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Explaining the DCF Valuation Model with a Simple Example

Discounted Cash Flow (DCF) valuation is one of the fundamental models in value investing. Using a DCF is one of the best ways to calculate the intrinsic value of a company. Using a DCF is a method that analysts use throughout finance, and some think that using this type of valuation is far too complicated for them.

We will show you in this post that once you understand the different components and how to put together the model, it is a matter of dropping in the values and out pops the valuation.

Using cash flows as an estimator of a company’s value is a better way to go than earnings, as earnings have the ability to be “adjusted” where cash flows are the cash left over for reinvestment or returning value to investors.

In today’s post, we will discuss:

  • What is a Discounted Cash Flow Model?
  • How to Find the Rates Needed to Perform a DCF
  • How to Perform a DCF Valuation
  • Limitations of the Discounted Cash Flow Valuation

Ok, let’s dive in.

What is a Discounted Cash Flow Model?

To sum it up, from Investopedia:

Discounted cash flow (DCF) is a valuation method used to estimate the value of an investment based on its future cash flows. DCF analysis attempts to figure out the value of an investment today, based on projections of how much money it will generate in the future.”

A discounted cash flow model is used to value everything from Walmart to a person’s home; financial analysts use these models to calculate the intrinsic value of just about anything that has a cash flow, i.e., bonds, buying new equipment, or valuing Walmart.

The calculation of the value comes from the projection of the future cash flows into the future and then discounting those cash flows back to the present to give us a value today for those future cash flows.

It sounds complicated, but it isn’t, think of it this way, the value of $100 in the future is worth less today because inflation causes money to lose value into the future.

The reason the model we refer to this model as a discounted cash flow is that we use discount rates to discount those future cash flows back to the present—more on this topic in a moment.

The neat part of using these models is once you arrive at your value, you can determine whether or not the company is under or overvalued. If the discounted cash flow result is above the current market value of the company, then theoretically, the company is undervalued and could generate positive returns into the future.

Ok, now that we have an understanding of what a discounted cash flow is, let’s discuss discount rates and other inputs needed to calculate a discounted cash flow.

How to Find the Rates Needed for a DCF

To perform a discounted cash flow or DCF as it will be known as going forward, we need to start with some numbers or assumptions.

The different rates we are going to need are:

  • The growth rate of the cash flows into the future
  • The discount rate that we will need to discount those future cash flows
  • The terminal rate that we will use to determine the final value of the DCF.

An important note before continuing, any DCF is sensitive to any inputs we enter, especially the growth rates, discount rates, and terminal rates we decide upon. Therefore we must be thoughtful about our inputs as they can substantially change our DCF valuations.

Growth Rate for Cash Flows

The two most sensitive parts of the DCF are the growth rates for cash flows and terminal rates. So when testing our DCF models, it is always best to be as reasonable as possible.

One of the ways I like to predict the future of cash flows is to look at the past growth rates of the cash flows and project those into the future if I feel those rates are reasonable.

Remember, we humans are terrible at predicting the future, so any number you choose is an estimate and don’t get obsessive about the “perfect” number for any of these inputs.

One of these easier ways to achieve this goal of finding the cash flow growth is to look at analysts’ predictions from your favorite website, or you can look back at past numbers and project those forward.

Let’s pick a company and start down the path of calculating the DCF for that company.

For my example today, I would like to use Darden Restaurants, Inc (DRI), which has a current market price of $75.44 and a market cap of $9.79B.

Using the predicted cash flow growth from gurufocus.com for the next year, they are predicting a number of 10.10%, and if I look at the growth of the cash flow over the last five years, including the trailing twelve months, or TTM I get a value of 7.72%.

Let’s use the 7.72% as our expected growth rate for our future cash flows.

Discount Rate

Next, we are going to find the discount rate for our cash flows. To arrive at our discount rate, we are going to use the method knows as the weight average cost of capital or WACC. For our purposes here, I will discuss the inputs, and how to calculate the WACC, if you are interested in learning more about the ins and out of this method, please check out this post:

Example WACC Calculator Calculation with Walmart (WMT)

Briefly, the weighted average cost of capital is fundamental to the capital asset pricing model (CAPM). We calculate the WACC as the weighted average of a firm’s cost of debt and cost of equity.

Assuming that we are analyzing Darden Restaurants, Inc (DRI), the steps for the calculation of WACC are the following:

  • The first step is to find the cost of debt and the cost of equity.

The cost of debt is derived as follows, and all numbers are taken from the latest annual report:

The company’s total debt is $928 million and the interest expenses are $54 million. The interest expenses will save Darden Restaurants $54 x 8.14% (tax rate) = $4.4 million. So, the after-tax cost of debt Rd = ($54 – $4.4) / $928 = 5.34%

The cost of equity is calculated using the formula Rs = RRF + (RPM * b), where,

  • RRF: the risk-free rate or 10-year Treasury Rate
  • RPM: the return that the market expects or Risk Premium
  • b: the stock’s beta (systemic risk)

To find the risk-free rate, use the Treasury.gov link. And the Risk Premium uses this link, and finally, the beta I used gurufocus.com.

Therefore, for a risk-free rate of  0.75%, an expected market return of 6% and a b=1.71, the cost of equity is:

Rs = RRF + (RPM * b) = 0.75% + (1.71 x 6%) = 11.01%

  • The second step is to calculate the weights of debt and equity

First, you need to find the Market value added (MVA) of the company, which represents the difference between the current market value of a firm and its book value. Darden is currently trading at $75.44, and the number of shares outstanding is 125.44 billion. Therefore, the company’s market value is $75.44 x 125.44 = $9.46 billion.

Given the company’s book value per share (BVPS) of $19.44, its book value is $19.44 x 125.44 = $2.44 billion.

Therefore, the market value added is market value – book value = $9.46 – $2.44 = $7.02 billion.

Now that you know the MVA and the total debt, you added them to derive the weights of debt and equity. Therefore:

The book value of debt + MVA of equity = $928 + $7.02 = $7.948. Therefore, the weight of debt Wd = $928 / $7.948 = 11.68% and the weight of equity We = $7.02 / $7.948 = 88.32%.

  • The final step is to calculate the WACC

The formula for WACC is (Rd*Wd) + (Rs*We). Therefore:

WACC = (5.34% x 11.68%) + (11.01% x 88.32%) = 0.62% + 9.72% = 10.34%.

Terminal Rate

Now, we are up to our last rate to determine before proceeding with our DCF valuation.

The terminal rate is arguably one of the more important inputs for a DCF; it has a large influence on the value that we arrive at in the future.

The simplest way to determine the terminal rate is to use the same rate that the economy is growing. If you try to use a terminal rate higher than that, you run the risk of the company outgrowing the economy over time, and unless you want to buy car insurance and milk from Darden Restaurants, that is probably not the way to go.

For me, I use the GDP rate for the US economy, which is currently at 2.2%.

Remember that the company, at some point, will have their growth come back to earth and will return to match the growth of the economy they reside in, that is why we use a lower Terminal Rate.

Now that we have our rates let’s look at how we calculate a DCF.

How to Calculate a DCF

The goal of a DCF valuation is to derive the fair value of the stock and determine whether it trades above this value (overvalued) or below this value (undervalued).

Remember that value investing is set out to find undervalued stocks, i.e. stocks that trade below their fair value and, therefore, they have room for growth.

Once you know the WACC, you can create a spreadsheet for the calculation of the free cash flow to the firm (FCFF) by using the sales and EBITDA of the current year and assuming a sales growth of 7.72% and a tax rate of 8.14% for the next five years.

Then, you discount the FCFF to its present value using the WACC. The changes in working capital are discounted using the WC/Sales ratio (working capital over sales), which in this case, is $80 / $8510 = 0.94%.

dcf valuation 1

Here is an example of the calculations:

Sales: 8510 x (1+7.72%) = $9166.97 x (1+7.72%) = $9874.66 x (1+7.72%) = $10,636.99 x (1+7.72%) =$11458.16 x (1+7.72%) = $12,342.73

EBITDA: $1173 x (1+7.72%) = $1263.56 x (1+7.72%) = $1361 x (1+7.72%) = $1466.18 x (1+7.72%) = $1579.37 x (1+7.72%) = $1701.30

Since there are depreciation expenses, EBITDA is equal to EBIT.

Taxes on EBIT: $1173 x 8.14% and so on up to year 5.

Capex: 452 x (1+7.72%) = $486.89 x (1+7.72%) = $524.48 x (1+7.72%) = $564.97 x (1+7.72%) = $608.59 x (1+7.72%) = $655.57.

Changes in WC: 0.94%* = $80 x (1+0.94%) = $80.75 and so on up to year 5.

Now that we have the free cash flow figured we could find the present value of those cash flows, the formula for that process is below.

PV of FCFF: FCFF / (1+WACC)1 for year 1, ^2, for year two and so on up to year 5.

An example of the first year is as follows:

PV = 956 / ( 1 + 10.34%)^1
PV = 956.07 / (1.1034)^1
PV = 866.48

Next chain would be:

PV = 866.41 / (1.1034)^2 and so on down the line for all five years.

The next step is we need to calculate the terminal value, assuming a growth of 2.2% beyond the forecast period.

Therefore, the FCFF in the year 5 with a growth of 2.2% = $1,312.48 x (1+2.2%) = $1341.35, and the terminal value is $1341.35 / (WACC – growth) = $1341.35 / (10.34% – 2.2%) = $1341.35 / 8.14% = $16,478.50.

Then, you discount the terminal value to its present value using the WACC. So, the Present Value of Terminal Value is $16,478.50 / (1+1034%)5 = $10,074.90.

Calculating the total PV of the FCF by adding up the PV of the cash flows, which equals $4141.76.

Then, you need to calculate the equity value of the firm by:

  1. Add the PV of the terminal value to find the total equity value. So, $4141.76 + 10,074.90 = $14,216.66
  2. Deduct the debt of last year to find the net asset value. So, $14,216.66B – $928M = $13,288B.

Now that we have our net asset value or intrinsic value of the cash flows, we can determine our per-share price by dividing that number by the shares outstanding.

DRI per share value = $13,288 / 125.4 shares outstanding
DRI per share value = $105.96

Which, when comparing to the current market price of $75.88, appears to tell us that Darden Restaurants is undervalued. All of that is based on the growth rates of the free cash flow, the discount rate we calculated, and the terminal rate.

The next job is to determine if we think those assumptions are reasonable.

So, according to the DCF valuation, Novartis is overvalued, as it trades at $75.21, and the DCF shows that the value per share should be $59.49 based on the company’s FCFF.

Some limitations of the DCF valuation

DCF Valuation is an extremely useful tool, provided that the growth rate assumed for the series of periods is justifiable by the firm’s operating performance. Although the growth rate cannot be accurately estimated, a firm that is expanding and seeks to enter into new markets is more likely to sustain an average growth of 7.72% for the next five years than a company that is contracting or losing market share. Also, the WACC calculation may not apply to the real world.

Another area that requires attention is the capex projections. In the above example, we assumed Darden’s capex is growing at 8% annually over the next five years.

In the real world, this may not be so true. If, for example, a company is expanding in year 3, its capex will be higher in year three and lower in years 1,2,4, and 5. So, before using constant growth for Capex, you need to dig into the company’s balance sheet to investigate the trend of capex throughout the investigation period.

Final Thoughts

Using the discounted cash flow model to find the intrinsic value of a company is a great way to dig into the financials of a company. The model requires you to estimate both growth rates and discount rates, which are open to interpretation and one of the weaknesses of the model.

However, there are no models that are completely estimated free; you either need to use forward estimates or historically based numbers, but either way, they are estimates because we have no real idea what the future will hold. But one of the most important issues is to be consistent with your assumptions, never mix and match rates to achieve the intrinsic value you are searching to find, that will lead to disaster.

In our examples, we used the free cash flow, but feel free to use Buffett’s owner earnings, or you can use earnings as well. Another bonus to using the DCF valuation is you are touching many different parts of the financials of a company, the sales, costs, debt, equity, free cash, which forces you to have a good pulse of the financials of any company.

But calculating intrinsic value is imperative to find a great price to pay for any company you are analyzing. The price you pay is incredibly important and goes a long way towards determining your overall returns and any decisions you make.

One thing to keep in mind when working on these models, don’t get bogged down in the minutiae, rather focus on your assumptions and try to determine if they are logical. Buffett and Munger have repeated often, “it is better to be approximately correct, as opposed to precisely wrong.”

Focus on your models, and your assumptions don’t worry about finding the “exact” number rather whether you think your intrinsic value is reasonable and logical based on what you know about the company and the market conditions.

That is going to wrap up our discussion today, as always, thank you for taking the time to read this post.

Until next time.

Take care, and be safe out there,

Dave

Note: Christina Pomoni also contributed to this post.