# Valuation Multiples

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To estimate a company’s stand-alone value, multiples can be used.  To apply multiples, first a peer group of companies is required, and these should ideally be the same approximate size of your company, and within the same industry and geographies.  Once you assemble a peer group, calculate the ratio you intend to use for your valuation, and average the peer group’s multiples.  For example, if you desired the P/E ratio, you would take the market cap of the firm, and divide it by the net income for the firm, or you could divide the firm’s stock price by its earnings per share (EPS) – either way you will end up at the same ratio.  Make sure to calculate the multiple for each firm in your peer group independently, then average the multiples, versus summing all of the market caps and earnings, and dividing these sums; you will not get the correct answer using this summation method.

Once you have the average multiple for your per group, multiply this by the denominator (earnings or EPS) to estimate your firm’s value (market cap or price).  Note that this is not an acquisition value, but rather a stand-alone valuation.  Acquisition multiples are collected for all M&A transactions that occur, and can be purchased by data companies such as Thomson/Reuters’ Thomson One product.  Why an acquisition multiple differs from a stand-alone multiple is that a premium is paid for the acquisition, with this premium being justified by the acquirer due to the cost take-outs and/or revenue synergies that they anticipate with their acquisition.

When applying multiples, be aware of whether you are valuing the firm’s equity, or the entire firm’s value.  The equations below show the relationship between firm value and equity value (all at market value):

Firm Value = Equity Value + Debt + Preferred Stock
Firm value also equals:

Firm Value = Value of Stand-alone Operations + Marketable Securities + Excess Cash
Common multiples that are used for valuation of the firm or equity are as follows: $\frac{P_{0}}{E_{0}}=\frac{Mkt Equity Value}{Latest Earnings}=\frac{Current Stock Price}{Latest Earnings Per Share (EPS)}$ $\frac{P_{0}}{FCFE_{0}}=\frac{Mkt Equity Value}{FCFE_{0}}$ $\frac{P_{0}}{B_{0}}=\frac{Mkt Equity Value}{Book Equity Value}$ $\frac{P_{0}}{S_{0}}=\frac{Mkt Equity Value}{Sales}$ $PEG=\frac{P_{0}/E_{0}}{g}=\frac{P_{0}/E_{0}}{Earnings Growth}$ $\frac{FV_{0}}{EBITDA_{0}}=\frac{Mkt Firm Value}{EBITDA_{0}}$ $\frac{FV_{0}}{EBIT_{0}}=\frac{Mkt Firm Value}{EBIT_{0}}$ $\frac{FV_{0}}{FCFF_{0}}=\frac{Mkt Firm Value}{FCFF_{0}}$

Where:

P0 = Current stock price, or current market value of equity, also known as market cap.
E0 = Last earning per share, or latest earnings release, usually annualized.
FCFE0 = Free cash flow to equity (shareholders) ≈ Net Income + DA – CapEx – ΔNOWC
FCFF0 = Free cash flow to firm (shareholders and bond holders) ≈ NOPAT + DA – CapEx – ΔNOWC
B0 = current book value of equity = common stock + additional paid-in capital + retained earnings.
S0 = Latest sales, usually annualized.
g = growth rate of earnings, use trailing 5-yr CAGR, or analyst’s 5-yr forward looking secular growth rate.
FV0 = Current market value of firm (see firm value equations above).
EBITDA0 = “Latest earnings before interest, taxes, depreciation, and amortization, usually annualized.  A proxy for free cash flow.
EBIT0 = Latest earnings before interest and taxes (includes DA), usually annualized.
DA0 = Current depreciation and amortization, usually annualized.

Let’s introduce a few more definitions, and we will then derive the valuation multiples above via the Gordon Dividend Discount (Growth) Model (DDM).

E0 = Current earnings, also known as net income, usually annualized.
PM0 = Latest profit margin, derived by dividing current earning by current sales.
PR0 = Payout ratio, derived by dividing latest dividends paid by latest earnings, or simply DPS/EPS.
DPS0 = Latest dividends per share.
EPS0 = Latest earning per share.
ROE0 = Return on equity, which equals E0/B0
D0 = Latest DPS or dividend payment depending on whether you are solving for stock price or equity value.
rE = Cost of equity.

Starting with the base DDM model:

And realizing that D0 can be represented in three different ways (A, B or C):
A   D0 = E0 × PR0
B   D0 = S0 × PM0 × PR0
C   D0 = ROE0 × B0 ×PR0

 Substituting A into the DDM for D0, one can derive: $\frac{P_{0}}{E_{0}}=\frac{PR_{0}(1+g)}{r_{E}-g}$ Substituting B into the DDM for D0, one can derive: $\frac{P_{0}}{B_{0}}=\frac{ROE_{0}PR_{0}(1+g)}{r_{0}-g}$ Substituting C into the DDM for D0, one can derive: $\frac{P_{0}}{S_{0}}=\frac{PM_{0}PR_{0}(1+g)}{r_{0}-g}$

This clearly shows that the use of multiples is based on firm valuation techniques since the main equity multiples can be directly derived from the DDM model.  Further expansion of these models into EBIT and EBITDA can also take place by introducing the interest and taxes to the P0/E0 ratio.  These equations are also derived under some hidden assumptions, such as depreciation is proportional to earnings, profit margin and return on equity are constant, etc. making all of these equations track with one another, so an undervalued or overvalued stock will remain under or over-valued for all of these ratios.

Another use of valuation multiples is to estimate your terminal (horizon) value when modeling an ongoing operation.  Instead of applying a perpetuity with growth (i.e., FCF0(1+g)/r-g), you can instead multiply your final operating metric by the appropriate multiple to result in the operation’s value at that point in time.  For example, if your model goes out for 10 years, and you then need a terminal value at year 10, you could multiple E10 by your P/E multiple.  Keep in mind whether you are using FCFE or FCFF in your cash flow model, because you will need to then derive a terminal firm or equity value.  Also note that multiples have a tendency to approach the market average over time (aka, central tendency), so a very high to low multiple today will probably erode or grow over the next 10 years, and will approach the market average multiple.

Watch for future posts to describe how to calculate your return on equity rE, estimate your growth rate g, determine FCFE and FCFF and when and how to use these, and how to value your stand-alone operations.