Discounted Cash Flow (DCF) Tutorial

Wednesday, January 31st, 2007

Tutorial Objectives

• Basic Underlying Principles– Time Value of Money– Present/Future Value– Opportunity Cost

• What is a business worth?• What is Free Cash Flow?• Basics of DCF Analysis

– Compostion– Computation– Forecasting

Present Value

• Time Value of Money: A dollar today is worth more than a dollar tomorrow.– A dollar today can be invested to earn a rate of return or

interest.

• What is today’s dollar worth tomorrow (future value)?

• What is tomorrow’s dollar worth today (present value)?

NiPVFV )1(

NiFVPV )1/(

Time Value: Example

• You are given $5,000 and decide to invest it in the stock market for 10 years and expect an average annual rate of return of 10%. What is that $5,000 worth 10 years from now?

• Likewise…

yearsFV 10%)101(*000,5$ 969,12$FV

yearsPV 10%)101/(969,12$ 000,5$PV

What is a Business Worth?

• A business is worth the present value of the expected future cash flows of the business.

• A company's stock price is a reflection of the market's concensus expectation regarding the value of the equity in the business.Ex. Target Corp (TGT):

$60 Share Pricex 858.89 Shares Outstanding (mm)= $51,533 Market Capitalization or Market Value of Equity

• Is the market always right?

Capital Budgeting

• The process of determining how a firm should allocate scarce resources to available long term investment opportunities

• Decisions whether a company should undertake a given project

• Goal: Increase (Maximize) shareholder wealth

• One capital Budgeting tool is NPV

Year 0 Year 1 Year 2 Year 3($30,000) $3,000 $10,000 $25,000

Discount Rate: 10%Net Present Value ($225.39)

Discount Rate

• The interest rate at which you discount expected future cash flows to the present

• Efficient Markets Hypothesis (EMH)– Finance theory which states that all stock market

prices at any given time reflect the accurate present value of the future cash flows of a business

– Assumes market as a whole has rational expectations and is always right

– Uses Capital Assets Pricing Model (CAPM) to establish the theoretical 'cost' of equity

Discount Rate

• EMH uses Beta as a measure of risk by quantifying the stock's volatility (up and down movements) relative to the market.– Since the stock price reflects the PV of future cash

flows, the more volatile the stock price, the more uncertain the future performance of the business.

– This 'extra risk' is reflected in a higher Cost of Equity. (Risk/Return)

Cost of Equity = Rf + B * (Mkt – Rf)

Discount Rate

"I'd be a bum on the street with a tin cup if themarkets were always efficient" – Warren Buffett

• The Opportunity Cost of Money – – Also known as the Hurdle Rate

• The expected rate of return available on alternative investment opportunities– Historically, the stock market has generated an

average annual return of about 10%.

Discounted Cash Flow Analysis

• Same Concept as capital budgeting: Is a $60 per share ‘initial investment’ in Target Corp. worth the projected future cash flows of this business given a discount rate of 10%?

• Instead of a CFO conducting Capital Budgeting analyses to evaluate the projected cash flows of projects for his/her company to invest in, we are a fund conducting DCF analyses to evaluate the projected cash flows of whole companies.

Free Cash Flow – Equity (FCFE)

• Net Income adjusted for all non-cash sources of revenue and expense, less capital expenditures– Ex. Subtract all revenue paid for on credit, and add

all expenses paid for on credit– Add back depreciation – largest non-cash expense

• The cash that is left for shareholders after debt-holders have been paid and necessary reinvestment has been made

• FCFE is what we care about!

Free Cash Flow – Equity (FCFE)

Net Income

Add: DepreciationLess: Capital Expenditures (CAPEX)

= Free Cash Flow to Equity

DCF ExampleLemonade Stand Business

Year 0 Year 1 Year 2 Year 3

Initial Cost (50,000)

Taxes (34%) (25,500) (28,560) (34,000)Operating Income 75,000 84,000 100,000

Income $49,500 $55,440 $66,000

Plus: Depreciation 3,750 4,200 5,000Minus: CapEx 4,500 5,040 6,000

Free Cash Flow ($50,000) $48,750 $54,600 $65,000

Discount Rate 10%

Discounted Values ($50,000) $44,318 $45,123 $48,835

Present Value $88,277

Terminal Cash Flow

• Going Concern Assumption: The business will operate and generate cash flows indefinatley.– Zero Growth: CF / i

• $48,835/0.10 = $488,350– 5% Growth: CF*(1+g) / (i-g)

• $48,835*(1.05)/(.05) = $1,025,535

• Liquidation: Sell off remaining assets in liquidation.– PV of Fixed Assets: $52,590/(1+10%)^3

=$39,511

Forecasting Cash Flows

• Historical performance is not important in terms of business value, but is important in terms of predicting future performance.

• The trickiest part of business valuation– Future performance is unknowable

• Things to consider when predicting the future:– Every projection should be backed by a rational

argument– The strongest arguments will include both

quantitative and qualitative support– Mean Reversion

Forecasting Cash Flows

• Historical Simple/Weighted Averages– Primarily used when there is no discernable trend,

or current trend is not expected to continueY ea r 1 Y ea r 2 Y ea r 3 Y ea r 4 Y ea r 5

N et Inco m e G ro w th 7 % 1 2 % 8 % 1 % 5 %

Sim ple A v era g e 6 .6 0 %

W eig hted A v era g e W eig ht G ro w th

3 3 .3 % 5 % 1 .7 %2 6 .7 % 1 % 0 .3 %2 0 .0 % 8 % 1 .6 %1 3 .3 % 1 2 % 1 .6 %

6 .7 % 7 % 0 .5 %1 0 0 .0 % 5 .6 %

Forecasting Cash Flows

• Historical Trend Exrapolation

Y ea r 1 Y ea r 2 Y ea r 3 Y ea r 4 Y ea r 5N et Inco m e M a rg in 4 % 4 % 4 % 5 % 6 %

Y ea r 6 Y ea r 7 Y ea r 8 Y ea r 9 Y ea r 1 0E stim a ted N I M a rg in 6 % 7 % 8 % 8 % 8 %

What We've Covered

• Basic Underlying Priciples– Time Value of Money– Present/Future Value– Opportunity Cost

• What is a business worth?• What is Free Cash Flow?• Basics of DCF Analysis

– Compostion– Computation– Forecasting