# Present Value Models

Discounted cash flow (DCF) models view the intrinsic value of a stock as the present value of its expected future cash flows. The four steps in applying DCF analysis to equity valuation are:

1. Selecting a specific definition of cash flow.
2. Forecasting the cash flows.
3. Choosing a discount rate methodology.
4. Estimating the discount rate.

Cash flows received in the future are worth less than the same amount of cash flows received today because the money received today gives an individual the option of immediately consuming it. Due to this, when valuing an asset, future cash flows need to be discounted to the present before adding them. This reduces the cash flows’ value depending on how far in the future they are received.

An asset’s value is, therefore, the present value of the expected future cash flows.

$$V_0= ∑_{t=1}^n\frac{CF_t}{(1+r)^t}$$

Where:

$$V_{0}=$$ Value of an asset at time $$t=0$$.

$$n=$$ The number of cash flows in an assets life.

$$\text{CF}_{t}=$$ The cash flow at time $$t$$.

$$r =$$ The required rate of return/discount rate.

The three types of cash flows used when working with the DCF model are:

• Dividends: Cash paid to shareholders.
• Free cash flow: Cash in hand to pay shareholders.
• Residual income: Economic profits.

The selected cash flow defines the type of DCF model that can be used. Namely:

• The dividend discount model.
• The free cash flow model.
• The residual income model.

## The Dividend Discount Model

The dividend discount model (DDM) describes cash flows as dividends. This is because investors who buy a company’s stock expect to receive cash in the form of dividends. The stability of dividends makes the DDM values less sensitive to short-term fluctuations.

Some companies may pay dividends, while others may choose not to pay. Generally, it is the large profitable companies that consistently pay dividends. These companies are usually reluctant to reduce their dividend levels.

The DDM is suitable when:

• The company is dividend-paying.
• There is a stable relationship between a company’s dividend policy and its profitability.
• An investor takes a non-control perspective.

## The Free Cash Flow Model

There are two definitions of cash flow:

### i. Free Cash Flow to the Firm (FCFF)

Free cash flow to the firm (FCFF) is the cash flow generated by the company’s operations that is available to bondholders and equity holders while maintaining the company’s operations. Capital expenditures are needed to support the company’s operations and are therefore deducted from cash operations to arrive at free cash flow to the firm. The total value of the firm can be estimated by discounting the expected future FCFF.

### ii. Free Cash Flow to Equity (FCFE)

FCFE is the cash flow from a company’s operations, less capital expenditures, and net payments to debtholders. The value of equity can be estimated by discounting the free cash flow to equity. Thus, the FCFE is a post-debt cash flow measure.

The free cash flow model may not be appropriate for companies with substantial capital expenditures that result in negative expected free cash flows.

The free cash flow model is suitable when:

• The company is not dividend-paying.
• The company is dividend-paying, but the dividends significantly exceed or fall short of FCFE.
• The investor wants to take a control perspective.
• The company’s free cash flows are in line with the company’s profitability.

## The Residual Income Model

Residual income is calculated as the earnings for a particular period above investors’ required return at the beginning of the period. For example, shareholders’ investment in a company is $100 million at the beginning of a period, and the required rate of return is 8%. If the company earns$11 million in that period, the residual income would be $3 million, i.e.,$11 million – (8% × $100 million) =$3 million. The amount above the required return amount represents the value-added or economic gain to shareholders.

The residual income model computes the value of a company as the sum total of its book value and the present value of anticipated future residual earnings.

The residual income model is most appropriate when:

• The company is not dividend-paying.
• The company’s anticipated free cash flows are negative.

## Question

Which of the following is least likely a type of cash flow used under the discounted cash flow model?

1. Dividends.
2. Residual income.
3. Book value.

### Solution

Book value is not a type of cash flow. Instead, book value is an input used in the residual income model to find the value of a company.

A is incorrect. Dividends are a type of cash flow used with the dividend discount model to estimate the value of a company.

B is incorrect. Residual income is a type of cash flow under the discounted cash flow model. It is calculated as the earnings for a particular period above investors’ required return at the beginning of the period.

LOS 23 (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.

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