discounted cash flow - wikipedia

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Excel spreadsheet uses Freecash flows to estimate stock'sFair Value and measure thesensibility of WACC and

Perpetual growth

From Wikipedia, the free encyclopedia

In finance, thediscounted cash flow

(DCF

) approach describes a methodof valuing a project, company, or asset using the concepts of the time value

of money. All future cash flows are estimated and discounted to give their

present values. The discount rate used is generally the appropriate

Weighted average cost of capital (WACC), that reflects the risk of the

cashflows. The discount rate reflects two things:

1. the time value of money (risk-free rate) - investors would rather have

cash immediately than having to wait and must therefore be compensated

by paying for the delay.

2. a risk premium (risk premium rate) - reflects the extra return investorsdemand because they want to be compensated for the risk that the cash

flow might not materialize after all.

Discounted cash flow analysis is widely used in investment finance, real estate development, and corporate

financial management.

Very similar is the net present value.

1 History

2 Mathematics2.1 Discrete cash flows2.2 Continuous cash flows

3 Example DCF4 Methods of appraisal of a company or project5 History

6 See also7 References8 External links9 Further reading

In 1938, John Burr Williams was the first to formally articulate the DCF method in a working paper released

with the title "The Theory of Investment Value".

Discrete cash flows

counted cash flow - Wikipedia, the free encyclopedia http://en.wikipedia.org/wiki/Discounted_cash_flow

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The discounted cash flow formula is derived from the future value formula for calculating the time value of

money and compounding returns.

Thus the discounted present value (for one cash flow in one future period) is expressed as:

where

DPVis the discounted present value of the future cash flow (FV), or FVadjusted for the delay inreceipt;

FVis the nominal value of a cash flow amount in a future period;iis the interest rate, which reflects the cost of tying up capital and may also allow for the risk that the

payment may not be received in full;

dis the discount rate, which is i/(1+i), ie the interest rate expressed as a deduction at the beginning of

the year instead of an addition at the end of the year;nis the time in years before the future cash flow occurs.

Where multiple cash flows in multiple time periods are discounted, it is necessary to sum them as follows:

for each future cash flow (FV) at any time period (t) in years from the present time, summed over all time

periods. The sum can then be used as a net present value figure. If the amount to be paid at time 0 (now) for

all the future cash flows is known, then that amount can be substituted forDPVand the equation can besolved for i, that is the internal rate of return.

All the above assumes that the interest rate remains constant throughout the whole period.

Continuous cash flows

For continuous cash flows, the summation in the above formula is replaced by an integration:

where FV(t) is now the rateof cash flow, and = log(1+i).

To show how discounted cash flow analysis is performed, consider the following simplified example.

John Doe buys a house for $100,000. Three years later, he expects to be able to sell this house for$150,000.

Simple subtraction suggests that the value of his profit on such a transaction would be $150,000 $100,000= $50,000, or 50%. If that $50,000 is amortized over the three years, his implied annual return (known as the

internal rate of return) would be about 14.5%. Looking at those figures, he might be justified in thinking that

the purchase looked like a good idea.


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1.1453x 100000 = 150000 approximately.

However, since three years have passed between the purchase and the sale, any cash flow from the sale must

be discounted accordingly. At the time John Doe buys the house, the 3-year US Treasury Note rate is 5% per

annum. Treasury Notes are generally considered to be inherently less risky than real estate, since the value

of the Note is guaranteed by the US Government and there is a liquid market for the purchase and sale of

T-Notes. If he hadn't put his money into buying the house, he could have invested it in the relatively safe

T-Notes instead. This 5% per annum can therefore be regarded as the risk-free interest rate for the relevantperiod (3 years).

Using the DPV formula above, that means that the value of $150,000 received in three years actually has a

present value of $129,576 (rounded off). Those future dollars aren't worth the same as the dollars we have

now.

Subtracting the purchase price of the house ($100,000) from the present value results in the net present

value of the whole transaction, which would be $29,576 or a little more than 29% of the purchase price.

Another way of looking at the deal as the excess return achieved (over the risk-free rate) is

(14.5%-5.0%)/(100%+5%) or approximately 9.0% (still very respectable). (As a check, 1.050 x 1.090 =1.145 approximately.)

But what about risk?

We assume that the $150,000 is John's best estimate of the sale price that he will be able to achieve in 3

years time (after deducting all expenses, of course). There is of course a lot of uncertainty about house

prices, and the outturn may end up higher or lower than this estimate.

(The house John is buying is in a "good neighborhood", but market values have been rising quite a lot lately

and the real estate market analysts in the media are talking about a slow-down and higher interest rates.

There is a probability that John might not be able to get the full $150,000 he is expecting in three years dueto a slowing of price appreciation, or that loss of liquidity in the real estate market might make it very hard

for him to sell at all.)

Under normal circumstances, people entering into such transactions are risk-averse, that is to say that they

are prepared to accept a lower expected return for the sake of avoiding risk. See Capital asset pricing model

for a further discussion of this. For the sake of the example (and this is a gross simplification), let's assume

that he values this particular risk at 5% per annum (we could perform a more precise probabilistic analysis of

the risk, but that is beyond the scope of this article). Therefore, allowing for this risk, his expected return is

now 9.0% per annum (the arithmetic is the same as above).

And the excess return over the risk-free rate is now (9.0%-5.0%)/(100% + 5%) which comes to

approximately 3.8% per annum.

That return rate may seem low, but it is still positive after all of our discounting, suggesting that the

investment decision is probably a good one: it produces enough profit to compensate for tying up capital and

incurring risk with a little extra left over. When investors and managers perform DCF analysis, the important

thing is that the net present value of the decision after discounting all future cash flows at least be positive

(more than zero). If it is negative, that means that the investment decision would actually losemoney even if

it appears to generate a nominal profit. For instance, if the expected sale price of John Doe's house in the

example above was not $150,000 in three years, but $130,000in three years or $150,000 infiveyears, then

on the above assumptions buying the house would actually cause John to losemoney in present-value terms(about $3,000 in the first case, and about $8,000 in the second). Similarly, if the house was located in an

undesirable neighborhood and the Federal Reserve Bank was about to raise interest rates by five percentage

points, then the risk factor would be a lot higher than 5%: it might not be possible for him to make a profit in


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discounted terms even if he could sell the house for $200,000in three years.

In this example, only one future cash flow was considered. For a decision which generates multiple cash

flows in multiple time periods, all the cash flows must be discounted and then summed into a single net

present value.

This is necessarily a simple treatment of a complex subject: more detail is beyond the scope of this article.

For these valuation purposes, a number of different DCF methods are distinguished today, some of which are

outlined below. The details are likely to vary depending on the capital structure of the company. However

the assumptions used in the appraisal (especially the equity discount rate and the projection of the cash flows

to be achieved) are likely to be at least as important as the precise model used.

Both the income stream selected and the associated cost of capital model determine the valuation result

obtained with each method. This is one reason these valuation methods are formally referred to as the

Discounted Future Economic Income methods.

Equity-ApproachFlows to equity approach (FTE)

Discount the cash flows available to the holders of equity capital, after allowing for cost of servicing debt

capital

Advantages: Makes explicit allowance for the cost of debt capital

Disadvantages: Requires judgement on choice of discount rate

Entity-Approach:Adjusted present value approach (APV)

Discount the cash flows before allowing for the debt capital (but allowing for the tax relief obtained on the

debt capital)

Advantages: Simpler to apply if a specific project is being valued which does not have earmarked debt

capital finance

Disadvantages: Requires judgement on choice of discount rate; no explicit allowance for cost of debt capital,

which may be much higher than a "risk-free" rate

Weighted average cost of capital approach (WACC)

Derive a weighted cost of the capital obtained from the various sources and use that discount rate to

discount the cash flows from the project

Advantages: Overcomes the requirement for debt capital finance to be earmarked to particular projects

Disadvantages: Care must be exercised in the selection of the appropriate income stream. The net cash flow

to total invested capital is the generally accepted choice.

Total cash flow approach (TCF)

This distinction illustrates that the Discounted Cash Flow method can be used to determine the value of

various business ownership interests. These can include equity or debt holders.


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Alternatively, the method can be used to value the company based on the value of total invested capital. In

each case, the differences lie in the choice of the income stream and discount rate. For example, the net cash

flow to total invested capital and WACC are appropriate when valuing a company based on the market

value of all invested capital.[1]

Discounted cash flow calculations have been used in some form since money was first lent at interest in

ancient times. As a method of asset valuation it has often been opposed to accounting book value, which is

based on the amount paid for the asset. Following the stock market crash of 1929, discounted cash flow

analysis gained popularity as a valuation method for stocks. Irving Fisher in his 1930 book "The Theory of

Interest" and John Burr Williams's 1938 text 'The Theory of Investment Value' first formally expressed the

DCF method in modern economic terms.

Adjusted present valueCapital asset pricing model

Capital budgetingCost of capitalEconomic value addedEnterprise valueInternal rate of return

Free cash flowFinancial modeling

Flows to equityMarket value addedWeighted average cost of capital

Net present valueValuation using discounted cash flowsTime value of money

^Pratt, Shannon; Robert F. Reilly, Robert P. Schweihs (2000). Valuing a Business(http://books.google.com/books?id=WO6wd8O8dsUC&printsec=frontcover&dq=shannon+pratt&ei=fcfUR6q-F4TCyQSrxfWABA&

sig=Fpqt8pGRjbLPZJ9e_QEQGFzQ7y0#PPA913,M1) . McGraw-Hill Professional. McGraw Hill. ISBN

0071356150. http://books.google.com/books?id=WO6wd8O8dsUC&printsec=frontcover&dq=shannon+pratt&

ei=fcfUR6q-F4TCyQSrxfWABA&sig=Fpqt8pGRjbLPZJ9e_QEQGFzQ7y0#PPA913,M1.

1.

Continuous compounding/cash flows (http://ocw.mit.edu/NR/rdonlyres/Nuclear-Engineering/22-812JSpring2004/67B1788B-6ADC-45A6-B85A-54D13B2F537F/0/lec03slides.pdf)The Theory of Interest(http://www.econlib.org/library/YPDBooks/Fisher/fshToI.html) at the Libraryof Economics and Liberty.Monography about DCF (including some lectures on DCF) (http://www.wacc.biz) . Wacc.bizFoolish Use of DCF (http://www.fool.com/news/commentary/2005/commentary05032803.htm) .

Motley Fool.Getting Started With Discounted Cash Flows (http://www.thestreet.com/university/personalfinance/10385275.html) . The Street.

International Good Practice: Guidance on Project Appraisal Using Discounted Cash Flow(http://www.ifac.org/Members/DownLoads/Project_Appraisal_Using_DCF_formatted.pdf) ,

International Federation of Accountants, June 2008, ISBN 978-1-934779-39-2Equivalence between Discounted Cash Flow (DCF) and Residual Income (RI) (http://papers.ssrn.com/sol3/papers.cfm?abstract_id=381880) Working paper; Duke University - Center for Health Policy,Law and Management


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Wikipedia is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization.Contact us

International Federation of Accountants (2007). Project Appraisal Using Discounted Cash Flow.Copeland, Thomas E.; Tim Koller, Jack Murrin (2000). Valuation: Measuring and Managing theValue of Companies. New York: John Wiley & Sons. ISBN 0-471-36190-9.Damodaran, Aswath (1996).Investment Valuation: Tools and Techniques for Determining the Valueof Any Asset. New York: John Wiley & Sons. ISBN 0-471-13393-0.

Rosenbaum, Joshua; Joshua Pearl (2009).Investment Banking: Valuation, Leveraged Buyouts, andMergers & Acquisitions. Hoboken, NJ: John Wiley & Sons. ISBN 0-470-44220-4.James R. Hitchnera (2006). Financial Valuation: Applications and Models. USA: Wiley Finance.ISBN 0-471-76117-6.

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