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Lesson 3 of 9 · 13 min

Present value models: DDM and FCFE

A share is worth the present value of the cash it will deliver: either the dividends expected (DDM) or the cash the company could pay out (FCFE), discounted at the required return on equity.

Video lesson · 5 min. Watch it first, then use the text below to go deeper.

In short

Present value models rest on a basic idea: people invest for future benefits, so value = PV of those benefits.
Dividend discount model (DDM): $V_0 = \sum D_t/(1+r)^t$ over all future years.
For an n-year holding period: PV of n dividends + PV of the expected sale price $P_n$ (the terminal value). The value does not depend on the holding period.
FCFE = CFO − fixed capital investment + net borrowing. It measures dividend-paying capacity and works for non-dividend payers.
The required return r often comes from the CAPM: $r = R_f + \beta \times$ equity risk premium. There is no single correct r.

Why discount dividends?

People defer consumption (they invest) because they expect future benefits. So the value of an investment should equal the present value of those expected benefits. For a common share, the benefits are cash flows, and the simplest choice of cash flow is the dividend.

If the company is a going concern and the required return r is constant, the dividend discount model (DDM) values a share as the sum of all expected dividends, each discounted at r: $V_0 = \sum_{t=1}^{\infty} D_t/(1+r)^t$ . Dividends are assumed to arrive at the end of each year.

Looking at the infinite future is reasonable: companies are set up to operate indefinitely, with no maturity date.

The holding period does not matter

A shareholder receives dividends while holding the share and the sale price when selling. For a one-year holder, value is $(D_1 + P_1)/(1+r)$ . For an n-year holder, it is the PV of n dividends plus the PV of the expected price at the end of year n. That expected sale price is the terminal stock value (or terminal value).

But what will the next buyer pay at time n? The PV of the dividends they expect after n. Substitute that in, and every holding period collapses back to the same infinite sum of dividends. So two investors with the same expectations and the same r arrive at the same value, whatever their holding periods.

The short-horizon investor depends directly on the dividends before the sale and indirectly on all later dividends, through the price they expect to sell at.

A three-year holder receives three dividends and the sale price. Discounted at 9%, they are worth 30.29 today, and the sale price alone supplies 26.25 of that.

Free cash flow to equity

Many analysts prefer to value the cash a company could pay out rather than the dividends it chooses to pay. Free cash flow to equity (FCFE) measures this dividend-paying capacity: the cash generated in a period that is available for distribution to common shareholders.

FCFE also helps with companies that pay no dividend. A DDM would need a forecast of when the first dividend arrives and how it grows, which is hard to make accurately. FCFE avoids that.

Start with cash flow from operations (CFO): net income plus non-cash expenses minus investment in working capital. Not all of CFO is available: the fixed capital investment (FCInv) needed to keep the company going is kept back. Net borrowing (new borrowing minus repayments) is added, because borrowed cash could be passed to shareholders. Reported capital expenditure is often used as FCInv.

Value is then the PV of all future FCFE discounted at the required return on equity, mirroring the DDM: $V_0 = \sum FCFE_t/(1+r)^t$ . Historical FCFE comes from the cash flow statement; future FCFE needs forecasts.

Net income 600 plus non-cash charges 280 minus 60 tied up in working capital gives CFO of 820. Keeping back 310 for fixed investment and adding 60 of net borrowing leaves FCFE of 570.

Estimating the required return

A common way to estimate the required return on a share is the capital asset pricing model (CAPM): the current expected risk-free rate plus the stock's beta (its non-diversifiable risk) times the market (equity) risk premium, the expected return on the market above the risk-free rate.

Other approaches add a judgment-based risk premium to a government bond yield, or add a risk premium to the yield on the company's own bonds. Some firms simply set required returns by policy.

Even analysts who agree on the CAPM can choose different inputs. So there is no uniquely correct required return, and different r values are a main reason analysts reach different valuations.

Formulas

Dividend discount model: $V_0 = \sum_{t=1}^{\infty} \dfrac{D_t}{(1+r)^t}$
D_t = expected dividend at the end of year t; r = required return on the share.
Finite holding period: $V_0 = \sum_{t=1}^{n} \dfrac{D_t}{(1+r)^t} + \dfrac{P_n}{(1+r)^n}$
P_n = expected sale price (terminal value) at the end of year n.
Free cash flow to equity: $FCFE = CFO - FCInv + \text{Net borrowing}$
CFO = net income + non-cash expenses − investment in working capital. Net borrowing = borrowing − repayments (can be negative).
FCFE valuation: $V_0 = \sum_{t=1}^{\infty} \dfrac{FCFE_t}{(1+r)^t}$
Discount at the required return on equity.
CAPM required return: $r_i = R_f + \beta_i \left[E(R_m) - R_f\right]$
R_f = current expected risk-free rate; the bracket is the market (equity) risk premium.

Worked examples

Example 1 Three-year holding period

An investor expects Ostrava Industries to pay dividends of CZK 1.50, 1.60 and 1.70 over the next three years and to sell the share for CZK 34.00 at the end of year 3. The required return is 9%. What is the share worth, and what is it worth if the shares trade at CZK 27.50?

Example 2 Same value for a one-year holder

A second investor shares the same forecasts but plans to sell after one year. What price should she expect at t = 1, and what value does she get today?

Example 3 Calculating FCFE

Velde Logistics reports net income of EUR 600 million, non-cash expenses of 280 million and a 60 million increase in working capital. Capital expenditure is 310 million and it borrowed a net 60 million. It has 150 million shares. Find FCFE in total and per share.

On the exam

Expect a short holding-period valuation, a direct FCFE calculation, a CAPM required return, and concept items: holding-period independence, why FCFE suits non-dividend payers, and that FCFE reflects capacity to pay rather than actual dividends.

Discounting the sale price one period too few or too many: it is received at the same time as the last dividend.
Believing a shorter holding period gives a different intrinsic value.
Subtracting net borrowing in FCFE: net borrowing is added (a net repayment is negative).
Labelling price-to-free-cash-flow a present value model: it is a multiple.

Check yourself

Q1A share is expected to pay dividends of 1.80 and 1.95 over the next two years and to sell for 40.00 at the end of year 2. With a required return of 8%, its value today is closest to:
Q2A company has CFO of 450, fixed capital investment of 180 and repaid a net 40 of debt during the year. Its FCFE is closest to:
Q3Two investors have identical expectations and required returns for a share, but one plans to hold it for two years and the other for ten. Compared with the ten-year investor, the two-year investor's estimate of intrinsic value will most likely be:
Q4An analyst who wants to value a share on the company's capacity to pay dividends, rather than on the dividends it actually pays, will most likely use:
Q5The risk-free rate is 2.5%, the equity risk premium is 6.0% and a share's beta is 0.8. The CAPM required return is closest to:

0/5Check yourself

Answer the 5 questions: +10 XP for each one you get right first time.

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