The Mosaic of Stock Analysis Part 4: DCF analysis

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Introduction Discount rate and growth rate Five intrinsic value models Value at Risk

The Mosaic of Stock AnalysisPart 4: Detailed discounted cash flow analysis

David J. Moore, Ph.D.

www.efficientminds.com

February 11, 2013


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Outline

1 IntroductionThe basicsDetails

2 Discount rate and growth rateWeighted average cost of capital

Growth rates

3 Five intrinsic value models

Residual income modelDividend discount model

Direct discounted free cash flow modelWhole firm discounted free cash flow modelEquity discounted free cash flow model

4 Value at RiskIsoVaR - VaR for asset held in isolation

PortVar - VaR for an asset held in a portfolio


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The basics

Outline



Growth rates







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The basics

Which stocks should I analyze?

Stock tips from your friends in industry.Stocks from the J.O. Cornerstone Value II screen.

Stocks you believe are a good value.

Closest competitors of those stocks!


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The basics

Does the stock appearover or under valued?

Graph of company stock vs. overall market in the past 3 to12 months.

Any recent news that impact the assessment of future cash

flows?

Who is buying what they are selling?Market multiple analysis:

What is the P/E compared to industry/sector average?What is the P/E compared to industry leader?What is the P/E ratio over time?

Is the stock over or under valued based on the P/Enumbers?Cheap target: forecasted earnings historical average P/EMaybe repeat with J.O.s P/sales instead, or P/CF.

The basic analysis here could be used to place a stock onones watch list.

I d i Di d h Fi i i i l d l V l Ri k


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The basics

Buy, sell, or hold

Look at DuPont over time and vs. competitors:

ROE= PMTATREMWith this single equation you can measure operationalefficiency PM= NI/Sales, investment efficiency

TATR = Sales/A, and financing efficiency EM= A/E.

Buy

Estimates for WACC and g.Sensitivity analysis of intrinsic value vs. WACC and g.Identical analysis of closest competitor to illustrate just how

good of a buy this stock is.

Sell or Hold

Forecast vs. actual numbers for sales, free cash flow,residual income, etc.If we are meeting or exceeding forecasts, why sell?

Compare intrinsic value with current market value.

I t d ti Di t t d th t Fi i t i i l d l V l t Ri k


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Details

Outline



Growth rates








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Details

Intrinsic value

The goal is to obtain the intrinsic value of a share of

common stock. In general:

V0 =

t=

CFt

(1

+r

)

t(1)

The trick is in accurately (as possible) forecastingcashflows (CFt) and using the appropriate discount rate(r).

If we presume constant growth of cash flows at rate g, Eq.1 simplifies to:

V0 =CF1

1gHowever, discount rates (r), cash flows (CFt), and growth

rates (g) all vary over time.



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Details

Getting to the valuation goal

Several different paths (models) to the summit of valuation:

Residual income model (RIM)Dividend discount model (DDM)

Direct discounted free cash flow model (D-DCF)Whole firm discounted free cash flow model (F-DCF)Equity discounted free cash flow model (E-DCF)Value at Risk (VaR)

A little philosophy behind model selection (Occams razor):

select among competing hypotheses that which

makes the fewest assumptions and thereby offers the

simplest explanation of the effect -Wikipedia

2012.03.08



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Details

Models to achieve the goal

Model Comments Fin?

RIM Adds current book value to expected futureadditions to book value. Very simple butneed to consider OBS items and FMV ofassets and liabilities.

Y

DDM Discounts future dividends by rs. Simple butonly works for dividend-paying firms.

N*

D-DCF Discounts free cash flows available to allinvestors by WACC. Easiest FCF extraction.

N

F-DCF Similar to D-DCF. Moderately complex FCF

extraction.

N

E-DCF Discounts free cash flows available to equityinvestors by rs. High complexity FCFextraction.

Y

VaR Universal applicability based solely onhistorical returns.

Y


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Weighted average cost of capital

Outline



Growth rates3 Five intrinsic value models







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g



WACC = wdrd (1 ) + wpsrps+ wcsrcs (2)

Lazy approach: just use 10%.

Precise approach:

1 Estimate the expected target weights for long-term debt wd,preferred stock wps, and common stock wcs.

Do not include suppliers (AP) and employees (ACC) assources of capital. We already adjust for AP and ACC whencomputing FCF.

2 Estimate the cost of debt rd, cost of preferred stock rps, andcost of common stock rcs

Q: is there any particular order about the capital components in Eq. (2)?



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g


WACC weights

Morningstar.com (enter ticker symbol the select bonds) has weightsbased on book value.

IFM10, CWS4, and RWJ4 suggest weights should be based on marketvalues. Ideally you would use the target market weights as stated by the

company in their SEC filings. Not all companies do this.Market value of debt MVd. MHS approximation:

MVd BVnotes payable +BVST debt+BVcurrent port. of LT debt +BVLT debt

Market value of preferred stock MVps. Since the income stream of

preferred stocks is more stable Dps= rpsPps we can presumeMVps= BVps.

Market value of common stock MVcs. Just go to Yahoo and look at themarket cap. Be mindful of the timing relative to MVd.

MVtot = MVd+MVps+MVcs and wd =MVd

MVtot, wps=

MVpsMVtot

, wcs=MVcsMVtot



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WACC component costs

Cost of debt rd: Do not use rates on existing debt. Theseare historical rates. Use the current rate - the rate of a 10

year bond commensurate with their credit rating. Obtaincredit rating from morningstar.com and current market

rates for that rating on bonds.yahoo.com.Cost of preferred stock rps: Given the book value of

preferred stock Pps and the most recent preferred dividendDps the cost of preferred stock is:

rps = DpsPps

In theory this number is between rd and rcs.

Cost of common stock rcs. Use the capital asset pricing

model (CAPM).



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The cost of common stock rcs

rcs = Rf +(E[Rm]Rf) (3)

Do not mix historical (i.e., geometric average) for E[Rm]and current Rf.

Use the 10-year Treasry bond for Rf.E[Rm] estimation

Use the forward-looking arithmetic average (a B.L.U.E.estimator), orCGM DDM with a total stock market ETF such as VTI, or

E[Rm] = rvti =D1P0

+ g (4)

Analysts estimate.

The market risk premium (E[Rm]

Rf) should be between

3.5% and 6.5% (IFM10).



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Application: EQR WACC



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Growth rates

Outline










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Growth rates

Nominal vs. real

Do not mix nominal cash flows with real discount rates or

vice versa. If WACC is nominal use nominal FCFs and g.

From IFM10:

In other words, if g is real then the forecasted cash flowsare real and likely inconsistent with the WACC estimate.

I recommend staying nominal on everything. This avoids

confusion and introduction of inflation measurement error.



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Growth rates

Growth rate

In the long run nothing can grow faster than the economy.

From 1930 to 2011 real GDP growth was 3.62%, inflation was 3.73%, andnominal GDP growth was 7.48% (see next slide).

In the short-run (3 to 5 years) a company may grow faster than the economy.

Can base the estimate on sales or units depending on data availability.

Approaches to estimating g:Arithmetic average? sensitive to time frame chosen

Geometric average? sensitive to initial/end data points

Regression?

Behind the scenes of LOGESTfunction of Excel:

salest = (1 + g)tsales0

ln [salest] = tln[1 + g] + ln [sales0]

= a0 + a1t (5)

with a0 = ln [sales0] and a1 = ln[1 + g]. LOGEST estimates a0 and a1 and

reports exp[a1] = exp[ln[1 + g]] = 1 + g



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Growth rates

Application: GDP growth rate

The rate of 7.48% should be used for the long-run growth rate.

One can infer the average rate of inflation over the time period from the data withthe Fisher equation:

1 + rnom = (1 + rreal) (1 + INFL)

INFL =1 + rnom1 + rreal

1

=1.0748

1.0362 1 = 3.73%



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Growth rates

Application: EQR growth rate

Note: If performing a two-stage multi-growth model use the rateof 10.12% as the super-normal growth rate.



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Residual income model

Outline










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RIM Theory

Define book value (book value of common stock) as:

BV BVcs= TSEPSwhere TSE is total stockholders equity and PS is the book value ofpreferred stockholders.

Define residual income as the net income available to common stockholders less the cost of equity used to generate that net income:

RIt = NItBVt1 rsTherefore the current value of common stock is equal to the book valueplus discounted future residual income:

V0 = BV0 +

t=1

RIt

(1+ rs)t

If we presume constant growth of residual income the model simplifiesto:

V0

= BV0

+RI1

rsg



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Application: AAPL

Apple has no preferred stock. Therefore total stockholdersequity = book value of common equity.



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Comments

Apple was a simple case. No debt, no preferred stock.

Greater care must be taken when calculating book value ofcommon equity for financial institutions.

Specifically, adjustments must be made to a financial

institutions assets (outstanding debts and loans).The adjustments should account for default risk, interest

rate risk, and market risk.

According to the residual income model Apple isundervalued with a market value of P0 = 541.99 (YahooFinance 2012.03.08) and an intrinsic value ofV0 = 1,257.61.

Even if you use the proverbial 10% discount rate Apple isstill undervalued with an intrinsic value of approximately

V0 = 700.



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Dividend discount model

Outline

1

IntroductionThe basicsDetails



Residual income modelDividend discount modelDirect discounted free cash flow model

Whole firm discounted free cash flow modelEquity discounted free cash flow model





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DDM Theory

The present value of a share of common stock is thediscounted value of all future dividends:

P0 =

t=1

Dt(1 + rs)

t

If we presume dividends grow at a constant rate g thisformula simplifies to:

P0 =D1

rsg



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Application: GE

Presume GE is in the mature long-run constant growth phase.



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Comments

The constant growth DDM model suggest GE isovervalued with market value P0 = 19.03 and intrinsicvalue V0 = 11.35.

However, if you set the discount rate to the proverbialrs = 10% you obtain an intrinsic value V0 = 19.05 that isclose to the market value.

We know that the growth rate will vary over time going

forward.However, if we are accurate with our estimate for the

average growth rate going forward the CGM still holds.


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Direct discounted free cash flow model

D-DCF Theory

The value of any asset is the present value of discountedexpected future cash flows.

The constant growth model is utilized in all three approacheshere.

This can complicated as needed (although Occams Razorsuggests that will not help).

The three ingredients of the constant growth model are free cashflows FCF, the weighted average cost of capital WACC, and thegrowth rate g.

V0 = FCF1WACCg

In the direct approach we obtain FCF directly from the statementof cash flows:

FCF = NCFoperationsNetCAPEX


Di di d f h fl d l


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D-DCF Theory... continued

Now that we have FCF we can compute the intrinsic value byfollowing these steps:

1 Compute the value of operating assets.

Vop =

FCF1

WACCg2 Compute the value of non-operating assets.

Vnon-op = short term inv. + long term inv.

3 Compute the total value of the firm.Vtotal = Vop + Vnon-op

4 Compute the value of common stock.

V0 = Vcs = VtotalVdebtVps


Di t di t d f h fl d l


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Application: AAPL

Presume Apple in the mature long-run constant growth phase.




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Comments

Value increases with growth rate.

Value decreases with WACC.At a current market price of $541.99 on 2012.03.08 the

stock is a buy (or hold) .

g= 6.51% is a conservative estimate given AAPL has

grown at 11% the last couple decades.


Whole firm discounted free cash flow model


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Outline

1

IntroductionThe basicsDetails










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F-DCF Theory

FCFis the cash available to all investors after paying taxes and makingnecessary investment.

Lets dive into the FCF equation:

FCFt = NOPATtTNOCt

= EBITt (1 ) ((OCAtOCLt + FAt) (OCAt1OCLt1 + FAt1))= EBITt (1 ) ((FAtFAt1) + (OCAtOCAt1) (OCLtOCLt1))= (EBITt (1 ) + DEPt) (FAt + DEPt + OCAtOCLt)= (EBITt (1 ) + DEPt) (FAt + DEPt) (OCAtOCLt)

= Operating cash flow

Gross fixed asset exp.

Change in working cap

Where OCA = cash+AR+INV and OCL = AP+ ACC

Note that depreciation is added in operating cash flow because it is a non-cashexpense.

However, it is effectively removed because in the long run the dollar amount

associated with depreciation must be spent to maintain equipment.




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Application: AAPL

Same theory as direct discounted cash flow only free cash flowis calculated differently.




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o e d scou ted ee cas o ode

Comments

V0 V0Model (WACC = 8.63%) (WACC = 10.36%) 2012 Forecast ($million)

RIM 1256.73 705.12 RI2012 = 23,217D-DCF 1869.65 1065.13 FCF2012 = 35,435

F-DCF 1689.87 966.03 FCF2012 = 31,881Average 1605.42 912.09

Sales in 2012 is forecasted to be between 115,296 @g= 6.51% and 120,432 @ g= 11.25%.

In all cases AAPL is a buy/hold.

Prior to 2012 one could verify AAPL is on track to meet thefour forecasts here.


Equity discounted free cash flow model


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q y

Outline

1 Introduction

The basicsDetails








Equity discounted free cash flow model


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E-DCF Theory

The approach is the same as direct (D-DCF) and wholefirm (F-DCF) with a different calculation of FCF and

discounting by rs as opposed to WACC.

In this approach free cash flows are calculated as:

FCFcs = NOPATTNOC INTPRIN

You will need to make decisions regarding future interestand principal payments.

This will involve in-depth financial statement gyrations toextract FCFcs. However, once you have FCFcs you can getto Vcs relatively easily.

Google-ing can reveal this approach has been applied tobank valuation. Good luck! I wont cover this here.



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VaR Theory

Value at risk measures the worst-case loss in value over afuture period.

VaR is used by financial institutions to measureinterest-rate, exchange-rate, market risk, etc.

We will use it to measure market risk two ways:

1 Worst case loss in dollars of an investment in stock X inisolation.

2 Worst case loss in dollars of a portfolio that contains stock

X.The second approach is interesting because it enables usto examine the impact of correlation without evermeasuring correlation!


IsoVaR - VaR for asset held in isolation


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Outline

1 Introduction

The basicsDetails










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In isolation...

Begin by defining worst case. In the context of normaldistributions, the 5% worst case would be 1.65 below themean.

In other words, given daily returns compute and define

the daily earnings at risk as:

DEAR= dollars invested1.65

The N-day 5% VaR is computed as:

VaR= DEAR

N

The end result is interpreted as a 5% chance of losing VaR

dollars over the next N days.




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IsoVaR application: BAC

Interpretation: There is a 5% chance that we would lose$4,490 over the next year on a $6,250 investment in BAC.


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In a portfolio...

Compute the last 500 days of returns for hypothetical

portfolio containing stock of interest and remaining

portfolio.

Sort by the portfolio return.

Consider the return on the 25th worst day the price

volatility (note 25/500 = 5%).

Compute DEAR and VaR as before.




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PortVaR application: BAC

The following results are for a portfolio with $6,250 BAC and $243,750 SPY.

We have a 5% chance of losing $89,178 over the next year with aportfolio containing BAC compared to $85,336 with just SPY.

From a VaR perspective, we are better off without BAC, at least with theportfolio weights under analysis.




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Summary

Five approaches to measuring intrinsic value and twoapplications of the Value-at-Risk model were presented.

The model matrix provides guidance on what scenarios

these models work best.

The residual income model puts more emphasis onmeasurable current value (book value). In contrast the

DDM and DCF models place more empahsis on futurecash flows.

Only constant growth models are presented here. One

could easily expand the models to multi-growth.Bear in mind Occams razor as you complicate any of themodels.

Do not be affraid to apply as man models as possible. You

are painting the mosaic of stock analysis.




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Where to obtain data

Source Descriptionfinance.yahoo.com Stock quotes, beta, links to SEC filings, historical prices,

etc.zacks.com Stock screening tools. See my presentation on stock

screening.mergentonline.com Corporate bond datamorningstar.com Capital structure data, SEC filings, etc.Naders comp sheet Pulls data from multiple sources. Data includes stock

prices, historical financial statements, ratios, etc.Probably very useful for financial firms.

Compustat Historical SEC filings for all companies going back

multiple decades. I am working on getting this loaded onthe TAH2009 SIF office machine.

valueline.com Historical P/E ratios plus a lot more.




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References

IFM10 Brigham and Daves (2010), Intermediate Financial

Management, 10th edition.

CWS4 Copeland, Weston, and Shastri (2005), FinancialTheory and Corporate Policy, 4th edition.

RWJ4 Ross, westerfield, and Jaffee (1996), Corporate

Finance, 4th edition.

MHS Mark Hoven Stohs, Finance Department Chair,CSU Fullerton.

The Mosaic of Stock Analysis Part 4: DCF analysis

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