In finance, the discounted cash flow (or DCF) approach describes a method to value a
project, company, or financial asset using the concepts of the time value of money.
All future cash flows are estimated and discounted to give them a present value. The discount rate used is generally the appropriate cost
of capital, and incorporates judgments of the uncertainty (riskiness) of the future cash flows.
Discounted cash flow analysis is widely used in investment finance, real estate
development, and corporate financial management.
Mathematics
The discounted cash flow formula is derived from the future value formula for
calculating the time value of money and compounding returns.
The simplified version of the Discounted cash flow equation (for one cash flow in one future period) is expressed as:
where
- DPV is the discounted present value of the future cash flow (FV), or FV adjusted for the opportunity cost of
future receipts and risk of loss;
- FV is the nominal value of a cash flow amount in a future period;
- d is the discount rate, which is the opportunity cost plus risk factor (or the time value of money: "i" in the
future-value equation);
- n is the number of discounting periods used (the period in which the future cash flow occurs). I.e. if the receipts
occur at the end of year 1, n will be equal to 1; at the end of year 2, 2—likewise, if the cash flow happens instantly, n becomes
0, rendering the expression an identity (DPV=FV).
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) for all time periods. The sum can then be used as a net present value figure or used to further calculate the internal rate of return for a cash flow pattern over time.
Example DCF
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 13.6%. Looking at those
figures, he might be justified in thinking that the purchase looked like a good idea.
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%.
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. By not doing
so, he has incurred an opportunity cost from his decision.
So, calculating exclusively for opportunity cost, we get a discount rate of 5% per year (taking the comparable-period Treasury
rate of return directly). 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, which would be $29,576 or a little more than 29%. Amortized
over the three years, that implies a discounted annual return of 8.6% (still very respectable, but only 63% of the profit he
previously thought he would have). Note that the original internal rate of return (13.6%) minus the discount rate (5%) equals the
discounted internal rate of return (8.6%). The discount rate directly modifies the annual rate of return.
But what about risk?
- 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 due to 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.
For the sake of the example, let's then estimate his risk factor is about 5% (we could perform a more precise probablistic
analysis of the risk, but that is beyond the scope of this article). Therefore, this analysis should now include both opportunity
cost (5%) and risk (5%), for a total discount rate of 10% per year.
Going back to the DPV formula, $150,000 received three years from now and discounted at a rate of 10% is only worth $111,261
(rounded off) in present-day dollars. The present-value profit on the sale is now down to $11,261 discounted dollars from $50,000
nominal dollars. The implied annual rate of return on that discounted profit is now 3.6% per year.
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 opportunity cost and 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 lose money even 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 $130,000 in three years or $150,000 in five years,
then buying the house would actually cause John to lose money in present-value terms (about $6,000 in the first case, and
about $9,000 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 discounted terms even if he could sell
the house for $200,000 in three years.
In this example, only one future cash flow was considered. For a decision which generates multiple cash flows in multiple time
periods, DCF analysis must be performed on each cash flow in each period and summed into a single net present value.
Methods
Depending on the financing schedule of the company four different DCF methods are distinguished today. Since the underlying
financing assumptions are different they do not need to arrive at the same value of the project or company:
- Equity-Approach
- Entity-Approach:
History
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.
See also
External links
Literature
- Tom Copeland, Tim Koller, Jack Murrin: Valuation. J. Wiley & Sons, 2nd edition, 1998.
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