discounted cash flow (DCF) - Mathematics, Example DCF, History

A notion used in business to assess if a capital expenditure proposal will generate an adequate return on the investment (ie sufficient profit). It is useful where projects are expected to last several years, recognizing the ‘time value’ of money - a given sum received next year is better than the same sum received in three years' time. The expected sums of cash flowing in and out are discounted back to their present value, using a discount rate which may be the rate at which a firm can borrow, adjusted for risk, or the return on the best available alternative project. If the present discounted value exceeds the initial cost of the project, then the investment is expected to be profitable.

In finance, the discounted cash flow (or DCF) approach describes a method to value a project or an entire company. The DCF methods determine the present value of future cash flows by discounting them using the appropriate cost of capital. This is necessary because cash flows in different time periods cannot be directly compared since most people prefer money sooner rather than later (put simply: a dollar in your hand today is worth more than a dollar you may receive at some point in the future). The same logic applies to the difference between certain cash flows and uncertain ones, or "a bird in the hand is worth two in the bush".

DCF procedure involve three problems

the forecast of future cash flows, the incorporation of taxes (firm income taxes as well as personal income taxes), the determination of the appropriate cost of capital.

Discounted cash flow analysis is widely used in investment finance, real estate development, and corporate financial management. Since the underlying financing assumptions are different they do not need to arrive at the same value of the project or company:

Equity-Approach Flows to equity approach (FTE) Entity-Approach: Adjusted present value approach (APV) Weighted average cost of capital approach (WACC) Total cash flow approach (TCF)

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; n is the number of discounting periods used (the period in which the future cash flow occurs). 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.

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

So, calculating exclusively for opportunity cost, we get a discount rate of 5% per year. Note that the original internal rate of return (13.6%) minus the discount rate (5%) equals the discounted internal rate of return (8.6%). 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 DCF 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.

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). 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.

History

Discounted cash flow calculations have been used in some form since money was first lent at interest in ancient times. Following the stock market crash of 1929, discounted cash flow analysis gained popularity as a valuation method for stocks.