## Discounted Cash Flow model (DCF): A sound theory base…

In 1938 in “The Theory of Investment Value” John Burr Williams explicated the Discounted Cash Flow method for company valuation:

*“A cow for her milk, a hen for her eggs, and a stock, by heck, for her dividends”*. The idea behind this, is that the intrinsic value of an assets is determined for what it can produce from now on (the wealth it can generate for the owner). And it makes sense.

In this article:

What DCF does, is trying to assess how much is worth *today* all the future benefits that something will provide. In the case of a hen, the benefit may be the eggs. In the case of a company, the cash flow it can use to reward the shareholders.

First, there’s the concept of the value of money through time: is it the same to you to receive one thousand dollars now that in ten years? Probably not. There’s a right amount of dollars today, that makes it indifferent for you to receive it right now or wait to get the full thousand dollars in the future. And it depends on the implied interest rate.

The math behind this is called Present Value calculation. Say, if the interest rate you pretend is 7% yearly, then it could be indifferent to you to get 508 dollars now or wait 10 years and get the full thousand. The higher your rate, the lower you accept today instead of in the future.

That’s what DCF does, it tells us how much we may offer today to purchase something that will provide some cash flow in the future. In general terms, it can be applied to anything of economic value, including stocks.

### Discounted Cash Flow model versus Dividends Discount model

When John Burr spoke of dividends as the benefits that stock provide, he was specifically referring to the Dividend Discount Model, a particular case of the Discounted Cash Flow, where the cash flow is comprised exclusively of dividends paid. But what if the company does not pay dividends? Well, in that case, a profitable company will eventually be able to pay dividends, after making all the investments it needs to keep in business, even if it takes a long time.

Sure, there’re many companies that won’t provide a dividend to stockholders for the foreseeable future, even if they’re very profitable. That’s a management decision. What could be measured instead, is the cash flow they genuinely generate, even if they don’t distribute it. And why is that? Because even if the company doesn’t distribute cash, as an owner, it’s still your wealth (on a pro rata basis of the shares you own).

What about a dying business? Then the cash flow may come from liquidating all the assets, paying all the creditors, and return the remaining (if any) to the stockholders. The present value of that final net payments could be a fair valuation of the dying business.

So, how do we calculate the Discount Cash Flow of a company?

## Calculating the Discount Cash Flow of a company: things are starting to get tricky

First, you need an estimation of all the future benefits (cash flow) the company will be able to generate in the future. Is it difficult to do? Yes, because you’ll have to make assumptions, like how much the business is going to grow onwards, among many others.

Not necessarily the cash flow generated will be constant through all the years, perhaps the company is growing (or shrinking!), or it must use some of the cash to make reinvestments, among many other possible reasons.

You will have to estimate revenues, costs and necessary reinvestments, to come up with a yearly net cash flow generated.

Growth could be positive, or negative, so the growth rate should be of the appropriate sign, depending on the company situation.

And what about if the company lasts forever, or at least has no ending date in the foreseeable future? Then you estimate the cash flow it’ll provide through a certain time horizon and calculate a terminal value for all the flows from then on.

Deciding the time horizon of the model is therefore a very important decision. Usually, you should use a period in which you feel comfortable about the projection of the cash flow. Also, if any change in growth is expected, you could project the profits during the time horizon, and from the growth rate change on, use the terminal value as approximation.

Ok, and what about the terminal value? The terminal value is an estimation, of the present value (what’s worth today) of all the payments you’ll get after the time horizon. If there’re no payments, nor any net asset (or debt) after the time horizon, then there will be no terminal value, but that isn’t usually the case.

Beside projecting the cash flow through a time horizon and possible beyond, you’ll need to decide the appropriate discount rate, meaning the required rate of return to invest in the company or project. A company (or in general terms, any economical project) may be funded with equity (by the owners) or by borrowing money. The cost of capital is therefore a weighted average of this mix.

To decide the appropriate discount rate, you’ll have to assess how risky is the business, that is, the probability that those cash flows won’t materialize, or be different (lower) than expected. Most likely it isn’t the same to you, to invest in a company that’s very likely to deliver the estimated cash flow, than in one that’s much more volatile. You’ll also have to consider the estimated future inflation. The higher the risk or the inflation, the higher the discount rate.

The discount rate (also called weighted average cost of capital, WACC for short) is a combination (weighted average) of the cost of capital sources: the cost of debt (required rate for creditors) and the cost of equity (the required rate for owners, in this case the stockholders)

Finally, you calculate the Present Value, by discounting the inputs of the model. The PV you get, is the maximum amount you’ll be willing to pay to purchase the company to get the desired rate of return.

If the present value (theoretical value) you came up with is higher than the market capitalization (what it sells for currently), then you’ll be willing to buy at that price, for the company seems to be undervalued. And the other way round.

DCM isn’t only used for company valuation, but also in investments projects, say when a firm is deciding on the convenience of a certain investments, like buying a new machine for the production facilities. In that case, the present value (the cost of the investment) is usually known, so the model is used to try to calculate the rate of return. And also to calculate the Net Present Value (the present value of the future benefits it’ll generate minus the cost of the investment).

## …with many limitations in practice: Discounted Cash Flow shortcomings

So, the theory looks conceptually sound, the calculation seems a bit complex, what about the Discounted Cash Flow shortcomings?

### Estimating the future cash flow accurately

It’s quite difficult to estimate the future cash flows with high accuracy. A lot of things could go different than the projections. Sales volume could be higher or lower than expected, competition could increase and bring industry margins down, consumer preference might change for better or worse, commodity prices may vary substantially, among many others. Try reading the risk section of the 10-K form of your favorite company (EDGAR database), and you’ll get an idea.

The more stable the business, the easier it could be to project the cash flows. A lower rate could be used for those business, but how much lower? That’s a whole new criticism for a coming bullet point.

You could use pasts cash flows to help estimate future ones, but what if there’s a game changing event, or any other reason for them not to be representative?

### Determining the growth rate

Growth rate is very difficult to predict yet is has a big impact in discounted cash flow valuation. The higher the project growth rate, the higher the theoretical valuation.

One common pitfall is that if you use a very high growth rate, you can justify almost any high-flying valuation you desire. Say, if you project your hen will give birth to 200 chickens a day, and each of them so on, in a couple of weeks you could have a chicken army. So that hen could potentially be worth millions! Right? Ok, no, that’s very unlikely.

Surely you’ve seen more than one glamourous stock turn very sour in a financial statement’s reporting day when they don’t meet expectations. That’s because price already includes all the future expected growth. The higher the expected growth, the more likely the firm won’t be able to keep up with expectations forever. Benjamin Graham used to advise that the future isn’t for speculation, but to be prudent, cautious. Remember it’s your money you’re risking.

That isn’t to say growth is bad, on the contrary growth is very good. You should actively look for growing companies and be prepared to pay a fair price for them (Growth at a Reasonable Price strategy). Just beware of not using too high a growth rate in your model, as to make the valuation an illusion.

On the contrary, some companies could be undervalued, if in a challenging environment (they could even be shrinking) the growth rate used in the model is lower than reasonable. Contrarian investors aware of this could turn a profit by holding the stock (as the company may deliver better cash flows than expected). You must be very sure and have guts to do so. And there’s also room for miscalculation and failure.

### The importance of terminal value

One of the common problems of the DCF model, is that usually a large portion of the valuation is due to the terminal value. The terminal value is estimated at the end of the time horizon, for all the remaining cash flows from then on (it could even be the liquidation of the business). As a general rule, the shorter the time horizon considered, the more important it becomes.

The terminal value depends heavily on a few estimations, like a constant net cash flow from then on, the terminal growth rate and the future discount rate. It’s recommended to use a vegetative growth rate for the terminal rate. Why? Because not doing so would imply that the company could grow at a higher rate than the economy itself, forever, to the absurd of eventually surpassing it.

If the company you’re valuating grows higher than average, it’s recommended then to extend the time horizon projection until grows gets to more normal levels, at which point you could then try to assess the terminal value.

### The difficulties of using an appropriate discount rate

Ah, here we found some major problems.

Remember that one of the main goals of the Discounted Cash Flow model is to determine the present value of the future cash flows of the company. And remember that to do so, the model uses a discount rate, which normally is a weighted average between the creditors rate (debt), and the stock owners’ rate (equity), called Weighted Average Cost of Capital (WACC for short). You should use market valuations of both debt and equity to calculate the weighted average. But wait, aren’t we trying to calculate the equity value in the first place?

That’s know as the recursive problem of the use of WACC for equity valuation. There’re some methods to overcome it, yes, but with their own issues.

Another big problem is that to estimate WACC, many practitioners turn to the CAPM model (that goes for Capital Asset Pricing Model). Well, bad news is, that model is seriously flawed. For example, it relies on the estimation of a metric called Beta. And Beta may vary nonsensically depending on the time horizon comprised to estimate it. Also, Beta has many other interesting uses, like telling us a financial asset is very risky (but only **after** it collapsed, duh!). A whole new article will be coming on that.

For the third and final strike on the discount rate problems, the fact that the rate isn’t always constant through time. Sure, you could use a particular rate for every year over the time horizon, but what about the terminal rate? Ouch!

### Sensitivity Analysis

To further complicate matters, DCF has serious sensitivity analysis problems.

Wait, what’s sensitivity analysis? It’s when you try to gauge how much the result of the model varies if you change some assumptions, say in case of the DCF model changing the discount rate, or the growth rate. Or the final net cash flow estimated in the terminal value.

Truth is, DCF is largely sensitive to small variations. Try using an online DCF calculator. Try making a small change in the rate, or the growth rate, and see for yourself the impact on the present value of the model. That’s why online DCF calculators aren’t recommended, for tweaking the input parameters allow for a wild range of change in the resulting outputs, sometimes justifying unreasonable valuations.

You’ll come to realize that in some cases, using the DCF model for company valuation leaves you the feeling of the accuracy you get while scratching your toes with your military boots on.

### Complexity of the model

There’re thousands of companies out there, waiting to be priced. Will you have an always-updated DCF projection for all of them? That’s why many retail investors (and many institutional managers) rely on multiples and other ratios to evaluate if a company is under or overvalued, or how much they should be willing to pay for them.

Sure, in merger situations, or any due diligence for the matter, a specific and very costly analysis using DCF (and an army of financial analysts) is used to assess a price range of the company. The results aren’t necessarily much better than the reasonable valuation range you can come up with financial metrics and business sense. And usually, traditional financial ratios are used to assess the reasonability of the DCF suggested price range anyway.

It’s known that sometimes when CEOs are determined to buy a company they can’t wait to get they hands on, inputs and assumptions are often tweaked as to provide a DCF model that justifies the asked price. In such a case, ego could be fueling companies getting bigger, but not necessarily making smart capital allocations with a good return on investment.

## Discounted Cash Flow: summary

Discounted Cash Flow is a sound model in theory. The correct and right way to value an economic asset. However, calculating it in any serious way is time consuming and a lot of specific and accurate assumptions are to be made. There’re many pitfalls over the input estimation, which could lead to a non-reasonable stock valuation.

If you use too much of a complex spreadsheet and your model can’t sustain a drop in the growth rate, say from 7% to 6%, or a rise in WACC of a percentual point, then you’re probably doing something wrong. We aren’t looking for perfection in asset pricing, but rather a reasonable valuation range. Else, DCF may end up being like going to war with a mega alien laser. The only problem being it only fires on Tuesdays. (And only if it’s raining).

If you’re looking for undervalued companies, then the mispricing should be manifest, self-apparent. Otherwise, in Value Investing, we would say there’s no Margin of Safety (no difference between the intrinsic value and the asked market price). Peter Lynch (from Growth Investment school) advocated in favor of being able to justify your investment in a single page written in crayon.

Many investors resort to using other financial metrics (ratios), which are easier to understand, easier to keep up to date, and can provide a more stable range of pricing for company valuation. By all means use DCF, but please double check its reasonability with other financial key indicators. As John Maynard Keynes used to state, *“it’s better to be roughly right than precisely wrong”*.