VALUATION

VALUATION

TerminologyEquity 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 interestEquity

Debt

Preferred Stock

Minority Interest

EnterpriseValue

LiabilitiesAssets

=

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

DIVIDEND DISCOUNT MODELS

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

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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%?

2.00 2.1633.33

?

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 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 + i(km – krf) or some other asset pricing model.

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 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.) 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.) 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)

0 1 2 3 4

2.1275 2.4466 2.8136 3.0387 …

g = 15% g = 8%

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.

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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:

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PV of the first N dividends + PV of stock price at period N

DDM Rationale

Time

$

Growth Transition Maturity

Earnings per share

Applying DDM Rationale1. Growth stage: Rapidly expanding sales,

high profit margins, abnormally high growth in EPS. Payout ratio is low.

2. 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.

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

Multistage model

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

stage Mature

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EARNING AND FREE CASH FLOW

MODELS

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 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:

k

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1

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).

brg

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:

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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

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Vo = value with growth

NGVo = no growth component value

PVGO = Present Value of Growth Opportunities

Partitioning Value: Example

DIV1=$3

EPS1=$5

K=15%

G=8%

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.

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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:1.Free cash flows to all capital providers (debt and equity)2.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

DCF1. 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

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

3. Estimate the terminal value of the business at the end of the forecast period

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

5. 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?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?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? 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..) 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 – WACCWeighted 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..)Cost of debtConsult 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 (contd..)Cost of equityUse 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

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ROIC 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 valueTerminal value is the value of all future

cash flows after the explicit forecast period of 10 years

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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..)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

DCF – Terminal value: exit multiple

DCF – Terminal value: perpetuity growth

DCFValidate and test projection assumptionsCarefully consider all variables in the

calculation of the discount rateConsistency 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.)

DCF – Walmart exampleDecember 2007 Treasury rates3-month 3.00%1-year 3.26%5-year 3.49%

20-year 4.57%

December 2007 AAA yield 5.49%

Risk premium for AA rate bonds 2.2%

Equity risk premium 5.0%Tax Rate 33%Beta 0.71

Cost of debt (rd) 6.80%=rf+risk premium

Cost of equity (re) 8.13%=rf+ *(rm-rf)

Net debt (D) 37.00Market cap (E) 192.00Total Value (V=D+E) 229.00D/ V 16.2%E/ V 83.8%

WACC 7.56%=rd(1-tax) D/ V + re E/ V

Walmart FCF assumptionsThe 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

Walmart FCF’s

2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017

Sales 370,000 407,000 445,665 485,775 527,066 569,231 611,923 654,758 697,317 739,156 779,810 Sales growth 10.0% 9.5% 9.0% 8.5% 8.0% 7.5% 7.0% 6.5% 6.0% 5.5%

COGS 308,913 337,814 367,732 398,462 429,769 461,390 493,033 524,383 555,106 584,857

% of Sales 76.0% 75.9% 75.8% 75.7% 75.6% 75.5% 75.4% 75.3% 75.2% 75.1% 75.0%

SGA 69,597 76,654 84,039 91,709 99,615 107,698 115,892 124,122 132,309 140,366

% of Sales 17.0% 17.1% 17.2% 17.3% 17.4% 17.5% 17.6% 17.7% 17.8% 17.9% 18.0%

D&A 6,919 7,576 8,258 8,960 9,677 10,403 11,131 11,854 12,566 13,257

% of Sales 1.7% 1.7% 1.7% 1.7% 1.7% 1.7% 1.7% 1.7% 1.7% 1.7% 1.7%

Capex 14,245 15,598 17,002 18,447 19,923 21,417 22,917 24,406 25,870 27,293

% of Sales 3.5% 3.5% 3.5% 3.5% 3.5% 3.5% 3.5% 3.5% 3.5% 3.5% 3.5%

NWC 1,850 2,035 2,228 2,429 2,635 2,846 3,060 3,274 3,487 3,696 3,899

% of Sales 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5%

EBIT 21,571 23,620 25,746 27,934 30,169 32,432 34,702 36,958 39,175 41,330Tax 7,118 7,795 8,496 9,218 9,956 10,703 11,452 12,196 12,928 13,639NOPLAT 14,453 15,826 17,250 18,716 20,213 21,729 23,250 24,762 26,247 27,691+D&A 6,919 7,576 8,258 8,960 9,677 10,403 11,131 11,854 12,566 13,257- NWC 185 193 201 206 211 213 214 213 209 203-Capex 14,245 15,598 17,002 18,447 19,923 21,417 22,917 24,406 25,870 27,293FCF 6,942 7,610 8,305 9,022 9,756 10,501 11,251 11,997 12,733 13,451Discount factor 0.930 0.864 0.804 0.747 0.695 0.646 0.601 0.558 0.519 0.483Discounted cash flows 6,454 6,579 6,675 6,742 6,778 6,783 6,757 6,699 6,610 6,492Total (excl Cont Value) 66,569

Walmart continuation value

Continuation Value 381,123PV(Continuation Value) 183,953 73%

Firm value 250,522Less Debt value 37,000Equity value 213,522Number of shares 4,170Equity value per share 51.20

NOPLATT+1(1-g/ ROIC)/ (WACC-g)

Walmart sensitivity analysis

51.20 2.0% 2.4% 2.8% 3.2% 3.6% 4.0% 4.4% 4.8% 5.2% 5.6% 6.0%6.0% 46.32 45.28 44.04 42.52 40.66 38.33 35.36 31.46 26.17 18.63 7.096.4% 47.54 46.87 46.06 45.06 43.81 42.24 40.22 37.56 33.92 28.72 20.736.8% 48.62 48.28 47.84 47.29 46.59 45.69 44.51 42.93 40.76 37.62 32.777.2% 49.59 49.53 49.43 49.27 49.06 48.75 48.32 47.71 46.84 45.54 43.48

7.6% 50.45 50.64 50.84 51.05 51.26 51.49 51.73 51.99 52.28 52.62 53.05

8.0% 51.22 51.65 52.12 52.65 53.25 53.96 54.80 55.84 57.18 58.99 61.678.4% 51.92 52.56 53.27 54.09 55.05 56.19 57.57 59.32 61.60 64.76 69.468.8% 52.56 53.38 54.32 55.41 56.69 58.22 60.10 62.48 65.63 70.00 76.55

51.20 2.0% 2.4% 2.8% 3.2% 3.6% 4.0% 4.4% 4.8% 5.2% 5.6% 6.0%6.0% 71.48 71.72 71.97 72.22 72.47 72.71 72.96 73.21 73.45 73.70 71.336.4% 64.99 65.21 65.44 65.66 65.88 66.11 66.33 66.55 66.78 67.00 67.226.8% 59.32 59.52 59.72 59.93 60.13 60.33 60.53 60.73 60.94 61.14 61.347.2% 54.32 54.51 54.69 54.88 55.06 55.24 55.43 55.61 55.80 55.98 56.16

7.6% 49.90 50.06 50.23 50.40 50.57 50.74 50.90 51.07 51.24 51.41 51.58

8.0% 45.95 46.11 46.26 46.41 46.57 46.72 46.87 47.03 47.18 47.34 47.498.4% 42.42 42.56 42.70 42.84 42.98 43.12 43.26 43.40 43.55 43.69 43.838.8% 39.24 39.37 39.49 39.62 39.75 39.88 40.01 40.14 40.27 40.40 40.53

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Terminal growth rate

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Terminal growth rate

RELATIVE VALUATION

MODELS

TerminologyEquity 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 interestEquity

Debt

Preferred Stock

Minority Interest

EnterpriseValue

LiabilitiesAssets

=

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 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 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: 1EPSE

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PE

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E1 - expected earnings for next year– E1 is equal to D1 under no growth

k - required rate of return

P/E Ratio: No Expected 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

gr

b

ROEbr

b

E

P

ROEbr

bE

gr

DP

11

1

1

0

110

No Growth:

E0 = $2.50 g = 0 k = 12.5%

P0 = D/k = $2.50/.125 = $20.00PE = 1/k = 1/.125 = 8With Growth:b = 60% ROE = 15% (1-b) = 40%

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

D1 = $2.73 (1-.6) = $1.09k = 12.5% g = 9%

P0 = 1.09/(.125-.09) = $31.14PE = 31.14/2.73 = 11.4PE = (1 - .60) / (.125 - .09) = 11.4

Numerical Example:

How to compare P/E’sComparison 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 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

P/E Ratios for Different Industries, 2006

Forecasting PETIME SERIES APPROACH PE ratios depend on the current economic

conditionsOne 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

CROSS-SECTIONAL APPROACHOne 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)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

where,

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

Regression 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.)

y = 192.8x + 3.7131

R2 = 0.1437

0

10

20

30

40

50

60

70

80

90

100

0% 5% 10% 15% 20% 25% 30%

Growth Rate

P/E

Price to book ratioPrice-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

gr

gROE

gr

ROEratioPayout

B

P

E

ROEP

B

)/1(

P/B and ROEFirms 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

PB ratios versus ROE

y = 11.132x + 2.4981

R2 = 0.1103

0

1

2

3

4

5

6

7

8

9

10

0% 5% 10% 15% 20% 25% 30% 35% 40%

ROE

P/B

P/B ratios cautionP/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 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:

1SalesSPVCS

Comparative Value Approaches

Using multiples1. Determine the peer group (your comps universe)

2. Gather the appropriate financial information

3. Enter the financial information into your spreadsheet– normalize for non-recurring items (why?)

4. Calculate relevant historical or forward multiples (P/E; EV/EBITDA) – Medians are better than means (why?)

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

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

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

Using Multiples

Operational Industry Product Markets Distribution channels Customers Seasonality Cyclicality

Financial Size (revenues, assets,

market cap) Leverage Margins 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 MultiplesEven 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 MultiplesCertain 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 Multiples

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)