Equity valuation models: present value, asset-based and relative
Absolute models estimate intrinsic value directly: present value models discount expected dividends, free cash flows or residual income, and asset-based models subtract liabilities from the fair value of assets. Relative models compare multiples such as price-to-earnings with peers. Each has strengths and weaknesses, so analysts usually combine several.
Before this: Market price, intrinsic value and perceived value, Price return, total return and the price of a share
On the exam
- Describe major categories of equity valuation models and explain their advantages and disadvantages
Describe the major categories of equity valuation models and explain their advantages and disadvantages. Expect: which category a described method belongs to, which cash flow (dividends, free cash flow to equity or to the firm, residual income) suits a company and at which discount rate, when an asset-based model fits, a trailing price-to-earnings (P/E) ratio cleaned of a one-time gain, a firm's enterprise value to earnings before interest, taxes, depreciation, and amortization (EV/EBITDA) multiple against the peer composite, and a weighted value from several models.
How deeply to learn each part
- Know the idea
- Understand it in general. It frames other topics, but you will not calculate with it.
- Use it
- Understand it well enough to solve a question with it. Recognize when it applies.
- Memorize
- Learn it by heart. The exam will not give it to you.
You know this one. The full lesson is folded away. The takeaways, formulas and checkpoint below are your quick refresher, and the checkpoint is a fair test of whether you still do.
You tested strong here. The full lesson is folded away. The takeaways, formulas and checkpoint below are your quick refresher, and the checkpoint is a fair test of whether you still know it.
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.
- 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
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- 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
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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.
Here is the expected cash flow in period , is the expected price at the end of the forecast (the terminal value), and is the required rate of return. Four features set the models apart:
- the cash flow measure, ;
- the required rate of return;
- the length of the forecast period, ;
- the terminal value, .
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, . 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.
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 () against book equity: net income − × book value of equity (BVE). It is smaller than earnings or FCFE.
Here is the expected residual income per share and 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 | mature firms with stable dividends or a consistent dividend policy | |
| FCFE | free cash flow to equity | 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 | firms without book value distortions, with irregular dividends or negative cash flow |
- 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).
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.
The weights sum to 1 and is each model’s value.
Try this 0 of 3
- Pick a model: find a company profile where FCFF is the right choice
- FCFF and FCFE: make FCFE smaller than FCFF
- Combine models: change only the weights until the verdict flips
Describe the company:
A mature firm with stable, regular dividends: the dividends themselves are a good guide to what shareholders receive.
Dividends, FCFE and residual income belong to shareholders and are discounted at the required return on equity, rₑ. FCFF belongs to lenders and shareholders and is discounted at WACC.
Memorize this
MemorizePresent value models and their uses
| Model | Discount at | Use for |
|---|---|---|
| Dividend discount | mature, stable dividend payer | |
| Free cash flow to equity (FCFE) | non-payer or irregular payer, stable capital structure | |
| Free cash flow to the firm (FCFF) | weighted average cost of capital (WACC) | high or changing leverage, negative FCFE |
| Residual income | no book distortions; irregular dividends or negative cash flow |
Memory hook Shareholders' money at ; everyone's money (FCFF) at WACC.
Know it cold FCFF = cash flow from operations + interest × (1 − tax rate) − capital expenditures; FCFE = cash flow from operations − capital expenditures + net debt issuance.
MemorizeStrengths and weaknesses
| Approach | Strength | Weakness |
|---|---|---|
| Present value | rigorous, flexible | detail and sensitive inputs |
| Asset-based | simple, market prices | misses going-concern value |
| Relative | simple, easy to compare | depends on the peer group |
Memory hook Detail is the present value model's strength and its weakness.
Know it cold Composite EV/EBITDA above the firm's: firm undervalued vs peers; firm's above the composite: overvalued.
- 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
-
- 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
Quick example
Cash flows 1.50 and 1.60, expected price 30.00 at the end of year 2, required return 8%: 1.50 ÷ 1.08 + 31.60 ÷ 1.08² = 1.39 + 27.09 = 28.48.
- CF2NDCLR WORK
- 0ENTER↓1.5ENTER↓↓31.6ENTER
- NPV8ENTER↓CPT 28.48
CF cash flow worksheet · 2ND second function (the shifted label above a key) · CLR WORK clear the worksheet · ENTER enter (on the HP, puts the number on the stack) · NPV net present value · CPT compute
- fCLEAR REG
- 0gCF01.5gCFj31.6gCFj8i
- fNPV 28.48
f gold shift key · CLEAR REG clear all registers · g blue shift key · CF0 cash flow at time zero · CFj cash flow j · i interest rate per period · NPV net present value
Quick example
Cash flow from operations 500, interest 40, tax 30%, capital expenditures 220: 500 + 28 − 220 = 308.
- 40×0.7+500−220= 308
- 500ENTER40ENTER0.7×+220− 308
ENTER enter (on the HP, puts the number on the stack)
Quick example
Cash flow from operations 500, capital expenditures 220, borrowing 60, repayment 100: 500 − 220 − 40 = 240.
- 500−220+60−100= 240
- 500ENTER220−60+100− 240
ENTER enter (on the HP, puts the number on the stack)
Quick example
Book value 20.00 per share and positive expected residual income: value above 20.00, so price-to-book above 1.
Quick example
Price 63.00, earnings per share 4.20: 63.00 ÷ 4.20 = 15.0.
Quick example
Discounted cash flow 32, comparables 28, residual income 45 with weights 50%, 30%, 20%: 16.0 + 8.4 + 9.0 = 33.40.
- (0.5×32)+(0.3×28)+(0.2×45)= 33.40
- 0.5ENTER32×0.3ENTER28×+0.2ENTER45×+ 33.40
ENTER enter (on the HP, puts the number on the stack)
How it is asked
-
Name the approach
Value = 11 × EBITDA from peers, then add cash and subtract debt.
Relative valuation (enterprise value multiple). Trap: present value.
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Best fit for asset-based
Which firm suits an asset-based model?
One whose value rests on the market prices of what it owns: a miner's reserves, a retailer's owned stores. Not a software firm.
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Which cash flow?
Irregular dividends, debt-funded buybacks, rising leverage.
FCFF at WACC. Trap: FCFE, which needs a stable capital structure.
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Firm against composite
Firm EV/EBITDA 7.4, composite 9.5, similar peers.
Undervalued relative to peers. Trap: reversing the rule.
Exam traps
- Treating relative valuation as absolute valuation. It is relative: the whole peer group could be mispriced.
- Discounting FCFF at the required return on equity. FCFF goes with WACC; dividends and FCFE go with r_e.
- Leaving a one-time gain in earnings per share, or using a P/E when earnings are negative or near zero. Use EV/EBITDA instead.
- Getting the sign of net debt issuance wrong in FCFE: repaying more than you borrow lowers FCFE.
- Using an asset-based model for a firm whose value lies in its going concern and intangibles.
Checkpoint
5 exam-style questions. About 90 seconds each.
1Kestrel Supplies trades at GBP 24.00 and has 10 million shares outstanding. Its net income for the past year was GBP 30 million, which includes a one-time gain of GBP 6 million on the sale of land. The trailing price-to-earnings (P/E) ratio an analyst should compare with peers is closest to:
2Valuing a company at 9 times its earnings before interest, taxes, depreciation, and amortization (EBITDA), then adding its cash and subtracting its debt to reach a value for the shares, is an example of:
3A company pays a small and irregular dividend, buys back large amounts of its shares with newly borrowed money, and its debt ratio is expected to keep rising. The present value model that is most appropriate is a model that discounts:
4An asset-based valuation model is most appropriate for:
5Compared with relative valuation models, present value models are most likely to be criticized for their:
Key takeaways
- Absolute models: present value (dividends, FCFE, FCFF, residual income) and asset-based. Relative models: price and enterprise value multiples.
- Dividends, FCFE and residual income are discounted at r_e; FCFF at WACC.
- Present value models are rigorous but input-sensitive; asset-based models are simple but miss going-concern value; relative models are simple but depend on the peers.
- Most analysts weight several models; the weights can flip the verdict.
Quick example
Cash flows 1.50 and 1.60, expected price 30.00 at the end of year 2, required return 8%: 1.50 ÷ 1.08 + 31.60 ÷ 1.08² = 1.39 + 27.09 = 28.48.
- CF2NDCLR WORK
- 0ENTER↓1.5ENTER↓↓31.6ENTER
- NPV8ENTER↓CPT 28.48
CF cash flow worksheet · 2ND second function (the shifted label above a key) · CLR WORK clear the worksheet · ENTER enter (on the HP, puts the number on the stack) · NPV net present value · CPT compute
- fCLEAR REG
- 0gCF01.5gCFj31.6gCFj8i
- fNPV 28.48
f gold shift key · CLEAR REG clear all registers · g blue shift key · CF0 cash flow at time zero · CFj cash flow j · i interest rate per period · NPV net present value
Quick example
Cash flow from operations 500, interest 40, tax 30%, capital expenditures 220: 500 + 28 − 220 = 308.
- 40×0.7+500−220= 308
- 500ENTER40ENTER0.7×+220− 308
ENTER enter (on the HP, puts the number on the stack)
Quick example
Cash flow from operations 500, capital expenditures 220, borrowing 60, repayment 100: 500 − 220 − 40 = 240.
- 500−220+60−100= 240
- 500ENTER220−60+100− 240
ENTER enter (on the HP, puts the number on the stack)
Quick example
Book value 20.00 per share and positive expected residual income: value above 20.00, so price-to-book above 1.
Quick example
Price 63.00, earnings per share 4.20: 63.00 ÷ 4.20 = 15.0.
Quick example
Discounted cash flow 32, comparables 28, residual income 45 with weights 50%, 30%, 20%: 16.0 + 8.4 + 9.0 = 33.40.
- (0.5×32)+(0.3×28)+(0.2×45)= 33.40
- 0.5ENTER32×0.3ENTER28×+0.2ENTER45×+ 33.40
ENTER enter (on the HP, puts the number on the stack)
All Equities formulas, every lesson
Practice exam-style questions on Introduction to Equity Valuation
Questions about this lesson?
Where this comes back
- Dividends, FCFE, FCFF or residual income: which cash flow, which discount rate Discounted Cash Flow and Growth Models
- Valuing with multiples: comparables and forecasted fundamentals Relative Valuation with Multiples
- Book value, market capitalization and enterprise value Introduction to Equity Valuation
Questions candidates ask
What are the major categories of equity valuation models?
Absolute valuation, made of present value models (dividend discount, free cash flow to equity, free cash flow to the firm and residual income models) and asset-based models; and relative valuation, which compares multiples such as P/E or EV/EBITDA with peers.
When should you use FCFF instead of FCFE?
When leverage is high or changing, or FCFE is negative. Discount FCFF at the weighted average cost of capital to value the whole business, then subtract debt for equity. FCFE suits a stable capital structure and is discounted at the required return on equity.
What are the disadvantages of relative valuation?
The result depends heavily on the peers chosen, multiples differ with fundamentals, company-specific factors may be missed, and a whole peer group can be mispriced.
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