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Equity Valuation

Self-Paced Tutorial

Online tutorials for mini classes at: http://www.bentley.edu/trading-room/

2007© Hughey Center for Financial Services. All Rights Reserved.

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Introduction: This tutorial is to be used in conjunction with the FI 640 Final Project or any other equity valuation. In it we will introduce the Dividend Discount, Free Cash Flow to Equity, and Free Cash Flow to the Firm models, as well as Relative Value analysis. We will discuss when to use these models, the variables associated with their employment, and how to search for those variables using Bloomberg, Reuters Knowledge, and Thomson One. A cautionary note: The data this tutorial will lead you to analyze is historical data, with the exception of earnings estimates. You will apply growth rates to these historical data to estimate future revenues and costs. What must be remembered throughout this tutorial is that future revenues and future costs are what we seek to analyze, and that we download historical data to estimate these figures. Our valuation is thus based on estimated future data, not historical data alone! The instructions provided for the retrieval of input variables suggest the repeated opening of Reuters Knowledge and other software. If you seek to retrieve more than one variable over the course of your analysis, it is not necessary to repeatedly open and close these software. You must simply leave the application running and change the required ticker information.

Dividend Discount Models The DDM is the simplest present value approach to valuating common stocks. It estimates the company value based on the idea that the value of the equity equals all future dividends discounted back to today. Gordon Growth Model or Constant Growth Model: The Gordon Growth model (a.k.a the Constant Growth Model) relies on the principle that dividends grow indefinitely at a constant rate. Use this model if your stock meets the following criteria:

• It pays out 90% or more of its Net Income in dividends; • Its leverage is expected to remain stable into the future; • Its growth rates are expected to be comparable to or lower than the

economy’s nominal growth rate.

0P = )1(

)1(0

ergDPS

++

+ 2

20

)1()1(

ergDPS

++

+ …+ ne

n

rgDPS

)1()1(0

++

+ …

This equation is a geometric series that can be simplified algebraically into:

3

0P = )(

)1(0

grgDPS

e −+

, or 0P = )(

1

grDPS

e −

where 1DPS = Expected dividends next year er = Cost of Equity g = Growth rate in dividends forever 0P = Value of a share of stock today The Variables g = Growth rate in dividends forever The implied dividend growth rate g equals the earning retention ratio (b) times the return on equity (ROE).

g = b × ROE where g = dividend growth rate b = earning retention rate (1 – dividend payout ratio) ROE = return on equity Here the assumption is very strong because we are using the concept of sustainable growth rate as the rate of dividend (and earnings) growth that can be sustained for a given level of return on equity, keeping the capital structure constant over time.

Finding ROE and b:

1. Open Thomson One Analytics 2. Enter the company’s ticker symbol (i.e. HD for Home Depot), and click OK 3. Select Key Ratios under the Financials tab on the left navigation bar. Under

Profitability you will find the Return on Total Equity % and under Leverage you will find the Dividend Payout %.

For the FY 2004 the ROE = 21.5 % while the Dividend Payout is 14.4%, this implies that the dividend growth rate is:

g = (1 – 0.144) × 0.215 = 0.18404

er = Cost of Equity The cost of equity can be found using the Capital Asset Pricing Model. The CAPM equation is as follows:

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)( fmfe rrrr −+= β rf = the risk free rate (typically a US treasury yield that matches your investment horizon) β = Beta (a measurement of a stocks return relative to the market) rm - rf = 5.5% = the historically accepted risk premium is 5.5% r f = the risk free rate

1. Use the Bloomberg terminal and enter the following command: <GOVT> TK 2. Click on the corresponding country (we will choose #14: USA) 3. Choose option #12 on the next screen for the most currently issued Bills, Notes,

and Bonds

And it brings us to the following page:

4. Select the treasury bill/note/bond whose maturity most appropriately represents

your holding period, and use its yield as the risk free rate. For example, 5.23% if the holding period is 1 month, or 4.61% if the holding period is 5 years.

β = Beta Beta is a measure of risk. We will begin by entering the ticker of a company in which we are interested into Bloomberg. For example, let’s say we’re interested in Microsoft. So we enter the following command: MSFT <EQUITY> BETA <GO> And it brings us to the following page:

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1. In the range box we type the dates that give us an appropriate timeline by which to measure beta. The greater the number of years in your forecast, the greater the number of years you should use in your beta calculation. Five is generally a safe minimum.

2. The market index set as the default in the S&P500. You should change this if you feel another index better represents the risk associated with your market, or if you believe the S&P500 is not large enough a market.

3. For all intensive purposes we will use the raw beta as it presents us with a larger and more conservative cost of equity.

If you were to repeat this process with Home Depot, the Raw Beta you would pull is 1.08 and the cost of equity will be:

)( fmfe rrrr −+= β

er = 0.0461 + 1.08 * (0.055) = 10.55 %

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In order to find the Country Risk Premium (CRP) use Bloomberg and enter in the command CRP <go>

Top 14 countries are listed with their Country Risk Premium.

0DPS = Most recent total dividends per share

1. Open Thomson One Analytics

2. Fill in the fields , enter the company’s ticker symbol (i.e. HD for Home Depot), and click GO

3. Scroll down and choose “Detail” under “Estimates”. Select “Full Summary” and you will see EPS forecasts broken down by quarter. Numbers in the Earnings Estimates section with the letter A next to them (i.e. 0.39A for the 1st quarter of 2004 for Home Depot) are actual recorded earnings. Numbers without an A next to them represent the consensus estimates of the analysts following the stock.

4. You can use these estimates to predict Dividends per Share (Earnings per Share * Payout Ratio = Dividends per Share), or you can grow the dividends at what you believe to be realizable growth rates.

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0EPS = $ 2.26 1−EPS = $ 1.88

Notice that earnings for the company grew from $ 1.88 (FY 2004) to $ 2.26 (FY 2005), which is exactly 20.21 % growth rate, really close to our g = 18.40 %. Valuation using the Gordon Growth Model Because HD has a growth rate that is higher than the growth rate of the economy and it pays out only 14.4 % of its net income in dividends the Gordon Growth Model is not a reasonable model for this company.

0EPS = $ 2.26 g = 18.4 % er =10.55 %

EXAMPLE If we estimate a required rate of return on J.C. Penny (JCP) stock as 5.3 % using the CAPM and we believe that a stable growth rate of 4 % is a good description of the long-term prospects of JCP, with the current dividend of $ 0.50 JCP has a fair value of $ 40.

0P = )(

)1(0

grgDPS

e −+

= )04.0053.0(

)04.01(*50.0$−

+ = $ 40

Because the constant growth model indicates an intrinsic value for JCP ($ 40) that is less than its market value ($ 46.46 as April 22, 2005), we conclude that JCP is overvalued according to this model.

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Multistage Dividend Discount Models The stable dividend growth rate assumption leading the Gordon Growth Model is not realistic for many firms. Practitioners in particular assume that growth falls in three different stages:

• Growth Phase • Transition Phase • Mature Phase

The two-stage DDM, the H-Model and the three-stage DDM are models that are attempting to capture patterns that realistically approximate the future growth of a company. Two-Stage Dividend Discount Model This model is based on two stages of growth – an initial phase where there is an extraordinary growth phase that last n years and a subsequent stable growth phase that is expected to last forever.

0P =∑=

= ++nt

tt

hge

thg

rgDPS

1 ,

0

)1()1(*

+ )(*)1(

)1(*)1(*

,,

0

sgsgen

hge

sgn

hg

grrggDPS

−+++

0P = Value of a share of stock today

0DPS = Most recent dividends per share

er = Cost of equity; hg: high growth period, sg: stable growth period

hgg = extraordinary high-growth rate for n years

sgg = stable growth rate after year n

Assumptions:

hgg : Extraordinary growth rate for the first n years = Retention rate * ROE • Extraordinary growth can be defined as growth that cannot be sustained

indefinitely. In a two-stage model, it can be used to grow variables like EPS, DPS, and assorted balance sheet items in the first stage. It can be found by multiplying the company’s Return on Equity by its Retention Rate (the % of earnings the company does not pay out in dividends). Retention rate = 1 – Dividend Payout Ratio.

For the FY 2004 the ROE = 21.5 % while the Dividend Payout is 14.4%, this implies that the dividend growth rate is:

g = (1 – 0.144) × 0.215 = 18.40 %

sgg : Steady state growth rate forever after year n

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• A company experiencing rapid growth is expected to have those growth rates

approach levels that are more sustainable. Terminal growth rates are what mature companies reach, and these rates are best approximated by the growth rate of the industry or sector.

1. Click on Reuters Knowledge Reuters Knowledge.url . Enter the username and password located under the keyboard, and click on the fundamentals tab.

2. Enter your company’s ticker into the lookup search (i.e. enter HD for Home Depot)

3. Under Fundamentals select Company Comparison. 4. Under the Management Effectiveness section you will find Return on Equity –

5 Yr. Avg. for the Company, Industry, Sector, and the S&P 500. Select the one you believe is most feasible.

Declining Beta: It is reasonable to assume that a high growth firm has a high beta, but unreasonable to assume that this beta will remain unchanged when the firm becomes stable. Payout Ratio: The payout needs to be consistent with the estimated growth rate. In particular a stable company can pay out more of its earnings in dividends than a growing firm.

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Two-Stage Dividend Discount ModelHome Depot (HD)

Extraordinary PeriodStable Period

Payout Ratio 0.144 0.6 PayoutRetention Rate b 0.856 0.4ROE 0.215 0.115 Sector ROE

Growth Rate 0.18404 0.046

Beta 1.08 1Risk Free Rate 0.0461 0.0461Risk Premium 0.055 0.055

Cost of Equity 0.1055 0.1011

EPS0 $2.26

Year 0 1 2 3 4 5 62004 2005 2006 2007 2008 2009 2010

EPS $2.26 2.68$ 3.17$ 3.75$ 4.44$ 5.26$ DPS $0.33 $0.39 $0.46 $0.54 $0.64 $0.76PV of Dividends $0.35 $0.37 $0.40 $0.43 $0.46Cumulative PV of Dividends during extraordinary growth period $2.01

Expected EPS after 5 years $5.50Expected DPS after 5 years $3.30

Terminal Price $59.91PV of Terminal Price $37.01

Fair Value $39.02

Market Value on April 22, 2005 $36.02

Extraordinary Period

H-Model A variant of the two stage model is the H-model in which growth begins at a high rate and declines linearly over time to reach the normal rate at the end. Three-Stage Dividend Discount Model This model combines the features of the two-stage model and the H model. In the first stage, dividends growth is at a high, constant rate for the entire period. In the second period, dividends decline linearly as they do in the H-model and finally, on stage three, dividends growth at a constant stable rate.

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Strengths and Weaknesses of Dividend Discount Models Strengths: These models can accommodate different patterns of future expected dividends; The expected return values can be adjusted to reflect the actual market value.

Weaknesses: Valuations are very sensitive to the models’ inputs; The output from the model will not be useful if the inputs are not appropriate for

the company being valued.

Discounted Cash Flow Models In the Discounted Cash Flow models (DCF) the intrinsic value of a security is viewed as the present value of its expected future cash flows. There are a number of reasons why cash flow models are so popular and widely used:

• Company valuations produced by the DCF model fit very well with the way capital markets value companies in practice;

• This model works well for all types of companies, from the smallest to mature firms;

• Any accounting measures that do not affect cash flows do not affect the DCF model;

• This model is theoretically correct. In general, analysts like to use the free cash flow to equity (FCFE) and the free cash flow to the firm (FCFF) when one of the following conditions is present:

• The company is not paying dividends; • The company pays out less to shareholders, in the form of dividends and stock

buy-backs, than what it has available; • In a hostile takeover, the bidder can change the dividend policy to capture the

actual capacity to pay dividends. Depending on the company being analyzed, an analyst may have reasons to prefer using FCFF or FCFE. If the firm’s capital structure is relatively stable, FCFE is more direct and simpler to use than FCFF. In the case of levered1 companies with negative FCFE, working with FCFF to value stock may be easier.

1 Leverage is another word for debt. To say a firm is leveraged is to say that they are borrowing money and must pay it back.

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Free Cash Flow to Equity Model: Free cash flow to equity is the cash flow available to the company’s shareholders after all operating expenses, interest, and principal payments have been paid and necessary investments in working capital2 and fixed capital have been made. FCFE is the amount that the company can afford to payout as dividends. For this reason this model is not totally different from the dividend discount model and the following versions are simple variants of the models we described previously. Calculating Free Cash Flow to Equity FCFE is most frequently calculated from a starting basis of net income:

Net Income available to shareholders $ 5,001 + Non cash charges (depreciation, amortization) $ 1,319 - Capital Expenditures $ 3,948(-) +/- Changes3 in Working Capital $ 795 (-) - Preferred dividends + New Preferred stock issued $ 0 + New Debt issued – Debt repayments usually called New borrowing $ 485 FCFE $ 2,062 On a Bloomberg terminal enter the ticker of your company followed by <equity> followed by “FA.”

Example: HD <equity> FA Click on “16) Income Statement Summary” and under Income (Loss) before Extraordinary Items you will find the Net Income ($ 5,001 for FY2004). Click on “24) Cash Flow” and you will find the Non-cash charges ($ 1,319 for FY 2004) under Depreciation & Amortization. Click on “24) Cash Flow” and in the Cash Flow from Investing you will find the Capital Expenditures ($ 3,948 for FY 2004). Click on “19) Assets” and “22 Liabilities” to get the following information:

FY 2003 FY 2004 Changes (+) Accounts Receivable $ 1,097 $ 1,499 + $ 402 (+) Inventory $ 9,076 $ 10,076 + $ 1,000 (-) Account Payable $ 5,159 $ 5,766 + $ 607 Change in Working Capital + $ 795

2 Changes in working capital are calculated as follows: (+/-) in liquid cash, (+/-) in account receivables, (+/-) in inventory, (+/-) in account payables, (+/-) in other non-interest-bearing operating debts = (+/-) changes in working capital. 3 Increases in WC drain a firm’s cash flows, while decreases in WC increase the cash flows available to equity investors.

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P.S. When finding the increase in working capital we ignore Cash & Near Cash Items because the change in cash is what we are calculating. Click on “16) Income Statement Summary” and you will find the Preferred Dividends and the New Preferred Stock issued ($ 0 for FY2004). Click on “24) Cash Flow” and in the Cash Flow from Financing you will find the New Debt Issued ($ 995 under Increase in LT Borrowing) and the Debt Repayments($ 510 under Reimbursement of LT Borrowings) for the FY 2004. Estimating Growth in FCFE To estimate the fundamental growth of the FCFE we could use the same approach that we used to estimate the growth rate in dividends. We need to replace the retention rate with the equity reinvestment rate, which measures the percent of net income that is invested into the firm.

g = Equity Reinvestment Rate × ROE Where g = Expected growth in FCFE

Equity Reinvestment Rate = NetIncome

FCFE−1

ROE = return on equity Equity Reinvestment Rate = 1- (2062/5001) = 0.588 Cost of Equity The cost of equity can be found using the Capital Asset Pricing Model. The CAPM equation is as follows:

)( fmfe rrrr −+= β

er = 0.0461 + 1.08 * (0.055) = 10.55 % Constant Growth FCFE Model In the constant growth FCFE model the cash flow remaining for stockholders is a function of the expected FCFE in the next period, the stable growth rate (g) and the cost of equity ( er ).

Value of Equity = )(

)1(0

grgFCFE

e −+

, or Value of Equity = )(1

grFCFE

e −

The growth rate used in this model needs to be reasonable, relative to the growth rate in the economy in with the firm operates. To determine if a company’s growth rate qualifies as a candidate for the constant model we need to estimate the economy growth rate (GDP gross rate + long run inflation rate). For example, an estimate of the GDP

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growth rate in the United States is 3.4 % as late 2004 (Source: www.wordbank.org). With expected inflation of 3 %, 6.4 % is the estimated growth rate in the United States economy. The return on equity that Home Depot would need to maintain to grow at a 6.4 %, based on its Equity Reinvestment Rate of 58.6 %, is 10.92 %, close to the sector level.

ROE = g / Equity Reinvestment Rate ROE = 0.064/0.586 = 10.92 %

Value of Equity = )064.01055.0()064.01(062,2

−+

= $ 52,867 MM

HD has a Market Value of $ 77,777 MM on April 22, 2005. Two-Stage FCFE Model The two-stage model is based on two stages of growth – an initial phase where the firm is expected to growth much faster than a stable company for n years and a subsequent stable growth phase that is expected to last forever.

)()1()1(1

10

ss

nn

n

t H

nt

H

t

grFCFE

Pwherenr

Pr

FCFEP

−=

++

+= +

=∑

Where P0 = value of equity at time 0

FCFEt = expected FCFE in year t rH = cost of equity of the firm in the high growth period rs = cost of equity of the firm in the stable growth period gs = growth rate in FCFE in the stable growth period

The value of equity is equal to the summation of the present value of the first n years of FCFE, and the terminal value discounted at the cost of capital for n years. The value per share is calculated by dividing the total value of equity by the number of outstanding shares. The free cash flow models are much more complex than the DDM because an analyst needs to forecast sales, profitability, financing and investment costs to find FCFE and FCFF. Several methods exist for forecasting FCFE and FCFF. One approach is to apply some constant growth rate to historical free cash flow. For example we can compute capital expenditure and changes in working capital as a proportion of sales increases. This method recognizes that capital expenditures contain one component that is necessary to maintain existing capacity and a component necessary for growth.

FCFE0 $2,062 g 0.064

0.1055 er

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It is reasonable to adjust beta and debt ratio to reflect the fact that stable growth firms tend to have average risk (beta closer to 1) and use more debt than high-growth firms.

Assumptions:Sales Growth rate = 12% annually for 3 years and 5% annually thereafter

Net Profit Margin = 7% forever

Capital Expenditure (net of depreciation) = 35% of the sales increase

Annual increase in working capital = 15% of the sales increase

Debt financing = 20 % of net capiatl expenditure and change in working capitalduring the first 3 years and 35% annually thereafter

Two-Stage FCFE Valuation Model Extraordinary Period Stable Period

with a constant growth rate in each stageHome Depot (HD) Growth Rate 0.12 0.05

Beta 1.08 1Risk Free Rate 0.0461 0.0461Risk Premium 0.055 0.055

Shares Outstanding 2,158 MM Cost of Equity 0.1055 0.1011

0 1 2 3 42003 2004 2005 2006 2007 2008

% Change 12.77% 12.00% 12.00% 12.00% 5.00%Revenue $64,816 $73,094 $81,865 $91,689 $102,692 $107,826Revenue per share 30.04 33.87 37.94 42.49 47.59 49.97

Net Income $4,304 $5,001 $5,731 $6,418 $7,188 $7,548Net Profit Margin 6.64% 6.84% 7.00% 7.00% 7.00% 7.00%

Earning per share ($) 1.99 2.32 2.66 2.97 3.33 3.50

Net Capital Expenditure $2,432 $2,629 $3,070 $3,438 $3,851 $1,797% Change 31.76% 35.00% 35.00% 35.00% 35.00%

Net Capital Expenditure per share ($) $1.22 1.42 1.59 1.78 0.83

Change in working capital $164 $795 $1,316 $1,474 $1,650 $770% Change 9.60% 15.00% 15.00% 15.00% 15.00%

Change in working capital per share ($) 0.37 0.61 0.68 0.76 0.36

Debt financing $494 $877 $982 $1,100 $89914.43% 20.00% 20.00% 20.00% 35.00%

Debt financing per share ($) 0.23 0.41 0.46 0.51 0.42

FCFE per share ($) 0.96 1.03 1.15 1.29 2.72PV of EPS ($) $0.93 $0.94 $0.96 $1.82

Cumulative PV of EPS $4.66during extraordinary growth period

Terminal Price $53.31PV of Terminal Price $35.69

Fair Value $40.35

Extraordinary Period

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In another version of the two-stage FCFE model, the growth rate declines in stage 1, reaching the stable rate at the beginning of stage 2. This model is similar to the H-model for the DDM. Free Cash Flow to the Firm Model: The Free Cash Flow to the Firm is the cash flow available to all capital providers (bondholders, stockholders, and preferred stockholders). This measure should be used to approximate the value of a firm in its entirety, not just the firm’s equity value. The differences between FCFF and FCFE arise primarily from cash flow associated with debt: equity valuation (FCFE) builds in the leverage into the cash flows in the form on interest payments and net debt issues, whereas firm valuations (FCFF) build in the leverage into the discount rate. When leverage is expected to change significantly over time FCFF tends to be a much more robust valuation model. Calculating Free Cash Flow to the Firm Cash Flow from Operations is usually used as starting point to compute FCFF because CFO incorporates adjustments for non cash expenses (depreciation and amortization) as well as for the changes in working capital. FCFF from CFO Cash Flow from Operations $ 6,109 + Interest Expense *(1 – Tax Rate) $ 44.247 - Capital Expenditures $ 3,948(-) FCFF $ 2,205.247 Alternatively it can be computed from the Net Income:

FCFF from Net Income

Net Income available to shareholders $ 5,001 + Non cash charges (depreciation, amortization, …) $ 1,903 - Capital Expenditures $ 3,948(-) +/- Changes4 in Working Capital $ 795 (-) + Interest Expense * (1 – Tax Rate) $ 44.247 FCFF $ 2,205.247

4 Increases in WC drain a firm’s cash flows, while decreases in WC increase the cash flows available to equity investors.

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FCFF can also be computed from the EBIT (Earnings Before Interest and Taxes) EBIT * (1 – Tax Rate) $ 5,001 + Non cash charges (depreciation, amortization, …) $ 1,903 - Capital Expenditures $ 3,948(-) +/- Changes in Working Capital $ 795 (-) FCFF $ 2,205.247 On a Bloomberg terminal enter the ticker of your company followed by <equity> followed by “FA.”

Example: HD <equity> FA Click on “24) Cash Flow” and you will find the Cash Flow from Operations ($ 6,904 for FY2005). Click on “16) Income Statement Summary” and under Income (Loss) before Extraordinary Items you will find the Net Income ($ 5,001 for FY2005). Click on “24) Cash Flow” and you will find the Non-cash charges ($ 1,903 for FY 2004): “Depreciation & Amortization ($ 1,319), “Other Non cash Adjustments ($ 563)”, and Changes in “Non cash working capital ($ 21)”. Click on “24) Cash Flow” and in the Cash Flow from Investing you will find the Capital Expenditures ($ 3,948 for FY 2004). Click on “19) Assets” and “22 Liabilities” to get the following information:

FY 2004 FY 2005 Changes (+) Accounts Receivable $ 1,097 $ 1,499 + $ 402 (+) Inventory $ 9,076 $ 10,076 + $ 1,000 (-) Account Payable $ 5,159 $ 5,766 + $ 607 Change in Working Capital + $ 795 Click on “16) Income Statement Summary” and you will find the Interest Expenses ($ 70 for FY2004). Tax rate On a Bloomberg terminal enter the ticker for your company followed by the yellow <equity> key and the letters “FA.”

HD <equity> FA

Click on 6) Profitability and you will find the “Effective Tax Rate” under 7).You will use this rate as the company’s tax rate.

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Interest Expense *(1 – Tax Rate) = $ 70 * (1 – 0.3679) = $ 44.247 Click on “16) Income Statement Summary” and you will find the EBIT ($ 7,912 for FY2004). EBIT (1 - tax rate) = $ 7,912 * (1 – 0.3679) = $ 5,001.175 P.S. You should notice that dividends, share repurchases and share issuance are not included in the FCFF and FCFE. The reason is that transactions between the firm and its shareholders do not affect free cash flow. FCFE and FCFF are cash flows available to capital providers; dividends and store repurchases are uses of these cash flows. Estimating Growth in FCFF As we did previously in the DDM and FCFE models, the Expected growth rate in FCFF for Home Depot is a function of the forces that determine growth: the firm’s reinvestment policy and its project quality.

g = Reinvestment Rate × ROC Where g = Expected growth in FCFF

Reinvestment Rate = EBITFCFF−1

ROC = return on total capital Equity Reinvestment Rate = 1- (2,205.247/5,001) = 0.559

ROC = EquityofvalueBookDebtofBookvale

tEBIT+

− )1(* = 0.1285

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EBIT 7912Tax Rate 0.3679Book Value of Debt 14862Book Value of Equity 24158

Return on Capital: 0.12817 The Expected Growth in FCFF for Home Depot is:

g = 0.559 × 0.1285 = 0.07186 Estimating Cost of Capital To value a company you need also to estimate the cost of capital of the firm. The weights in the cost of capital have to be market value weights. Bloomberg offers a good approximation of the cost of capital even if the debt capital structure is calculated at the book value. On a Bloomberg terminal enter the ticker of your company followed by <equity> followed by “WACC.” Example: HD <equity> WACC The Weighted Average Cost of Capital is next to the title “Weighted Avg. Cost Cap.”

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Constant Growth FCFF Model In the constant growth FCFF model the cash flow remaining for stockholders is a function of the expected FCFF in the next period, the stable growth rate (g) and the cost of capital (WACC).

Value of Equity = )()1(0

gWACCgFCFF

−+

, or Value of Equity = )(

1

gWACCFCFF

−

The characteristics of the firm have to be consistent with assumptions of stable growth. In particular, the reinvestment rate used to estimate FCFF should be consistent with the stable growth in the economy (6.4 %). In the current situation we observe that the ROC (12.85%) used to compute the reinvestment rate is significantly higher than the cost of capital (WACC: 9.73%). Another logical assumption during a constant growth phase is that HD will find the way to earn a ROC equal to its cost of capital.

In Millions Current ConstantSituation Growth

FCFF 0 $2,205.25 $2,205.25ROC 0.128542 0.0973Reinvestment Rate 0.559039 0.6577595

Expected Growth in FCFF 0.07186 0.064WACC 0.0973 0.0973

Value of operating assets $92,913 $70,462

Value of Cash 506$ 506$ Value of Debt 2,159$ 2,159$

Value of Equity 91,260$ 68,809$ Shares Outstanding (MM) 2,158 2,158

Value per share $42.29 $31.89 Two-Stage FCFF Model The two-stage FCFF model is designed to value a firm which is expected to grow much faster than a stable firm in the initial period and a stable rate after that.

)()1()1(1

10

ss

nn

n

tn

H

nt

H

t

gWACCFCFF

PwhereWACC

PWACCFCFF

P−

=+

++

= +

=∑

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Where P0 = value of operating assets at time 0 FCFFt = expected FCFF in year t WACCH = cost of capital of the firm in the high growth period WACCs = cost of capital of the firm in the stable growth period gs = growth rate in FCFF in the stable growth period

The FCFF is considered the best discounted cash flow valuation model because cash flows relating to debt do not have to be considered explicitly since FCFF is a pre-debt cash flow, while they have to be taken into account in estimating FCFE. In case where the leverage is expected to change significantly over time, this is a significant saving, since estimating new debt issues and debt repayments when leverage is changing can become increasingly problematic the further into the future you go.

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Two-Stage FCFF Valuation Model Extraordinary PeriodStable Period

with a constant growth rate in each stage FCFFHome Depot (HD) Growth Rate 0.07186 0.05

Equity Weight 0.9762 * 0.9Debt Weight 0.0238 * 0.1Beta 1.08 1Risk Free Rate 0.037124 * 0.037124

Shares Outstanding 2,158 MM (5 yrs T-Note)

Risk Premium 0.0572 * 0.055The beta for HD will drop to 1, and the firm will raise its debt ratio to 10%. Cost of Equity 0.0989 0.092124

Cost of Debt 0.0301 0.0301

Cost of Capital 0.097263 0.085922Reinvestment Rate 0.559039 0.513875Tax Rate 0.3679 * 0.35

* On Bloomberg page

0 1 2 3 4 52003 2004 2005 2006 2007 2008 2009

EBIT $6,843 $7,912 8480.556 9089.969 9743.174 10443.32 10965.480.07186 0.07186 0.07186 0.07186 0.05

EBIT(1-Tax Rate) $5,001.2 5512.362 5908.48 6333.063 6788.157 7127.565

Reinvestment Rate $2,795.85 $3,081.62 $3,303.07 $3,540.43 $3,794.84 $3,662.67

FCFF $2,205.32 $2,430.74 $2,605.41 $2,792.64 $2,993.31 $3,464.89

PV of FCFF($) $2,215 $2,164 $2,114 $2,065

Cumulative PV of FCFF $8,558during extraordinary growth periodTerminal Value $96,457PV of Terminal Value $66,541

Value of operating assets $75,099Value of Cash 506$ Value of Debt 2,159$

Value of Equity 73,446$ Shares Outstanding (MM) 2,158

Fair Value $34.03

Extraordinary Period

Common errors in FCFE / FCFF model valuation The assumptions about capital expenditures and growth rate are strongly linked in the cash flow valuation models. When one changes, so should the other. In general, there are two types of errors that show up in these valuations. In the first, high growth firms with high net capital expenditures are assumed to keep reinvesting at current rates, even as growth drops off. Not surprisingly, these firms are not valued very highly in these models. In the second, the net capital expenditures are reduced to zero in stable growth, even as the firm is assumed to grow at some rate forever. Here, the valuations tend to be too high.

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To avoid both errors, make the assumptions about reinvestment a function of the growth and the return on capital. As growth changes, the reinvestment rate will also change.

RELATIVE VALUATION TECHNIQUES

Price/Earning (P/E) multiple Price/Book Value (P/BV) multiple Price/Replacement Value Price/Cash Flow multiple Price/EBITDA multiple Price/Sales multiple Industry-specific multiples (price/kwh, price per ton of steel,…) The objective is to value assets based upon how similar assets are currently priced in the market. It has two components: - to value assets on a relative basis, price have to be standardized, usually by

converting prices into multiples of earnings, book value, replacement value, cash flow, EBITDA and sales.

- To find similar firms, which is difficult to do since no firms are identical and firms in the same business can still differ on risk, growth potential and cash flows.

Now study this equation.

gkgoPayoutRati

EP

DPSP

e

n

−+

==)1(*

0

0

Now read it again. Pause. Think about it. It is essential that you understand this relationship. P0 is the current price, DPS0 is the current Dividend per Share, P/E is the Current Price divided by the Net Income per Share, the Payout Ratio is the percentage of earnings the firm chooses to pay to its stockholders, g is the growth rate and ke is the cost of equity. The fundamental principle is that stocks (given similar growth rates, payout ratios, and betas) with high P/E ratios are overvalued and stocks with low P/E ratios are undervalued. Using these variables you can calculate the P/E ratio of a list of companies in a given industry. The analysis consists of valuing stocks relative to other stocks in their industry based on their P/E ratios. The conclusion we should reach is to long (buy) the stocks with low P/E ratios (because they are undervalued), and short (sell) the stocks with high P/E ratios (because they are overvalued). The P/E ratio is an estimate of how many dollars an investor is willing to pay for a dollar of expected earnings. The investor must decide if they agree with the prevailing P/E ratio based upon how it compares to the P/E ratio for the aggregate market, for the firm's industry, and for similar firms.

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Price / Cash Flow Ratio

1+

=t

t

i CFP

CFP

Used in place of the P/E ratio since some firms have a propensity to manipulate earnings; whereas cash flows are generally less prone to manipulation. Price / Sales Ratio

1+

=t

t

i SP

SP

Advocated in the belief that strong and consistent sales growth is a requirement for a growth company and that sales information is less prone to manipulation versus other Balance Sheet and Income Statement items. Only compare similar firms from the same industry since this ratio varies from industry to industry. Conclusion: Equity valuation is a process that continues to intrigue and puzzle investors to this day. There are no correct answers, only educated guesses. Try these valuation models on stocks that interest you, chart their performance, and draw your own conclusions.

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References

Investment Valuation: Tools and Techniques for Determining the Value of Any Asset by Aswath Damodaran. The Dark Side of Valuation Asset by Aswath Damodaran. Analysis of Equity Investments: Valuation by John Stowe, Thomas Robinson, Jerald Pinto, Dennis McLeavey.

Maximizing Shareholders Value by CIMA (The Chartered Institute of Management Accountants). Valuation: Measuring and Managing the Value of Companies by McKinsey & Company Inc.