Equity valuation models: present value, asset-based and relative

How are equity valuation models grouped?

There are two groups. Absolute valuation estimates the cash flows or asset prices that drive a share’s intrinsic value, and it has two kinds of model: present value models and asset-based valuation models . Relative valuation compares price-based or enterprise-value-based ratios across similar companies.

Choosing a model depends on three things: whether returns come mainly from price gains or from distributions, how well the model fits the firm and its industry, and whether reliable inputs exist. Lesson 1 showed how investors reach a perceived value; these are the tools analysts use.

Equity valuation modelsmost analysts combine several

• Absolute valuation Memorize cash flows or asset prices that drive intrinsic value
  • Present value models dividends, free cash flow to equity or to the firm, or residual income, discounted
  • Asset-based models fair value of assets minus liabilities
• Relative valuation Memorize multiples against peers
  • Price multiples price-to-earnings, price-to-book
  • Enterprise value multiples enterprise value divided by revenue or an operating profit measure

How do present value models work?

Present value models value expected future distributions and price gains at an appropriate discount rate. They are also called discounted cash flow models . Unlike a bond, a share has no maturity, so analysts forecast cash flows for a period and add a terminal value for everything after it.

$$IV_t = \sum_{i=1}^{n} \frac{E(CF_{t+i})}{(1 + r)^{i}} + \frac{E(P_{t+n})}{(1 + r)^{n}}$$

Here $E(CF_{t+i})$ is the expected cash flow in period $t+i$, $E(P_{t+n})$ is the expected price at the end of the forecast (the terminal value), and $r$ is the required rate of return. Four features set the models apart:

1. the cash flow measure, $E(CF)$;
2. the required rate of return;
3. the length of the forecast period, $n$;
4. the terminal value, $E(P_{t+n})$.

The forecast period should run as long as the analyst has confidence and inputs to quantify the story. A two-stage model forecasts fast growth first, then a terminal value from slower constant growth or a multiple (Learning Module 6 builds these).

Which cash flow: dividends, free cash flow or residual income?

The dividend discount model (DDM) discounts dividends at the required return on equity, $r_e$. It suits mature firms with stable, consistent distributions. For firms not expected to pay consistent dividends, free cash flow (operating cash flow in excess of capital expenditures) fits better. There are two kinds. Free cash flow to the firm (FCFF) is available to lenders and shareholders together. Free cash flow to equity (FCFE) is available to common shareholders only.

$$\text{FCFF} = \text{Cash flow from operations} + \text{Interest expense} \times (1 - \text{Tax rate}) - \text{Capital expenditures}$$

$$\text{FCFE} = \text{Cash flow from operations} - \text{Capital expenditures} + \text{Net debt issuance}$$

Net debt issuance is additional borrowing minus debt repayment. The two measures differ by net debt issuance and after-tax interest.

The residual income model works differently. Residual income is the profit left after charging the required return on equity ($r_e$) against book equity: net income − $r_e$ × book value of equity (BVE). It is smaller than earnings or FCFE.

$$IV_t = BVE_t + \sum_{i=1}^{n} \frac{RI_{t+i}}{(1 + r_e)^{i}} + \frac{E(P_{t+n}) - BVE_{t+n}}{(1 + r_e)^{n}}$$

Here $RI_{t+i}$ is the expected residual income per share and $BVE_t$ is book value of equity per share. The model suits firms whose book values are not distorted, with inconsistent dividends or negative cash flow, and it leans less on the terminal value. If a firm is expected to earn positive residual income, its price-to-book ratio should be above 1. This lesson does not value a share with the residual income model; Learning Module 6 computes residual income per share.

Free cash flow to the firm is discounted at the weighted average cost of capital (WACC) , the blended cost of the firm’s debt and equity financing, because it belongs to both groups of investors.

Model	Cash flow	Discount rate	Use for
Dividend discount	dividends	$r_e$	mature firms with stable dividends or a consistent dividend policy
FCFE	free cash flow to equity	$r_e$	non-payers or irregular payers whose capital structure should stay stable
FCFF	free cash flow to the firm	WACC	the whole business when leverage is high or changing, or FCFE is negative
Residual income	residual income per share	$r_e$	firms without book value distortions, with irregular dividends or negative cash flow

Present value modelmatch the cash flow to the company

• Dividends Memorize mature, stable payer; at r_e
• Free cash flow to equity Memorize non-payer or irregular payer, stable capital structure; at r_e
• Free cash flow to the firm Memorize high or changing leverage, or negative free cash flow to equity; at WACC
• Residual income Memorize no book distortions; irregular dividends or negative cash flow; at r_e

Exam tip Shareholders’ cash flows (dividends, FCFE, residual income) are discounted at r_e; the cash flow for everyone (FCFF) at WACC.

The Financial Statement Analysis lesson derives free cash flow from the cash flow statement.

Strengths and weaknesses of present value models

The strengths are a rigorous use of financial statements to estimate the size and timing of actual or potential cash flows, a flexible choice of cash flow, and room to build in changes in revenue, margins, investment and payout policy.

The weaknesses start with the same level of detail: different models and horizons make comparisons hard. Results are often very sensitive to uncertain inputs. And a focus on the company’s own cash flows can miss market dynamics or industry change. Forecasting a taxi company from its own history, for example, ignores ride-hailing apps.

Exam tip Detail is both the strength and the weakness of present value models.

When do asset-based models fit?

An asset-based model is an absolute approach: intrinsic value = fair market value of assets − fair market value of liabilities. The theory is that the firm’s value depends mainly on the prices of the resources it owns or controls, not on the cash it generates. That fits commodity producers, whose mineral or oil reserves rise and fall with commodity prices. Incidental assets such as owned real estate are often valued separately from the business, and intangibles often mean intellectual property such as a brand.

Two examples: a copper miner whose share price tracks the copper price, and a supermarket chain that owns most of its stores, so its property is a large part of its value.

The advantages: the method is fairly straightforward, it does not rest on the many assumptions and forecasts of present value models, and it uses market prices, so it helps to value a division or individual assets separately, or a firm being liquidated. The disadvantages: it misses the value of the firm as a going concern (margins, how efficiently assets are used, competition), and it may ignore taxes and financial and other liabilities.

How does relative valuation work?

Relative valuation, also called comparables models , uses ratios, or multiples , of a market value to a standardized income statement or balance sheet item. The numerator is the share price or enterprise value. The denominator is earnings, free cash flow, revenue or book value.

Price multiples look at value to shareholders. The best known is the price-to-earnings (P/E) ratio . Another is the price-to-book (P/B) ratio, the share price divided by book value of equity per share (Lesson 3 covers it).

The price-to-earnings ratio divides the share price by earnings per share (EPS).

$$P/E = \frac{P_t}{EPS_t}$$

The ratio comes in two versions, trailing and forward P/E . Trailing uses EPS for the past year and forward uses next year’s forecast. Use the same version for every peer. The denominator must be positive, so leave out firms with very low or negative earnings, and strip out one-time items.

Enterprise value multiples value the whole firm, for lenders and shareholders. Enterprise value (EV) is the market value of equity plus preferred shares plus debt, minus cash and short-term investments (Lesson 3 builds it). It is divided by revenue, earnings before interest, taxes, depreciation, and amortization (EBITDA), or earnings before interest and taxes (EBIT). The composite multiple is the average multiple of the peer group.

• If the composite EV/EBITDA is above the firm’s, the firm looks undervalued relative to its peers.
• If the firm’s is above the composite, it looks overvalued.

EBITDA is a rough measure of cash flow to all capital providers and is less often negative than EPS. So EV/EBITDA works where P/E is distorted by swinging earnings, and more peers qualify for an EV/EBITDA comparison than for a P/E comparison.

A justified price multiple is the estimated fair value of a multiple. It is supported by the method of comparables or the method of forecasted fundamentals (Learning Module 7 covers both).

The advantages of relative valuation: it is simple and quick, needs no explicit cash flow forecast horizon, makes comparisons among similar companies easy, and can use analysts’ forecasts. The disadvantages: the choice of comparable companies can change the answer a lot (a peer group of only the fastest growers is a trap), multiples differ with fundamentals, company-specific factors may be missed, and the method is relative only, so a whole peer group can be mispriced.

The three categories side by side

Category	Values the share as	Examples	Advantages	Disadvantages
Present value (absolute)	present value of expected cash flows plus a terminal value	dividend discount, FCFE, FCFF, residual income	rigorous, statement-based, flexible	detail cuts both ways; sensitive inputs; can miss market and industry change
Asset-based (absolute)	fair value of assets minus liabilities	resource producers, owned real estate, a division, a liquidation	straightforward; few forecasts; market prices	misses going-concern value; may ignore taxes and liabilities
Relative	a multiple compared with peers	P/E, P/B, EV/Revenue, EV/EBITDA	simple; no forecast horizon; easy peer comparison	peer choice drives results; fundamentals differ; company specifics missed

How do analysts combine several models?

Most analysts use more than one model, because each simplifies. A floating bar chart (Lesson 1) can show several models’ ranges against the trading range. If all lie above the trading range, the evidence for undervaluation is strong. If they spread widely, dig into assumptions, peers and market dynamics, and weight the models by your confidence in their inputs and their fit to the firm, industry and market.

$$IV_t = \sum_j w_j \times V_j$$

The weights $w_j$ sum to 1 and $V_j$ is each model’s value.