What is the Equation for Discounted Cash Flow?
The discounted cash flow model can be summarized by the following equation.
Here is a brief description of each variable:
● n = Number of periods. Most DCF models will be measured in years and generally won’t extend past 3 to 5 years. However, if the investor was interested in making their money back sooner, then they may use more detailed periods such as quarters or even months.
● CF = Cash flow. This is how much money the asset will produce for each period. Note that for a business, the CF would be the EBIT or "earnings before interest and taxes”. In other words, it's the revenue after all expenses such as COGS (cost of goods sold), overhead, and depreciation & amortization have been subtracted.
● r = Discount rate. This is a constant rate that represents how much growth the asset or another investment would have grown by. For instance, if the investor had chosen to invest in stocks instead of this investment, then they could have assumed that they would have been able to produce an average rate of roughly 8 to 10 percent each year.
The DCF model can be applied to any investment opportunity where rationale assumptions about cash flows and discount rates can be made. The following are the steps involved with this process.
Most models use a figure of 3 to 5 years because they don’t want to wait much longer to make their money back. However, this is subjective based on the investor’s preference.
Cash flows should be reasonable or even conservative estimates about how much the investment may return. They may be based on past average sales or projections about the future if some increase due to an expansion or trend is anticipated.
In some models, you may include the price you paid for the investment in year 0. This be shown as a negative value and will not be discounted since it's paid at the beginning of the model before any time has passed.
Again, the discount rate is an interest rate representing how much your investment would have grown. To put cash flows into “today’s dollars” or net present value (NPV), we have to adjust each one by its time value. This is done by multiplying the cash flow by this constant interest rate to account for its growth.
Note that when carrying out this calculator by hand, the discount rate will compound each year. For instance, suppose you choose a discount rate of 10%. In the first year, the denominator of the equation would be 1 + 0.1 = 1.1. However, in the second year, the discount rate would be 1.1^2 = 1.21, followed by 1.1^3 = 1.331 for the third year, and so on.
With the discount rate for each period established, multiply it by the corresponding cash flow to get the resulting NPV value. Observe that in each case this value should be less than the future value because you’ve reduced it using the discount rate.
In the final step, the DCF is found by summing the NPV of each year’s cash flow. Generally, if the DCF is positive, then the investment is a good opportunity. However, if it's negative, then it may not be as attractive.
While the DCF is a helpful way to approximate the value of an investment, it’s not a perfect tool. There are many pitfalls involved with this process.
It can be difficult to estimate how much earnings a company or investment will make in the future, especially after the first 2 to 3 years. In this case, it's best to make conservative forecasts.
In the DCF model, the discount rate is typically a constant interest rate. However, we know that in reality companies and stocks grow at different rates each year. Even if the analyst made a more complex calculation using different interest rate figures for each period, the validity of these estimations would still be questionable since we can’t see into the future.
While DCF may be very mathematical, fundamentally it is still just a guess. There are no guarantees that the company or stock will produce the outcome we expect it to.
Another critique of the DCF model is that it tends to focus on the initial 3 to 5 years of returns. However, the reality is that we know a company or stock should last for much longer than this. Therefore, if we plan to hold onto it beyond these first few periods, how do we account for these future earnings too?
The answer is another model called terminal value. Terminal value or TV is a way of estimating the discounted cash flow of a business or investment opportunity beyond its explicit forecast period. This will be done using one of two techniques: the perpetuity method or the exit multiple method.
Terminal value is generally a separate calculation from DCF because the short-term priority is for the investor to make their money back. Terminal value gives the investor some idea of how much additional money they could make if they continue to hold the asset for the long term.
Investors who are interested in quantifying the long-term prospects of an asset can use discounted cash flow to estimate its value. This will be done by taking the anticipated cash flow of each period and converting them back to net present value. While the DCF is not a perfect model for determining if an asset is a worthwhile investment, it does provide a reasonable mechanism for determining how much money could be earned based on rational assumptions.