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VALUATION. Terminology. Equity value Market value of shareholders’ equity (shares outstanding x current stock price) Enterprise value Market value of all capital invested in the firm Equity, debt (short-term and long-term), preferred stock, minority interest. Assets. Liabilities. Equity.

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  • Equity value

    • Market value of shareholders’ equity (shares outstanding x current stock price)

  • Enterprise value

    • Market value of all capital invested in the firm

      • Equity, debt (short-term and long-term), preferred stock, minority interest








Preferred Stock

Minority Interest

What is value
What is Value?

  • In general, the value of an asset is the price that a willing and able buyer pays to a willing and able seller

  • Note that if either the buyer or seller is not both willing and able, then an offer does not establish the value of the asset

  • There are several types of value, of which we are concerned with four:

    • Book Value – The carrying value on the balance sheet of the firm’s equity (Total Assets less Total Liabilities)

    • Tangible Book Value – Book value minus intangible assets (goodwill, patents, etc)

    • Market Value - The price of an asset as determined in a competitive marketplace

    • Intrinsic Value - The present value of the expected future cash flows discounted at the decision maker’s required rate of return

Common stock valuation
Common Stock Valuation

  • As with any other security, the first step in valuing common stocks is to determine the expected future cash flows.

  • Finding the present values of these cash flows and adding them together will give us the value:

  • For a stock, there are two cash flows:

    • Future dividend payments

    • The future selling price

Common stock valuation an example
Common Stock Valuation: An Example





  • Assume that you are considering the purchase of a stock which will pay dividends of $2 (D1) next year, and $2.16 (D2) the following year. After receiving the second dividend, you plan on selling the stock for $33.33. What is the intrinsic value of this stock if your required return is 15%?

The dividend discount model ddm
The Dividend Discount Model (DDM)

  • With these assumptions, we can derive a model that is variously known as the Dividend Discount Model, the Constant Growth Model, or the Gordon Model:

  • This model gives us the present value of an infinite stream of dividends that are growing at a constant rate.

Estimating the ddm inputs
Estimating the DDM Inputs

  • The DDM requires us to estimate the dividend growth rate and the required rate of return.

  • The dividend growth rate can be estimated in three ways:

    • Use the historical growth rate and assume it will continue

    • Use the equation: g = br

    • Generate your own forecast with whatever method seems appropriate

  • The required return is often estimated by using the CAPM: ki = krf + bi(km – krf) or some other asset pricing model.

The ddm an example
The DDM: An Example

  • Recall our previous example in which the dividends were growing at 8% per year, and your required return was 15%.

  • The value of the stock must be (D0 = 1.85):

  • Note that this is exactly the same value that we got earlier, but we didn’t have to use an assumed future selling price.

The ddm extended
The DDM Extended

  • There is no reason that we can’t use the DDM at any point in time.

  • For example, we might want to calculate the price that a stock should sell for in two years.

  • To do this, we can simply generalize the DDM:

  • For example, to value a stock at year 2, we simply use the dividend for year 3 (D3).

The ddm example cont
The DDM Example (cont.)

  • In the earlier example, how did we know that the stock would be selling for $33.33 in two years?

  • Note that the period 3 dividend must be 8% larger than the period 2 dividend, so:

  • Remember, the value at period 2 is simply the present value of D3, D4, D5, …, D∞

What if growth isn t constant cont
What if Growth Isn’t Constant? (cont.)










g = 15%

g = 8%

  • Let’s take our previous example, but assume that the dividend will grow at a rate of 15% per year for the next three years before settling down to a constant 8% per year. What’s the value of the stock now? (Recall that D0 = 1.85)

What if growth isn t constant cont1
What if Growth Isn’t Constant? (cont.)

  • First, note that we can calculate the value of the stock at the end of period 3 (using D4):

  • Now, find the present values of the future selling price and D1, D2, and D3:

  • So, the value of the stock is $34.09 and we didn’t even have to assume a constant growth rate. Note also that the value is higher than the original value because the average growth rate is higher.

Two stage ddm valuation model
Two-Stage DDM Valuation Model

  • The previous example showed one way to value a stock with two (or more) growth rates. Typically, such a company can be expected to have a period of supra-normal growth followed by a slower growth rate that we can expect to last for a long time.

  • In these cases we can use the two-stage DDM:

Ddm rationale
DDM Rationale


Earnings per share





Applying ddm rationale
Applying DDM Rationale

  • Growth stage: Rapidly expanding sales, high profit margins, abnormally high growth in EPS. Payout ratio is low.

  • Transition stage: Increased competition reduces profit margins, and earnings growth slows. With fewer investment opportunities, company begins to pay out a larger percent of earnings.

  • Maturity stage: Earnings growth rate, payout ratio, ad return on equity stabilize for the remainder of life.

Multistage model
Multistage model

  • What would be the likely growth rate during the mature stage?

Other valuation methods
Other Valuation Methods

  • Some companies do not pay dividends, or the dividends are unpredictable.

  • In these cases we have several other possible valuation models:

    • Earnings Model

    • Free Cash Flow Model

The earnings model
The Earnings Model

  • The earnings model separates a company’s earnings (EPS) into two components:

    • Current earnings, which are assumed to be repeated forever with no growth and 100% payout.

    • Growth of earnings which derives from future investments.

  • If the current earnings are a perpetuity with 100% payout, then they are worth:

The earnings model cont
The Earnings Model (cont.)

  • VCE is the value of the stock if the company does not grow, but if it does grow in the future its value must be higher than VCE so this represents the minimum value (assuming profitable growth).

  • If the company grows beyond their current EPS by reinvesting a portion of their earnings, then the value of these growth opportunities is the present value of the additional earnings in future years.

  • The growth in earnings will be equal to the ROE times the retention ratio (1 – payout ratio):

  • Where b = retention ratio and r = ROE (return on equity).

The earnings model cont1
The Earnings Model (cont.)

  • If the company can maintain this growth rate forever, then the present value of their growth opportunities is:

  • Which, since NPV is growing at a constant rate can be rewritten as:

The earnings model cont2
The Earnings Model (cont.)

  • The value of the company today must be the sum of the value of the company if it doesn’t grow and the value of the future growth:

  • Where RE1 is the retained earnings in period 1, r is the return on equity, k is the required return, and g is the growth rate

Partitioning Value: Example





Vo = value with growth

NGVo = no growth component value

PVGO = Present Value of Growth Opportunities

The free cash flow model concept
The Free Cash Flow Model - Concept

  • Free cash flow is the cash flow that’s left over after making all required investments in operating assets:

  • NOPAT is net operating profit after tax

  • The total value of the firm equals the value of its debt plus preferred plus common

  • We can find the total value of the firm’s operations (not including non-operating assets), by calculating the present value of its future free cash flows

  • Add in the value of its non-operating assets to get the total value of the firm

  • Then, subtract the value of the firm’s debt and the value of its preferred stock

  • Divide by the number of shares outstanding to get the per share value of the stock.

Discounted cash flow
Discounted cash-flow

  • DCF method entails estimating the free cash flow available to debt and equity investors (i.e., the annual cash flows generated by the business, and the terminal value of the business at the end of the time horizon) and discounting these flows back to the present using the weighted average cost of capital as the discount rate to arrive at a present value of the assets

  • DCF is often the primary valuation methodology in M&A

  • DCF is the PV of 2 main types of free cash flows:

    • Free cash flows to all capital providers (debt and equity)

    • Free cash flows to equity capital providers

  • Fundamental in nature, DCF allows for questioning all of the assumptions and for performing sensitivity analysis

  • One can easily estimate equity value from firm value by subtracting the market value of debt today


  • Project the free cash flows of a business over the forecast period

    • Typical forecast period is 10 years. However, the range can vary from five to 20 years

  • Use the weighted average cost of capital (WACC) to determine the appropriate discount rate range

  • Estimate the terminal value of the business at the end of the forecast period

  • Determine the value for the enterprise by discounting the projected free cash flows and terminal value to the present

  • Interpret the results and perform sensitivity analysis

  • Calculation of free cash flow begins with financial projections

    • Comprehensive projections (i.e., fully-integrated income statement, balance sheet and statement of cash flows) typically provide all the necessary elements

  • Quality of DCF analysis is a function of the quality of projections

    • Confirm and validate key assumptions underlying projections

    • Sensitize variables that drive projections

  • Sources of projections include

    • Target company’s management

    • Acquiring company’s management

    • Research analysts

    • Bankers

Fcf what is it
FCF: What is it?

  • Free cash flow is un-levered cash available to creditors and owners after taxes and reinvestment

    • Un-levered means free from financing considerations

    • Contrast with Cash Flow from Operations (which consists of Net Income plus Depreciation and Amortization plus Deferred Taxes and Non-Cash charges)

    • Free cash flows can be forecast from a firm’s financial projections, even if those projections include the effects of debt

Fcf how to calculate it
FCF: How to calculate it?

Net Sales (Revenue)

- Cost of goods sold (COGS)

- Selling, general, and administrative (SG&A)

=Earnings before interest, taxes, depreciation and amortization (EBITDA)

- Depreciation & Amortization (D&A)

= Earnings before interest and taxes (EBIT)

- Taxes (tax rate*EBIT)

=Net operating profit/loss after taxes (NOPLAT)

+ Depreciation & Amortization (D&A)

- Capital Expenditure (Capex)

- Change in Net working capital (NWC)

=Free cash flow (FCF)

Fcf how to forecast
FCF: How to forecast?

  • Project growth in Net Sales by basing assumptions on

    • Research reports

    • Client forecasts (if available)

    • Industry trends

    • percent growth is usually an input; aggregate sales is derived from this input

  • Estimate the following by percent of sales

    • Cost of Goods Sold (COGS)

    • Selling, General and Administrative (SG&A) Expenses

  • Determine Interest Expense

    • Refer to the debt schedule and calculate the weighted average interest rate.

    • If no debt schedule is available, then compute Interest Expense as a percent of average Long-Term Debt= (Beginning LTD + Ending LTD)/2

  • Assess tax rate based on the marginal tax rate (federal, state and local) and current tax regulation

Fcf how to forecast contd
FCF: How to forecast? (contd..)

  • Depreciation

    • Sometimes expressed as % of Property, Plant and Equipment (PP&E)

  • Capital Expenditures (Capex)

    • Expenditures necessary to maintain the required capital intensity

  • Working Capital excluding cash and cash equivalents and STD

    • WC = (Current Assets–Cash and Cash Equivalents)–(Current Liabilities–STD)

    • Estimate WC as a percent of sales

    • Possible to squeeze cash from WC by operating more efficiently

    • Three major components of working capital are: inventories, receivables and payables

  • Property, Plant and Equipment (PP&E):

    • Project by capital intensity/efficiency: sales divided by (PP&E)

    • Beginning PP&E–Depreciation+ CapEx = Ending PP&E

Dcf wacc

  • Weighted Average Cost Of Capital (WACC)

    • Ascertain the costs of the various sources of capital for the company, with a given capital structure

      • Debt

      • Equity

    • The after-tax costs of the various sources are then averaged to arrive at an appropriate discount rate to value unlevered cash flows

    • Debt and equity market values used should represent the “target” capital structure (the capital structure that includes planned debt and equity financings, if any)

Dcf wacc contd
DCF – WACC (contd..)

Cost of debt

  • Consult with the debt capital markets group for a 10-year maturity all-in new issue rate at the credit rating corresponding to the targeted capital structure. As part of this process, you should look at the yield on new issues of comparable companies since the cost of debt is a function of the risks associated with a given business/industry

  • If the company has public debt outstanding and you do not intend to change its capital structure, find the debt rating

Dcf wacc contd1
DCF – WACC (contd..)

Cost of equity

  • Use the Capital Asset Pricing Model (CAPM)

  • The risk-free rate can be taken as the interest rate on a generic 10-year government note

    • Roughly matches the maturity of projections

  •  = cov(r,rM)/var(rM), usually estimated using a regression

  • Estimation issues

    • Betas may change over time

    • Don’t use data from too long ago

    • Five years of monthly data is reasonable


  • Used to assess a company's efficiency at allocating the capital under its control to profitable investments. The return on invested capital measure gives a sense of how well a company is using its money to generate returns. Comparing a company's ROIC with its cost of capital (WACC) reveals whether invested capital was used effectively.The general equation for ROIC is as follows:

    Total capital includes long-term debt, and common and preferred shares. Because some companies receive income from other sources or have other conflicting items in their net income, net operating profit after tax (NOPAT) may be used instead.

Dcf terminal value
DCF – Terminal value

  • Terminal value is the value of all future cash flows after the explicit forecast period of 10 years

  • Key value drivers

  • Growth rate of NOPLAT (g)

  • Return on invested capital ROIC

    • Value is higher if ROIC is higher than WACC;

      • Higher growth rate is good because our projects have a ROIC greater

      • than the cost of capital.

    • Value is lower if ROIC is higher than WACC

      • Higher growth rate is bad because our projects have a ROIC lower than the cost of capital

Dcf terminal value contd
DCF – Terminal value (contd..)

  • Can also estimate terminal value using an exit multiple

    Terminal value = Statistic x Multiple

  • Forecast 10 explicit years of FCF, EBITDA, Net Income

  • Use a multiple of any relevant figure: Book Value, Net Income, Cash Flow from Operations, EBIT, EBITDA, Sales, etc.

    • Terminal Value should be an Enterprise Value; NOT ALL multiples produce an Enterprise Value (e.g., P/Es)

  • Multiply and estimate Terminal Value


  • Validate and test projection assumptions

  • Carefully consider all variables in the calculation of the discount rate

  • Consistency of assumptions concerning interest rates, inflation rates, tax rates and the cost of capital is critical

  • Thoughtfully consider terminal value methodology

  • Do sensitivity analysis (base projection variables, synergies, discount rates, terminal values, etc.)

Walmart fcf assumptions
Walmart FCF assumptions

  • The sales at the end of 2007 were $370 billion. They are projected to grow by 10% during the next year. The growth rate of sales will decline by 0.5% each year for the next 10 years

  • COGS is currently 76% of sales and is expected to decline by 0.1% during the next 10 years

  • SG&A is currently 17% of sales and is expected to increase by 0.1% during the next 10 years

  • D&A are currently 1.7% of sales and are expected to remain at the same level

  • Capex is currently 3.5% of sales and is expected to remain at the same level

  • NWC is 0.5% of sales and is expected to remain at the same level


  • Equity value

    • Market value of shareholders’ equity (shares outstanding x current stock price)

  • Enterprise value

    • Market value of all capital invested in the firm

      • Equity, debt (short-term and long-term), preferred stock, minority interest








Preferred Stock

Minority Interest

Terminology contd
Terminology (contd..)

Equity Value Multiples

Certain flows or values apply to equity holders only—these include net income and book value of equity. Since each of these values is after debt and preferred financing is taken into account, multiples of these flows or values should be based on the value of the equity only

Relevant ratios are Equity Value to: Net Income to Common Shareholders, Book Value and Cash Flow

Enterprise Value Multiples

Other flows apply to all capital providers (i.e., debt and equity), and therefore Enterprise Value should be used

Relevant ratios are: Enterprise Value to: Sales, EBITDA and EBIT

Relative value models
Relative Value Models

  • Professional analysts often value stocks relative to one another.

  • For example, an analyst might say that XYZ is undervalued relative to ABC (which is in the same industry) because it has a lower P/E ratio, but a higher earnings growth rate.

  • These models are popular, but they do have problems:

    • Even within an industry, companies are rarely perfectly comparable.

    • There is no way to know for sure what the “correct” price multiple is.

    • There is no easy, linear relationship between earnings growth and price multiples (i.e., we can’t say that because XYZ is growing 2% faster that it’s P/E should be 3 points higher than ABC’s – there are just too many additional factors).

    • A company’s (or industry’s) historical multiples may not be relevant today due to changes in earnings growth over time.

Price earnings ratios
Price Earnings Ratios

  • P/E Ratios are a function of two factors

    • Required Rates of Return (k)

    • Expected growth in Dividends

  • Uses

    • Relative valuation

    • Extensive Use in industry

  • As a rule of thumb, or simplified model, analysts often assume that a stock is worth some “justified” P/E ratio times the firm’s expected earnings.

  • This justified P/E may be based on the industry average P/E, the company’s own historical P/E, or some other P/E that the analyst feels is justified.

  • To calculate the value of the stock, we merely multiply its next years’ earnings by this justified P/E:

P e ratio no expected growth
P/E Ratio: No Expected Growth

  • E1 - expected earnings for next year

    • E1 is equal to D1 under no growth

  • k - required rate of return

P e ratio with constant growth
P/E Ratio with Constant Growth

  • ROE: Higher ROE implies higher P/E

  • Growth rate, g: Higher growth rate implies higher P/E

  • Market capitalization rate, r: Higher r implies lower P/E

  • Retention ratio, b: Higher b implies higher P/E

Numerical example
Numerical Example:

No Growth:

E0 = $2.50 g = 0 k = 12.5%

P0 = D/k = $2.50/.125 = $20.00

PE = 1/k = 1/.125 = 8

With Growth:

b = 60% ROE = 15% (1-b) = 40%

E1 = $2.50 (1 + (.6)(.15)) = $2.73

D1 = $2.73 (1-.6) = $1.09

k = 12.5% g = 9%

P0 = 1.09/(.125-.09) = $31.14

PE = 31.14/2.73 = 11.4

PE = (1 - .60) / (.125 - .09) = 11.4

How to compare p e s
How to compare P/E’s

  • Comparison across time

    • If the PE ratio of a firm is high today relative to the average PE ratio over time, is the stock overvalued?

  • Comparison across firms

    • If the PE ratio of a firm is high today relative to the average PE ratio of other comparable firms, is the stock overvalued?

Pitfalls in p e analysis
Pitfalls in P/E Analysis

  • Use of accounting earnings

    • Earnings Management

    • Choices on GAAP

  • Inflation

  • Reported earnings fluctuate around the business cycle.

  • Examine the time series of P/E ratios (for that matter, any valuation ratio) to examine if there are any abnormal changes across time

    • P/E ratio may be small if any large increase earnings are expected to be temporary.

    • P/E ratio may be large if any large decline in earnings is expected to be temporary

Forecasting pe
Forecasting PE


  • PE ratios depend on the current economic conditions

  • One can use a regression model to predict PE

    PEt = a + b*Tbond-ratet + c*Expected Inflationt

  • Then plug in the current/predicted values for interest rates to get the PE for the firm


  • One can use a regression model to predict PE

    PEi = a + b*FirmSizei + c*Leveragei + d*ExpectedGrowthi + e*Betai

  • Then plug in the characteristics for the firm to get it’s PE

Example cross sectional
Example (cross sectional)

1987 PE = 7.1839 + 13.05 PAYOUT - 0.6259 BETA + 6.5659 EGR

1988 PE = 2.5848 + 29.91 PAYOUT - 4.5157 BETA + 19.9143 EGR

1989 PE = 4.6122 + 59.74 PAYOUT - 0.7546 BETA + 9.0072 EGR

1990 PE = 3.5955 + 10.88 PAYOUT - 0.2801 BETA + 5.4573 EGR

1991 PE = 2.7711 + 22.89 PAYOUT - 0.1326 BETA + 13.8653 EGR


PE = Price-Earnings ratio at the end of the year

PAYOUT = Dividend Payout ratio at the end of the year

BETA = Beta of the stock, using returns from prior five years

EGR = Earnings growth rate over the previous five years


  • The basic regression assumes a linear relationship between PE ratios and independent variables

  • The basic relationship between PE ratios and independent variables itself might not be stable, and if it shifts from year to year

  • It is always useful to supplement with the analysis of what should be the PE based on fundamentals (growth, ROE etc.)

Price to book ratio
Price to book ratio

  • Price-to-Book

    • P/B is bigger when cost of capital is lower

    • P/B is bigger when growth rate is higher

    • P/B is bigger when ROE is higher

P b and roe
P/B and ROE

  • Firms which have high ROE usually sell for well above book value and firms which have low ROE sell at or below book value

  • The firms which should draw attention from investors are those which provide mismatches of price-book value ratios and returns on equity

    • low P/BV ratios and high ROE or high P/BV ratios and low ROE

P b ratios caution
P/B ratios caution

  • P/B ratio could be difficult to interpret when there are unusual write-offs, or negative book values

  • Several commercial services including Standard and Poor’s provide balance sheet numbers that adjust book values for any large and unusual write offs

  • Book value is an application of arbitrary accounting rules

The p s approach
The P/S Approach

  • In some cases, companies aren’t currently earning any money and this makes the P/E approach impossible to use (because there are no earnings).

  • In these cases, analysts often estimate the value of the stock as some multiple of sales (Price/Sales ratio).

  • The justified P/S ratio may be based on historical P/S for the company, P/S for the industry, or some other estimate:

Using multiples
Using multiples

  • Determine the peer group (your comps universe)

  • Gather the appropriate financial information

  • Enter the financial information into your spreadsheet

    • normalize for non-recurring items (why?)

  • Calculate relevant historical or forward multiples (P/E; EV/EBITDA)

    • Medians are better than means (why?)

    • Forward multiples are better than historical multiples (why?)

  • Forecast your company’s future financial performance (EBITDA, EPS, Cash Flow, etc.)

  • Apply appropriate multiples to your company’s financial stats and derive implied valuation range

Using multiples1
Using Multiples





Distribution channels





Size (revenues, assets, market cap)



Dividend yield

Growth prospects

Shareholder base

  • A comparable peer group should embody the same operational and financial attributes so that their public trading values represent a reasonable proxy for those of the company under consideration

Using multiples2
Using Multiples

  • Even with standard metrics, certain multiples are more relevant for some industries than others

    • For many industries, EV/EBITDA multiples are the most common trading metric (e.g. Industrials, Transportation, Distribution, etc.)

    • For other industries, P/E multiples are more widely followed (Pharmaceuticals, Restaurants, Biotech, etc.)

    • Financials usually trade on P/B (price-to-book)

  • Reading analyst reports will help you understand the metrics analysts use to value the sector and the industry

Using multiples3
Using Multiples

  • Certain sectors have unique metrics

    • Telecommunications: Enterprise value to

      • Number of subscribers

      • Route miles, fiber miles

      • Access lines

    • Natural resources: Enterprise value to

      • EBITDAX (Earnings Before Interest, Taxes, Depreciation, Amortization and Exploration Expenses)

      • Reserves

      • Production

    • Retail/Real estate: Enterprise value to

      • Square footage

      • EBITDAR (Earnings Before Interest, Taxes, Depreciation, Amortization and Rent)

Using multiples5
Using Multiples

  • Getting the correct numbers

    • Ensure you have correctly captured the equity and net debt components

      • Diluted shares (includes options and convertibles if in the money)

      • Net debt includes preferreds, out of the money converts, capital leases, etc.

    • Ensure your income statement projections are uniform across your comps

      • Adjust for extraordinary items and one time charges

      • Calendarize so that projections reflect the same time periods

      • Check analyst projections to make sure they are treating all expense components the same across the comps (e.g., amortization of intangibles)

  • Determining a value range

    • Thoughtfully consider the multiple range—using the mean/median is not thoughtful

    • Calculate the value correctly (Firm value versus Equity value issue)