Valuation: Principles and Practice

06/02/08Ch. 12

Valuation techniques Relative valuation

the value of an asset is derived from the pricing of 'comparable' assets, standardized using a common variable such as earnings, book value or revenues.

Discounted cash flow valuation The value of an asset is the discounted expected cash

flows on that asset at a rate that reflects its riskiness.

Residual Income valuation The value of an asset is based on the discounted

expected difference between net income and its associated cost of equity.

Relative valuation The value of the firm is determined as:

Comparable multiple * Firm-specific denominator value

where the denominator value can be earnings, book value, sales, etc.

A firm is considered over-valued (under-valued) if the calculated price (or multiple) is greater (less) than the current market price (comparable firm multiple)

Assumptions: Comparable firms, on average, are fairly valued Comparable firms have similar fundamental characteristics

to the firm being valued.

Relative valuation Examples of relative valuation multiples

Price/Earnings (P/E) Earnings calculations should exclude all transitory

components

Price/Book (P/BV) Book value of equity is total shareholders equity – preferred

stock

Price/Sales (P/S)

Enterprise Value/EBITDA Enterprise Value = Mkt Cap + Debt – Cash EBITDA = Earnings before Interest Taxes Depreciation and

Amortization

Advantages and drawbacks of P/E Advantages:

Earnings power is the chief driver of investment value Main focus of security analysts The P/E is widely recognized and used by investors

Drawbacks If earnings are negative, P/E does not make economic

sense Reported P/Es may include earnings that are transitory Earnings can be distorted by management

Assumption: Required rate of return, retention ratio (with DDM) and

growth rates are similar among comparable firms

Advantages and drawbacks of P/BV Advantages

Since book value is a cumulative balance sheet amount, it is generally positive

BV is more stable than EPS, therefore P/BV may be more meaningful when EPS is abnormally low or high

P/BV is particularly appropriate for companies with primarily liquid assets (financial institutions)

Disadvantages Differences in asset age among companies may make

comparing companies difficult

Assumption: Required rate of return, return on equity, retention ratio (with

DDM) and growth rates are similar among comparable firms

Advantages and drawbacks of P/S Advantages

Sales are generally less subject to distortion or manipulation Sales are positive even when EPS is negative Sales are more stable than EPS, therefore P/S may be more

meaningful when EPS is abnormally low or high

Disadvantages High growth in sales may not translate to operating

profitability P/S does not reflect differences in cost structure

Assumption: Required rate of return, profit margin, retention ratio (and

DDM) and growth rates are similar among comparable firms

Advantages and drawbacks of EV/EBITDA Advantages

This represents a valuation indicator for the overall company and not just equity.

It is more appropriate for comparing companies that have different capital structures since EBITDA is a pre-interest measure of earnings.

Appropriate for valuing companies with large debt burden: while earnings might be negative, EBITDA is likely to be positive.

Disadvantages Differences in capital investment is not considered.

Assumption: Required rate of return, growth rates, working capital needs, capital

expenditures and depreciation are similar among comparable firms

Benchmarks for comparison Peer companies

Constituent companies are typically similar in their business mix

Industry or sector Usually provides a larger group of comparables

therefore estimates are not as effected by outliers Own historical

This benchmark assumes that the firm will regress to historical average levels

Considerations: market efficiency, historical trends, comparable assumptions

Leading and trailing P/E

Trailing (or current) P/Es is calculated using the firm’s current market price and the four most recent quarters’ EPS.

Leading P/Es is calculated using the firm’s current market price and next year’s expected earnings.

PEG Ratio

“I don’t buy stocks with P/E’s over 30. To our Foolish ear, that sounds identical to: I don't buy hydrogenated milk; I am born in May.” Motley Fool

When comparable firm P/Es are used to calculate the value of a firm, the assumption is that the firm has characteristics that are similar to that of the average comparable firm.

However, differences may exist. For example, a higher P/E for a particular firm may be justified because the firm has higher growth.

PEG Ratio The Price/Earnings-to-Growth (PEG) accounts for

differences in the growth in earnings between companies.

PEG is calculated as: P/E divided by expected earnings growth

(%).

"The P/E ratio of any company that's fairly priced will equal its growth rate." Peter Lynch

Discounted Cashflow Valuation: Basis for ApproachThe intrinsic value of a firm is the present value

of all of the firm’s cash flows.

where, n = Life of the asset CFt = Cashflow in period t r = Discount rate reflecting the riskiness

of the estimated cashflows

Value = CFt

(1+ r)tt =1

t = n

What cash flow do we use?

Cash Flows

To Equity To Firm

The Strict ViewDividends +Stock Buybacks

The Broader View (FCFE) Net Income- Net Cap Ex (1-Debt Ratio)- Chg WC (1 - Debt Ratio)= Free Cashflow to Equity

EBIT (1-t)- ( Cap Ex - Depreciation)- Change in Working Capital= Free Cashflow to Firm (FCFF)

What cash flow do we use? Dividends (discount rate = cost of equity):

Firm pays out more than 75% of its net income and; Firm has stable leverage

FCFF (discount rate = WACC): Firm has changing leverage or; Firm currently has negative FCFE. With the FCFF, the intrinsic value of equity is determined by calculating

the firm’s total value and then subtracting the market value of debt and adding back the firm’s current cash balance.

FCFE is simpler to use than the FCFF.

Regardless of the model used, the approach used to calculate intrinsic value is similar.

We will use the FCFE to calculate value in our discussions.

Discounted cash flow valuation with FCFE The intrinsic value of equity is obtained by

discounting free cash flow to equity, i.e., the residual cash flows after meeting all expenses, tax obligations and interest and principal payments, at the cost of equity, i.e., the rate of return required by equity investors in the firm.

where,re = cost of equity

=t

1=tt

e

t

)r+(1FCFE =Equity of Value

Discounted cash flow valuation with FCFE Since we cannot estimate cash flows forever, we may estimate

cash flows for a “high growth period” and then estimate a terminal value, to capture the value at the end of the period

where terminal value is the present value at time N of cash flows after period N.

Note: If we do not expect the firm to have a ‘high growth period, the intrinsic equity value is just the terminal value.

Ner )1(

lueTerminalVa)r+(1

FCFE =Equity of ValueN=t

1=tt

e

t

Valuation steps

Estimate the discount rate

Estimate the current free cash flow to equity

Estimate growth rate(s) to estimate future cash flows

Estimate a terminal value

Compute the firm’s equity value and estimated stock price

Discount rate

The appropriate discount rate in valuing equity is the cost of equity which can be estimated using the CAPM.

Current FCFE We can use the estimated FCFE equation to

calculate CF to equity as this provides a better long run estimate than the exact FCFE equation.

FCFE = Net Income- (1- )(Cap Exp - Depr&Amort + Δ in WC) – Pref. Div.

When determining Cap Exp, Depreciation and change in working capital, we can either: take a historical average of these values if the firm

does not have smooth expenditure streams. Or use the current value.

Estimating future FCFE Depending on the insight you have into the firm’s

operations, we can approach future FCFE estimation in two ways: We can start with the top line (revenues) and

individually estimate the components of FCFE (expenses, cap. ex, etc.). We can use historical averages or regression models to estimate this.

We can assume that the relationship between the top line and FCFE remain stable into the future, in which case we need to estimate a growth rate in FCFE.

Current growth in FCFE We can estimate the current growth in FCFE by first

calculating the equity reinvestment rate (ERR).

The ERR represents the proportion of net income that the firm will retain for reinvestment. Whatever is left over can be paid out.

Normalized values (historical averages) are typically used to determine ERR.

IncomeInterest - IncomeNet ) - in WC)(1 Depr - Exp. Cap(

ERR

Current growth in FCFE The current growth rate then can be estimated as:

g = ERR * non-cash ROE

where non-cash ROE is defined as:

(Net Income – Interest Income)t

(BV of equity – (Cash + Marketable securities))t-1

Estimating future growth A key assumption in all discounted cash flow models

is the period of high growth, and the pattern of growth during that period. In general, we can make one of two assumptions: there is no high growth, in which case the firm is

already in stable growth there will be high growth for a period, at the end of

which the growth rate will drop to the stable growth rate (2-stage). Some advocate a smoother drop in growth between the first and second stages.

We need to determine the growth rates in each period as well as the length of the different periods if a 2-stage model is used.

Determinants of length of high growth period Size of the firm

Success usually makes a firm larger. As firms become larger, it becomes much more difficult for them to maintain high growth rates

Current growth rate While past growth is not always a reliable indicator

of future growth, there is a correlation between current growth and future growth. Thus, a firm growing at 30% currently probably has higher growth and a longer expected growth period than one growing 10% a year now.

Determinants of length of high growth period Barriers to entry and differential advantages

Ultimately, high growth comes from high project returns, which, in turn, comes from barriers to entry and differential advantages.

The question of how long growth will last and how high it will be can therefore be framed as a question about what the barriers to entry are, how long they will stay up and how strong they will remain.

Determinants of length of high growth period Questions to ask about firms:

What drives revenue growth? Can that be maintained?

What kinds of capital expenditure will be required to maintain free cash flow growth?

Can firms maintain their operating and gross margins?

Standard 1st stage lengths used are 5 years and 10 years.

Firm characteristics as growth changesVariable High Growth Firms Stable Growth

tend to Firms tend to

Risk be above-average risk be average risk Dividend Payout pay little or no dividends pay high dividendsNet Cap Ex have high net cap ex have low net cap ex

(just covering depreciation)

ROC earn high ROC and ROE earn ROC closer to WACC

or ROE closer to cost of equity

Leverage have little or no debt higher leverage

Ways of Estimating Terminal Value

Terminal Value

Liquidation Value

Multiple Approach Stable Growth Model

Most useful when assets are separable and marketable

Easiest approach but makes the valuation a relative valuation

Technically soundest, but requires that you make judgments about when the firm will grow at a stable rate which it can sustain forever, and the excess returns (if any) that it will earn during the period.

Estimating terminal value Estimating stable growth

This is the growth rate that we assume the firm FCFE will grow forever

The stable growth rate cannot exceed the growth rate of the economy (3-5%) but it can be set lower. If you assume that the economy is composed of high

growth and stable growth firms, the growth rate of the latter will probably be lower than the growth rate of the economy.

The stable growth rate can be negative. The terminal value will be lower and you are assuming that your firm will disappear over time.

No net capital expenditures and long-term growth You are looking at a valuation, where the terminal value is

based upon the assumption that operating income will grow 3% a year forever, but there are no net cap ex or working capital investments being made after the terminal year. When you confront the analyst, he contends that this is still feasible because the company is becoming more efficient with its existing assets and can be expected to increase its return on capital over time. Is this a reasonable explanation?

Yes No Explain.

Calculating terminal value Terminal value (commencing in period N+1) is

calculated as:

where g is the stable growth stage growth rate.

se

N

grFCFE

1 valueterminal

Calculating equity value Our estimate for the equity value of the firm is then calculated as

the present value of the individual future FCFEs during the 1st stage plus the present value of the terminal value. (For a single stage model, the equity value is simply the terminal value.)

To this we should add back the current cash balance of the firm.

Our estimated (intrinsic) value per share is:(Estimated equity value + cash) number of shares outstanding

DCF vs. relative valuation

DCF valuation assumes that markets make mistakes in estimating value (i.e., current price is not an accurate reflection of the value of the firm) and these mistakes tend to be corrected over time and can occur over entire sectors.

Relative valuation assumes markets are correct on average (i.e., comparables on average are correctly priced)

Basis for Residual Income Valuation

The appeal of the residual income (RI) model is based on the fact that traditional accounting does not include a “charge” for equity capital.

Specifically, a company may generate a positive net income but may not be adding value to its shareholders if it does not earn more than the cost of equity.

Basis for RI valuation

RI is sometimes referred to as the economic profit earned by firms.

One example of a residual income model is referred to as the Economic Value Added (EVA) model.

Strengths of the RI model Terminal value does not make up a large

portion of the total value

The model can be used for companies that do not pay dividends and/or firms that have near-term negative free cash flows

The model can be used when cash flows are unpredictable or difficult to forecast. This can be particularly true for financial institutions.

Weaknesses of the RI model

The model relies on accounting data that can be subject to manipulation

When book value and ROE are unpredictable, the resulting estimate is less valid.

The RI valuation model

The RI model analyzes the intrinsic value of equity into two components:

The current book value of equity, plus The present value of expected future residual

income

The RI valuation model

The intrinsic value of common stock can be expressed as:

where BV0 = current book value of equity per share

BVt = expected per-share book value at period t

EPSt = expected Earnings per share for period t

RIt = expected residual income per share for period t

t

1t

10

=t

1=t00 )1(

*BV1

BV =Equity of eValue/sharV te

tett

e

t

rBVrEPS

)+r(RI

The RI valuation model In the model book value each period is determined

by the following clean surplus relation:

The model also assumes that the growth in book value comes by the firm earning more than the cost of equity (ROE > re). The numerator of the second term can therefore be defined as:

DPS-EPSBV=BV tt1-tt

BV*)r-(ROE=BV*r-EPS 1-te1-tet

Single-stage RI valuation If we assume that the firm’s book value (and RI per

share) will grow at a constant rate, g, forever, we can value a firm using a single-stage RI model:

000 * V BVgrrROEBV

e

e

Multi-stage RI valuation If the assumption of constant growth is not appropriate, which

may be particularly true if the firm currently generates a high ROE relative to the cost of equity, we can model the firm using two stages.

During the first stage we calculate present values of residual incomes individually.

In the second (terminal) stage we make one of the following assumptions about continuing residual income: Residual income remains constant through perpetuity (and

ROE > re) from the terminal year forward Residual income is zero from the terminal year forward

(ROE = re)

Multi-stage RI valuation We can calculate the value today using a multi-

stage model using the following formula

If RI is expected to be constant through perpetuity from terminal year forward, terminal value = RIT / re

If RI is expected to be zero from terminal year forward, terminal value = 0

Te

T

tt

e

tet

rrBVrROEBV

)1(Value Terminal

)1(*)( V

1

100