Introduction to Firm Valuation

Equity vs. Firm Valuation

Value of Equity: The value of the equity stake in the firm, the value of the common stock for a publicly traded firmValue of Firm: The value of all investors who have claims on the firm

A General Valuation Model

The basic components of the valuation are:

An estimate of the future cash flow stream from owning the assetThe required rate of return for each period based upon the riskiness of the asset

The value is then found by discounting each cash flow by its respective discount rate and then summing the PV’s (Basically the PV of an Uneven Cash Flow Stream)

The Formal Model

The value of any asset should then be equal to:

nn

nt

t

t2

2

2

1

1

)r(1CF

)r(1CF

)r(1CF

r1CF

V

n

1tt

t

t

)r(1CF

V

Applying the general valuation formula to a firm

The only questions are what to use as the future cash flows when valuing the firm and what to use as the interest rate.We are going to look at discounted cash flow three models which differ by their choice of cash flows:

DividendsFree Cash Flows to the FirmFree Cash Flows to Equity

Elements Common to All Models

Choose Cash FlowsChoose discount rate consistent with the cash flowsEstimate short term growth of cash flowsEstimate long term sustainable growth of cash flows and when sustainable growth starts.Cash Flows are assumed to continue forever

Multi-Stage Growth Models

The growth of the cash flows can be broken down into general stages. The firm may experience all three or only two of the stages.

High growthTransition to Stable growthStable growth

Actually any path of growth could be assumed for the short term – the key is that at some point stable long term growth is assumed.

Two and Three Stage Growth Models

A two stage growth model is characterized by a period of fast growth followed by a period of stable growth.A three stage growth model is characterized by a period of fast growth followed by a transition period followed by a period of stable growth.

Stable Growth Period

Once a period of stable growth is reached you can approximate the terminal (horizon) value of the cash flows using the constant growth formula.

grgCFt

)1(

Generic DCF Valuation Model

Cash flowsFirm: Pre-debt cash flowEquity: After debt cash flows

Expected GrowthFirm: Growth in Operating EarningsEquity: Growth in Net Income/EPS

CF1 CF2 CF3 CF4 CF5

Forever

Firm is in stable growth:Grows at constant rateforever

Terminal ValueCFn.........

Discount RateFirm:Cost of Capital

Equity: Cost of Equity

ValueFirm: Value of Firm

Equity: Value of Equity

DISCOUNTED CASHFLOW VALUATION

Length of Period of High Growth

The Dividend Discount Model

The value of a share of stock should be the PV of the dividends you will receive in the future if you own the stock.

The Formal Model

Allowing the CF in the general valuation model to be the expected future dividends the model becomes:

)r(1)E(D

)r(1)E(D

)r(1)E(D

r1)E(D

Ve

te

t2

e

2

e

1

1tt

e

t

)r(1Dividend Expected

V

Estimating growth rates

Historical Growth RateComparison to analysts forecasted growthGrowth based upon investment policy

Dividends are based upon the amount reinvested in the firmg=(retention rate)(ROE)

Stable growth

Stable Growth

When the firm reaches stable growth the characteristics of the firm also change – this implies a change in riskiness of the firm and a change in the cost of equity.

Dividend Growth Model

The model can be changed to account for firms that are not currently paying a divided (high growth) but will start paying a dividend in the future.You can use a per share or aggregate measure of dividends – if there are equity options, warrants etc outstanding it is best to start with an aggregate estimate.

Free Cash Flow Choices

Free Cash Flow to EquityThe residual cash flow left over after meeting interest and principal payments and providing for reinvestment to maintain existing assets.

Free Cash Flow to the FirmThe cash flow from operations that is actually available for distribution to investors (stockholders, bondholders and preferred stockholders)

Free Cash Flow to Equity

Net Income+Depreciation

-Capital Expenditure-Changes in Net Working Capital

-Principal Repayments+New Debt Issues

Free Cash Flow to Equity

The Formal Model Again

The value of equity should be equal to:

1tt

e

t

)r(1FCFE

V

Value of Equity

After forecasting the free cash flows it is then possible to find the value of operations for the firm.

Notice, this depends upon a forecast of future free cash flow which much like dividends are not certain.

1tt

e

top )r(1

FCFEV

equityof value

Estimating Inputs

The length of high growth period and rate of return is the same as for the dividend growth modelE(growth) = (Equity Reinvestment Rate)(ROE)Similarly the growth rate in the stable period should be based on stable growthEquity Reinvest = Stable Growth Rate

Stable Period ROE

Dividends v FCFE

If Aggregate Dividends = FCFE then they produce the same value for the value of equity.IF FCFE > Dividends and

the $ are reinvested in projects with NPV =0 (fairly priced assets) then the values are close.The $ are invested in low return projects FCFE provides higher value of equity.

If FCFE does not equal DividendsWhat does the difference tell us?Which model is appropriate?

Free Cash Flow to the Firm

Net Operating Profit After Taxes+ depreciation

-Gross Capital Expenditure-Change in net operating working capital

Free Cash Flow

NOPAT

NOPAT = EBIT(1-Tax Rate)

NOPAT is the amount of profit a firm would earn if it had no debt and held no financial assets.

FCF

Five good uses of FCF1. Pay interest to debtholders (cost to firm

is after tax interest expense)2. Repay debt3. Pay dividend to shareholders4. Repurchase stock from shareholders5. Buy marketable securities or other

nonoperating assets.

The Formal Model Again

Using Free Cash Flow to the firm, the value of operations should be equal to:

1tt

t

)(1FCFF

VWACC

Value of Operations

After forecasting the free cash flows it is then possible to find the value of operations for the firm.

Notice, this depends upon a forecast of future free cash flow which much like dividends are not certain.

1tt

top WACC)(1

FCFVoperations

of value

Estimating Inputs

Expected growth during high growth period

g = (Reinvestment Rate)(ROC)

Remember that the assumption about the Cost of capital will change as the firm growsTerminal Value Based on assumptions concerning long run growth in economy

Equity) ValueBook Debt ValueBook ()1(

tEBITROC

Firm Value to Equity value

You can take the value of the firm and subtract the amount of debt to get to the value of equity. (use the same debt classifications you used for cost of debt)The value of equity obtained form the FCFE and FCFF valuations should be the same if you are consistent with your assumptions about financial leverage.

Other things impacting Value

Liabilities on lawsuitsUnfunded Pensions and Health Care ObligationsDeferred Taxes

Firm Characteristics as Growth Changes

Variable High Growth Firms Stable Growth Firms tend to tend to

Risk be above-average risk be average risk Dividend pay little or no dividends pay high

dividendsNet Cap Ex have high net cap ex have low net

cap exROC earn high ROC earn ROC

(excess return) closer to WACCLeverage have little or no debt higher leverage

Equity Valuation to per share

An estimate of the value per share can be found by dividing the value of equity by the number of outstanding shares.The value of outstanding options must also addressed

Value Enhancement

Changes in any of the four key inputs will impact value in all models.

Increases in cash flowChanges in growth ratesChange in length of growth periodReduction in cost of capital.

Relative Valuation

You can also value the firm by looking at multiples of similar firms and benchmarking Make sure to standardize ratios that you use across firms