Based on the financial information on Eastern Consolidated, Inc., provided in the following table, determine whether or not a dividend discount model is the appropriate model to value Eastern Consolidated common stock.

Earnings and Dividend Data for Eastern Consolidated

	20X5	20X4	20X3	20X2	20X1
Earnings per share	$7.50	$6.25	$5.85	$5.40	$5.00
Dividends per share	$1.25	$1.25	$1.25	$1.25	$1.25

Solution

Earnings have grown at a compound rate of ($7.50 / $5.00) $^{1/4}$ − 1 = 0.107 = 10.7% over the four years while dividends have been constant, resulting in a decrease in the dividend payout ratio. A dividend discount model is not appropriate in this case because the firm’s dividend policy is not consistent with its profitability trend.

Free cash flow. Free cash flow to the firm (FCFF) is defined as the cash flow generated by the firm’s operations that is in excess of the capital investment required to sustain the firm’s current productive capacity. Free cash flow to equity (FCFE) is the cash available to stockholders after funding capital requirements and expenses associated with debt financing.

One advantage of free cash flow models is that they can be applied to many firms, regardless of dividend policies or capital structures. The ability to influence the distribution and application of a firm’s free cash flow makes these models more pertinent to a firm’s controlling shareholders. Free cash flow is also useful to minority shareholders because the firm may be acquired for a market price equal to the value to the controlling party.

However, there are cases in which the application of a free cash flow model may be very difficult. Firms that have significant capital requirements may have negative free cash flow for many years into the future. This can be caused by a technological revolution in an industry that requires greater investment to remain competitive or by rapid expansion into untapped markets.

This negative free cash flow complicates the cash flow forecast and makes the estimates less reliable.

Free cash flow models are most appropriate:

For firms that do not have a dividend payment history or have a dividend payment history that is not clearly and appropriately related to earnings.
For firms with free cash flow that corresponds with their profitability.
When the valuation perspective is that of a controlling shareholder.

Residual income. Residual income is the amount of earnings during the period that exceeds the investors’ required return. The theoretical basis for this approach is that the required return is the opportunity cost to the suppliers of capital, and the residual income is the amount that the firm is able to generate in excess of this return.

The residual income approach can be applied to firms with negative free cash flow and to dividend and non dividend paying firms.

Residual income models can be more difficult to apply, however, because they require in depth analysis of the firm’s accounting accruals. Management discretion in establishing accruals for both income and expense may obscure the true results for a period. If the accounting is not transparent or if the quality of the firm’s reporting is poor, the accurate estimation of residual income is likely to be difficult.

The residual income approach is most appropriate for:

Firms that do not have dividend histories.
Firms that have negative free cash flow for the foreseeable future (usually due to capital demands).
Firms with transparent financial reporting and high quality earnings.

One Period DDM

We can rearrange the holding period formula to solve for the value today of the stock given the expected dividend, the expected price in one year, and the required return:

V_{0} = \frac{D _{1} + P _{1}}{1 + r}

Symbol	Meaning
V₀	Fundamental value
D₁	Dividends expected to be received at end of Year 1
P₁	Price expected upon sale at end of Year 1
r	Required return on equity

Worked example: Calculating value for a one period DDM

BuyBest shares are expected to pay a dividend at the end of the year of €1.25. The analyst estimates the required return to be 8% and the expected price at the end of the year to be €28.00. The current price is €26.00. Calculate the value of the shares today, and determine whether BuyBest is overvalued, undervalued, or properly valued.

Solution

The current value of the shares according to the DDM is equal to:

V_{0} = \frac{€ 1.25 + € 28.00}{1.08} = € 27.08

BuyBest is undervalued. The current market price of €26.00 is less than the fundamental value of €27.08.

Two Period DDM

The value of a share of stock using the two period DDM is the present value of the dividends in Years 1 and 2, plus the present value of the expected price in Year 2:

V_{0} = \frac{D _{1}}{( 1 + r ) ^{1}} + \frac{D _{2} + P _{2}}{( 1 + r ) ^{2}}

Symbol	Meaning
V₀	Fundamental value
D₁	Dividends expected to be received at end of Year 1
D₂	Dividends expected to be received at end of Year 2
P₂	Price expected upon sale at end of Year 2
r	Required return on equity

Worked example: Calculating value for a two period DDM

Machines Unlimited shares are expected to pay dividends of 1.55 Canadian dollars (C$) and C$1.72 at the end of each of the next two years, respectively. The investor expects the price of the shares at the end of this 2 year holding period to be C$42.00. The investor’s required rate of return is 14%. Calculate the current value of Machines Unlimited shares.

Solution

The value of Machines Unlimited shares can be determined with a two period DDM as:

\frac{C $1.55}{1.1 4 ^{1}} + \frac{C $1.72 + C $42.00}{1.1 4 ^{2}} = C $33.00

Multi Period DDM

The DDM can easily be adapted to any number of holding periods by adjusting the discount factor to match the time to receipt of each expected return. With this, the present value becomes the sum of the properly discounted values of all expected cash flows (dividends and terminal value):

V_{0} = \frac{D _{1}}{( 1 + r ) ^{1}} + \frac{D _{2}}{( 1 + r ) ^{2}} + \dots + \frac{D _{n} + P _{n}}{( 1 + r ) ^{n}}

Symbol	Meaning
V₀	Fundamental value
Dᵢ	Dividends expected to be received at end of year i, i = 1 to n
Pₙ	Price expected upon sale at end of year n
r	Required return on equity
n	Length of holding period

For example, if we extend the holding period to three years, we simply extend the formula.

Worked example: Calculating value for a three period DDM

Reliable Motors shares are expected to pay dividends of $1.50, $1.60, and $1.75 at the end of each of the next three years, respectively. The investor expects the price of the shares at the end of this 3 year holding period to be $54.00. The investor’s required rate of return is 15%. Calculate the current value of Reliable’s shares.

Solution

The value of Reliable Motors shares can be determined with a multi period DDM as:

\frac{$1.50}{1.1 5 ^{1}} + \frac{$1.60}{1.1 5 ^{2}} + \frac{$1.75 + $54.00}{1.1 5 ^{3}} = $39.17

When we have to calculate the total of three or more discounted cash flows, we can generally save a considerable amount of time (and improve accuracy) by using our financial calculators as shown in the following table:

Calculating the PV of Multiple Cash Flows With the TI BA II Plus™

Warm Up: The General Dividend Discount Model

If we extend the holding period indefinitely, the value simply becomes the present value of an infinite stream of dividends, represented by John Burr Williams’s (1938) original DDM formula:

V_{0} = t = 1 \sum \infty \frac{D _{t}}{( 1 + r ) ^{t}}

While the DDM is theoretically correct, applying it in practice requires the analyst to accurately forecast dividends for many periods, a task for which we rarely can expect to have sufficient information. We can use one of several growth models, including the:

Gordon constant growth model.
Two stage growth model.
H-model.
Three stage growth model.

With the appropriate model, we can forecast dividends up to the end of the investment horizon where we no longer have confidence in the forecasts and then forecast a terminal value based on some other method, such as a multiple of book value or earnings. Choosing the appropriate growth model is essential to accurate forecasts.

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