The Valuation Primer

Every investor should know how to value assets. Valuations forces investors to translate their assumptions about an asset into concrete fair value estimates and compare those estimates against the market value. This process is also a sanity check, which evaluates if an investor’s assumptions are possible, plausible, and probable. Since returns have an inverse relationship with price, a high enough price can make even the best performing companies poor investments. Conversely, a mediocre firm is an excellent investment if it can be had for free.

While some retail investors are intimidated by valuations, this process is not exclusive to institutional investors and investment banks. Value is what something is worth, and valuation is the process of determining that worth. There are three main approaches to valuation: market valuation, asset valuation, and earnings valuation.

Three Main Valuation Approaches

Out of the three approaches, only market value is concrete and immediately realizable. For publicly traded securities, the market value is the price and is updated instantaneously. Therefore, investors do not need to estimate the market value of stocks. Instead, market value is more useful as a reference to compare against.

In every transaction, there is an agreement on value between a buyer and a seller. The aggregate of all transactions for an item is the market for that item. The average price within a market is the market’s valuation for that item. There is a market for real estate, oranges, hair cuts, stocks, and countless other things.

Land, machinery, furniture, and warehouses are all examples of assets that firms own, and all of these assets have value. Asset based valuation is estimating a firm’s value based on its assets.

The goal of investments are to earn returns. In turn, the value of an investment is a function of its returns. Specifically, earnings based valuation is valuing stocks based on earnings. While products and services are meant to be consumed, assets are held to generate wealth in the future by earning income and growing in value.

Choosing the Right Approach

Valuation is both a science and an art. It is a science because there are processes and equations, it’s an art because the processes and equations depend on inputs and assumptions based on individual judgement.

When doing valuations, the valuation approach is determined by what firms derive their value from. For example, a gold mining firm and a car manufacturer are very different businesses. So the approach to valuing them should be different. Gold mining firms, like most natural resource firms, derive their value from resources that they own and and have the ability to extract. And so, they are valued based on their assets in most cases. Asset based valuations are commonly used in asset heavy industries such as natural resources, real estate, and financial services.

On the other hand, much of a car manufacturer’s value comes from its ability to generate earnings by producing and selling cars. While the assets it owns, such as its factory, are important, they can be replaced. The brand, the manufacturing technology, and the distribution partnerships are more valuable. And so, car companies, like most other firms, are valued based on their earnings in most cases.

While these two types of companies require separate valuation approaches, a mixed approach should often be used. For example, a conglomerate with disparate businesses could be valued based on the combined earnings of all of its businesses, or on the combined value of assets of all businesses. Often, both valuation approaches are used to triangulate a fair value.

Valuing Assets Using the Asset Approach

All asset valuations starts with estimating the value of a firm’s assets. Then, subtract all outstanding liabilities. The result is what shareholders own. There are three common methods to estimate asset value: Net Asset Value (NAV), Book Value (BV), and Liquidation Value (LV). The usage of each depends on a firm’s industry, financial health, and firm specific factors.

Book Value

Book Value estimates the value of a firm’s assets using the balance sheet, where the cost of every asset purchased and its corresponding depreciation are recorded. Book value is calculated by subtracting liabilities from the value of assets on the balance sheet.

A variation of Book Value is Tangible Book Value (TBV), which takes into account that intangible assets (such as copyright, trademarks, and good will) are typically hard to sell. TBV excludes the value of intangible assets from BV.

Fundamentally, BV and TBV are based on the cost of assets at the time of purchase, which often does not reflect the value of a firm’s assets accurately. For example, while land tends to increase in value, the value of furniture and fixtures might not even cover the selling expense. For these reasons, book value can be the start of valuations, but shouldn’t be considered in isolation.

Net Asset Value

While Net Asset Value calculation varies by industry, NAV’s purpose is to estimate the fair value of a firm’s assets regardless of industry. Specifically, real estate investment trusts (REITs) will estimate NAV using CAP rate, and natural resource firms estimate NAV of assets by discounting cash flows based on extraction plans, operating costs, and prices of the resource. NAV is commonly used in these and other industries where BV doesn’t represent the fair value of a firm’s assets.

Liquidation Value

When a firm is distressed and likely to liquidate its assets, Liquidation Value is used to value its assets. Since distressed companies often need to sell assets quickly, LV is discounted against NAV and BV. LV is typically calculated by estimating the value assets would fetch at an auction or simply discounted against market value. For underperforming, though not distressed firms, LV acts as a floor for the firm’s value.

Analyzing Fair Value of Assets

After estimating the value of the assets, the liabilities are subtracted to calculate the fair value of the firm. Then, price-to-BV (P/B), price-to-NAV (P/NAV), and price-to-LV (P/LV) ratios are used to compare the firm’s fair value against its market value. These ratios express whether a firm’s market value is higher or lower than the value of its assets, and by how much.

Investors can then compare a firm’s ratios against other firms in the same industry, or against itself historically. This analysis helps illustrate if a firm is expensive based on its assets. While these ratios don’t indicate that a firm is over or undervalued in isolation, they are an excellent starting point for analysis. For example, if a firm has a very low P/B ratio and low debt, further balance sheet analysis can uncover interesting insights. Although uncommon, it is possible that the firm has more cash than its liabilities and market cap combined, implying the assets of the firm are free at the current market value.

Ultimately, the value of assets is what they will fetch in the market. So, even if a firm is not and will never be profitable, the proceeds from selling the firm’s assets can be returned to investors. However, if a firm is profitable or has potential to be profitable, it can also be valued using the earnings approach.

Valuing Assets using the Earnings Approach

The price paid for any asset is the implicit market value for a firm’s ability to generate earnings. The earnings approach is an estimation of the fair value of a firm’s income generation ability.

Earnings Ratios

Earnings ratios are one way of estimating a firm’s income generation ability. They measure the value of the firm against its earnings in a fixed period. The most common ratio is Price/Earnings or P/E ratio.

P/E

P/E ratio measures a firm’s stock price divided by earnings per share in a certain time period. While P/E is simple to calculate, widely used, and easy to understand, P/E cannot be used when a firm doesn’t have earnings (such as start-ups or distressed firms). P/E also doesn’t fully consider capital structure, and is affected by non-cash costs such as depreciation & amortization.

EV/EBIT & EV/EBITDA

To resolve these issues, Enterprise Value (EV) is used instead of Market Cap on the denominator side. Since EV is the sum of Market Cap + debt, this normalizes the capital structure so that it is irrelevant whether a firm is funded by stock or debt. This neutralizes the beneficial effect of debt on P/E, which doesn’t change the value of the firm. As a real world example, the size of the mortgage (debt) doesn’t change the value of a house, what changes is how much of the house is financed by equity (stock).

On the numerator side, various measures are used to normalize profits. Earnings before Interest and Taxes (EBIT) adds back to interest and taxes to a firm’s earnings. Adding back interest normalizes the funding structure on the denominator side (as EV normalizes it on the numerator side). Adding taxes back normalizes tax rates between different firms, as some firms previously deferred or prepaid taxes, which distorts their ongoing tax rate. With these normalizations, EBIT provides a picture of operating profitability. However, EBIT doesn’t consider depreciation and amortization, which are non-cash costs that also provide tax benefits when they are recognized.

This is where Earnings Before Interest, Taxes, Depreciation, and Amortization (EBITDA) come in. EBITDA starts with EBIT, then adds back depreciation and amortization expense. Depreciation and Amortization follows capital expenditure, which can fluctuate significantly based on the timing of capital projects. EBITDA can be more representative of ongoing profitability as it normalizes EBIT for firms with discretionary capital expenditures. However, in asset-heavy industries, depreciation reflects required ongoing capital expenditure, which is a use of cash that is not reflected on the income statement. As a result, EBITDA overstates profitability for firms that require on-going CapEx. When EBITDA is not appropriate, EBIT should be used.

Although some unusual income and expenses are not normalized by EBIT or EBITDA, they cover the most common items that distorts ongoing profitability. The more complicated a ratio is, the less useful it is for comparing one firm to another, which defeats the purpose of ratios as a measure of relative value.

How to Choose the Right Ratio

While multiple ratios can be used for reference, one ratio is typically better at representing value than others. Simply, if the firm’s capital structure and tax rates are similar to the industry, and does not require capital expenditure, P/E works fine. If the firm’s capital structure is different versus the industry, have prepaid taxes, or have deferred tax liabilities, an EV ratio works better. Furthermore, if the firm requires ongoing capital expenditures, use EV/EBIT. Otherwise, EV/EBITDA better represents profitability by normalizing depreciation.

Analyzing Earnings Ratios

There are three ways of analyzing a firm’s ratios, comparing against itself historically, other firms, and other asset classes. It is straightforward to compare against a firm’s historical ratios or other firms. Against other asset classes such as bonds or real estate, the ratio must be inverted to calculate earnings yield, which is comparable to bond yields and real estate cap rates. A higher ratio (or lower yield), means the stock is more expensive against the comparisons.

In addition to ratios, growth and risk should be analyzed to generate a bigger picture (by comparing against historical data, industry peers, and other asset classes). Using multiple ratios can also help investors feel confident about a valuation and triangulate a firm’s value. After the analysis, there should be a range of ratios, growth, and risk profiles from the comparison set, which is a great starting point. Ultimately, relative valuation will point to a range of value that a firm deserves based on its earnings.

While ratios are an excellent tool for relative valuation, they don’t consider risk, change, or unusual expenses (and incomes). They also can’t be used to estimate intrinsic value nor value firms with negative profits. While most of these issues can be considered separately or normalized, it is impossible to estimate intrinsic value using ratios. To do so, use the discounted cash flow valuation method.

Discounted Cash Flow Valuations

Discounted cash flow valuations assume that assets are going concerns that generate cash flows in perpetuity. And since the future is uncertain and contains risk, the future cash flows are discounted at a rate that reflects the riskiness of the asset and its capital structure.

Dividend Discount Model (DDM)

Dividends are cash flows a firm pays to the investor for holding its shares. And so, the value of a share is the discounted future dividends it will pay. DDM represents this in a formula that calculates the value of a stock by estimating its future dividends and discounting them back to the present. A single stage DDM is represented by the equation below, where $V_0$ is the value of the stock to solve for, $D_1$ is dividends expected in the next year, $r$ is the discount rate, and $g$ is the expected constant growth rate of the dividend.

$V_0=\frac{D_1}{r-g}$

$D_1$ can be found on the investor relations section of a firm’s website, $g$ is an estimate (usually based on historical growth rate), and $r$ is the cost of equity, typically estimated with the CAPM model.

DDM assumes the firm pays a consistent dividend, is a going concern, and will generate sufficient cash flow to pay the dividend. For firms that don’t pay dividends, or don’t generate enough cash flow to cover their dividends, DDM is not the appropriate valuation method. In these cases, a Free Cash Flow model should be used.

Free Cash Flow to Equity (FCFE)

When firms produce cash flow, it must first pay interest and maturing debts. What remains is FCFE, which replenishes the cash balance of the firm. And since the cash balance is where dividends are paid out of, a firm can not sustainably pay a dividend that is higher than its FCFE. On the other hand, if a firm can afford to pay out a much higher dividend relative to its FCFE, investors will eventually demand more cash returns from management. FCFE can be thought of as cash flow that belongs to shareholders, and should be used to value firms when they don’t pay dividends or their dividend is meaningfully different from FCFE. The FCFE equation for any given period is below.

$FCFE = Net\ Income - Net\ Capital\ Expenditure - Increase\ in\ Working\ Capital\ + Net\ Debt\ Issuance$

To value a firm using a FCFE model, project the firm’s future FCFE, and discount it back to the present. A single stage FCFE model is represented by the equation below, where $V_0$ is the value of the stock to solve for, $FCFE_1$ is FCFE for the next year, $r$ is the discount rate, and $g$ is the expected constant FCFE growth rate.

$V_0=\frac{FCFE_1}{r-g}$

$FCFE_1$ can be estimated using the firm’s financial statements, $g$ is typically based on historical growth, and $r$ is the cost of equity, typically estimated with the CAPM model. The FCFE model requires that a firm generates FCFE and has a stable capital structure, it is also best used for comparison within an industry. Otherwise, use an FCFF model.

Free Cash Flow to Firm (FCFF)

FCFF is the cash flow an operating asset generates without taking into account capital structure. Compared to FCFE, FCFF ignores debt issuance and repayments, and adds back interest. Similar to DDM and FCFE, a FCFF model estimates a firm’s cash flows in perpetuity, and discounts them back to calculate the value of the firm. The difference is, investors must subtract the firm’s debt to calculate its equity value. The FCFF equation for any given period is below.

$FCFF = Net\ Income + Interest\ Expense * (1-Tax Rate) - Net\ Capital\ Expenditure - Increase\ in\ Working\ Capital$

To value a firm using the FCFF model, project the firm’s future FCFF, and discount it back to the present. A single stage FCFF model is represented by the equation below, where $V_0$ is the value of the stock to solve for, $FCFF_1$ is FCFF for the next year, $r$ is the discount rate, and $g$ is the expected constant FCFF growth rate.

$V_0=\frac{FCFF_1}{r-g}$

$FCFF_1$ can be estimated using the firm’s financial statements, $g$ is an estimate (usually based on historical growth rate), and $r$ is the Weighted Average Cost of Capital (WACC), which reflects the cost of debt, cost equity, and the % of the firm funded by debt or equity. The cost of debt is the firm’s average interest rate on its debt, after taxes. The cost of equity is typically calculated using the CAPM model. After calculating firm value, debt is subtracted to calculate the value of equity. The FCFF model requires that a firm generates FCFF. Otherwise, cash flow models cannot be used to value the firm.

Multi-Stage Cash Flow Models

An important assumption for using a single stage model is that the firm has reached a stable growth rate. This growth rate should not exceed the growth rate of the economy for more than 2%, or else the firm will become infinitely large and exceed the entire economy. Historically, this number can be as high as 8% globally, 2% above the 6% nominal GDP growth (consisting of around 3% real GDP growth and 3% inflation). For developed economies, this will be lower.

In addition, single-stage models are not good at handling change and volatility, since they assume a firm’s cash flow or dividend will steadily and slowly grow in perpetuity. While investors can normalize cash flows when valuing historically stable firms that experienced unusual incomes or expenses, young firms with significantly higher CapEx than depreciation, distressed firms, highly levered firms, and other volatile firms that are far from a steady state will be difficult to value with single stage models.

To address these issues, use multi-stage models, which work with all three discounted cash flow valuation methods. In multi-stage models, firms have one or more growth phases, and a stable phase. In the growth phases, firms start with high growth, which decelerates over time. Eventually, the firm reaches the stable phase and grows slowly into perpetuity. The equation below represents any multi-stage discounted cash flow model, where $V_0$ , the value of a stock equals $V_f$ , the value of cash flows in a forecast period plus $V_t$ , the terminal value (which is the value of cash flows for a stable company in perpetuity).

$V_0 = V_f + V_t$

The equation for $V_f$ is below. $CF_n$ , the estimated cash flows is discounted by $(1+r)^n$ , where $r$ is the discount rate and $n$ is the number of periods in the future.

$V_f = \frac{CF_1}{1+r} + \frac{CF_2}{(1+r)^2} + \frac{CF_3}{(1+r)^3} + \frac{CF_n}{(1+r)^n}$

The equation for terminal value is the stable growth value of the firm at period $n+1$ .

$V_{n+1} = \frac{CF_{n+1}}{(r-g)}$

And since the terminal value is $n+1$ periods a way, it is discounted back to the present to calculate $V_t$ .

$V_t = \frac{V_{n+1}}{(1+r)^{n+1}}$

How to Forecast Cash Flows

The simple way of forecasting cash flows is to review the firm’s historical growth rate, and its deceleration year by year, and apply it for the number of years required to reach stable growth. While simple, this approach can be sufficient in highly predictable firms.

In more complicated cases, forecast the firm’s revenue, gross margin, operating expenses, down to the after tax EBIT. Then, subtract Net CapEx, Net Working Capital increases to get FCFF. For FCFE, simply subtract After Tax Interest Expense and add Net Debt Issuance from FCFF. This process is repeated for every year before the stable growth phase. After reaching the stable growth phase, use a low constant growth rate into perpetuity.

In cases where a firm has multiple disparate lines of business that have varied growth dynamics, this process may be required for each line of business to increase the accuracy of the forecast.

Choosing the Right Cash Flow Model

Theoretically, valuation does not depend on the model used. Any cash flow model with any number of stages will yield the same result with the right input and assumptions . The reason for using one over another is to balance effort and accuracy. For example, a firm with no debt that pays a consistent dividend funded by 100% of its FCFE can be valued with all three models, but there is no need for a multi-stage FCFF model when a single stage DDM will do.

Simply, if the firm consistently pays a dividend that is consistently between 70% and 100% of FCFE and has a stable capital structure, use DDM. In addition, if the dividend growth rate is stable, use a single stage model. If the growth is higher but moderating, use a multi-stage model.

If the firm does not pay a dividend, or pays a dividend that does not resemble FCFE, and the firm’s capital structure is stable, use FCFE. In addition, if FCFE growth is stable, the industry is stable, working capital as a percentage of revenue resembles the industry average, and capital expenditures don’t significantly outpace depreciation relative to the industry, use a single stage model. Otherwise, either normalize the issues (working capital, capital expenditures), or use a multi-stage model.

If the firm is in process of adjusting its leverage, or if leverage cannot be calculated (e.g the division of a firm), use FCFF. In addition, if cross industry comparability is required, FCFF will neutralize differences across industries. Furthermore, if FCFF growth is stable, use a single stage model. Otherwise, use a multi-stage model.

Valuation is a Continuous Process

Regardless of model, a valuation is only as good as its assumptions, and small changes in assumptions have large effects on fair value. In addition, valuations are a snapshot at a moment in time. Therefore, to be accurate over time, investors must continuously examine, question, and refine assumptions both on a regular basis and as new information becomes available.

Furthermore, since the world is probabilistic, it is impossible to take everything into account. So using multiple sets of assumptions based on how the firm would perform, and assigning probability to those assumptions to arrive at a range of values will help investors triangulate the price range in which the firm is reasonably valued. For example, different growth and discount rates can be used for cash flow models. And a range of multiples can be used for earnings ratios.

Markets Value Considerations

The market value is not necessarily the fair price to pay for an asset. While the market tries to be efficient (and can be at times), markets are made of people. People are not always rational, nor do they always estimate returns and risk accurately. Ultimately, market value is a function of supply (the price shareholders are willing to exchange shares for cash) and demand (what investors willing to pay for a security). And fair value is based on individual assumptions about a firm’s future cash flows and the discount rate, or the value of its assets.

Comparing Against Market Value

Individual fair value estimates rarely match the exact market value, but are often close enough. When there are large discrepancies between fair value and market value, investors should investigate the reasons behind it. These discrepancies can be opportunities to generate excess returns at no additional risk, if the investor is right. Although they could also drive underperformance if the investor is wrong.

Below is an equation that illustrates the components of $R_a$ actual returns, where $R_e$ , market’s expected return, is affected by $R_o$ , the return due to over or under performance, and $R_r$ , the return due to random events.

$R_a = R_e + R_o + R_r$

Randomness aside, being right more often than wrong generates potential excess returns. Below is a framework that illustrates how actual return varies based on investor and market judgements.

Actual Returns Pending Market and Individual Judgement	Individual Right	Individual Wrong
Markets Right	Expected return + Randomness	Expected return + Randomness + Potential Under-performance
Markets Wrong	Expected return + Randomness + Potential Over-performance	Randomness

Valid Reasons that Drive Intrinsic Value and Market Value Gaps

While gaps between intrinsic value and market value can be opportunities, there can also be valid reasons behind discrepancies between intrinsic value and market value. In these situations, investors should question if and when these issues will resolve, view these assets as informed speculations, or stay away all together. Some of the common reasons that drive discrepancies are below.

Drivers of discrepancy between market value and intrinsic value	Issues	Examples
Lack of price discovery	Lack of marginal buyers and marginal seller	Controlled entities (one share holder owns majority of shares)
Low Liquidity	Large bid-ask spread, low volume, high transaction cost	Micro caps, stocks that are not widely followed
Value of strategic asset	Assets that are not priced based on earnings or tangible assets	Sports teams, fine art
Tax implications	Value of all subsidiaries exceed conglomerate parent, but spin off creates large tax bill	Conglomerates, holding companies

Outperforming the Market

It’s helpful to think about valuation systematically. Intrinsic value equals valuation plus errors plus randomness. Reducing error and randomness increases the accuracy of intrinsic value estimates. And since the difference between intrinsic value and market value is potential for over or underperformance, accuracy directly translates to potential to outperform.

There are two strategies to outperform the market as an investor. One is investing in assets with a higher expected risk, the other is investing in undervalued assets. While both are valid strategies (which can be used together), the latter can produce excess returns at no additional risk. And that is the point of valuation, to identify the fair value of assets accurately, as the gap between fair value and market value is potential to over (or under) perform. This is systematically illustrated by the equation below, where $V_i$ , intrinsic value, equals $V_f$ , fair value estimate, plus $V_{\epsilon}$ , valuation errors and $V_r$ , randomness affecting valuation.

$V_i = V_f + V_{\epsilon} + V_r$

To reduce randomness, diversify. To reduce errors, investors must continuously improve their valuation skills. These are two basic concepts that are often misunderstood and ignored, yet they can give investors seeking to beat the market a significant edge when mastered.

Valuation Demands Action

Ultimately, valuations are only useful if they inspire action. And taking action to buy, sell, and rebalance when stocks become undervalued or overvalued is a part of disciplined portfolio management.

When a stock is overvalued beyond any reasonable valuation range, investors should trim it, exit the position, or use hedging instruments to reduce risk. Even firms with excellent fundamentals can be overvalued and reallocating funds to other assets will improve expected return. On the other hand, when an asset is surely undervalued compared to market value and to the rest of the portfolio, investors should enter the position or add to it.

All this is not to say valuations are the only factor investors should consider. In fact, investors should avoid firms with poor fundamentals even if they are undervalued in most cases. For these firms, investors endure little to no returns while they wait for market value and fair value to converge, something that is not guaranteed and may take years if it does happen. In addition, a firm’s value may drop due to poorer performance against already low expectations. As Warren Buffet said, “it’s far better to buy a wonderful company at a fair price than a fair company at a wonderful price.”

As investors hold stocks for long periods of time, prices can move stocks from being over to undervalued and vice versa. The decision on whether an investor should take action is to analyze how over or undervalued each stock is. Again, small changes in assumptions have large effects on a firm’s fair value estimates. So, using a price range to buy and sell will prevent over-optimizing, unnecessary transaction costs, and avoidable taxes.

The goal of investing is to produce returns and build wealth over time. Since price and return have an inverse causal relationship, investing in an asset without knowing its value is investing blind. Valuations are not difficult, nor complex, it is a skill that anyone can develop using free tools and publicly available information. And the better an investor is at valuations, the more likely they will be able to achieve higher returns. Never forget, price is what you pay, value is what you get.