13 minutes

In our search for the best way to evaluate a company, we look at intrinsic value formulas to help us determine a fair price for a company. Using a discounted cash flow evaluation is one of the ways we can do this.

Accounting scandals and manipulations of financial earnings have given a rise to the importance of analyzing free cash flows. These numbers are much more difficult to “fudge” and lead to a truer value of the company.

Use of this formula will also give you much greater insight into the company. You will get a better understanding of its growth in operating earnings, capital efficiency, the capital structure of the balance sheet, the cost of the equity and debt, and the expected length of the growth of the company.

Another advantage is this formula is less likely to manipulated by dishonest accounting practices

We are going to take a look at this formula today and try to break it down and make it as easy to understand as we can. I am not going to lie to you there will be math involved but it is not difficult math.

In the business of finding the best intrinsic value for a company, we will be required from time to time to utilize math to find that intrinsic value.

So what is a discounted cash flow analysis?

According to Investopedia

“DCF analysis uses future free cash flow projections and discounts them (most often using the weighted average cost of capital) to arrive at a present value, which is then used to evaluate the potential for investment. If the value arrived at through DCF analysis is higher than the current cost of the investment, the opportunity may be a good one.”

What does all that mean?

Simply to estimate the money you would receive from an investment while adjusting the time value of money.

The reason you do this is the value of the dollar today is not what it will be worth in the future. It could be more or it could be less. So to try to adjust for that we use the discounted cash flow model or formula to help us find the closest intrinsic value we can find.

The discounted cash flow formula is powerful, but it can be flawed. Remember that it is just a mathematical tool to be used to find an intrinsic value.

**You should never buy a company based on this value alone.**

It is only as good as the information you put into it. As my music teacher used to say to me. “Garbage in, garbage out.” Small changes or errors in our calculations can have a huge impact on our value.This is why we don’t base a buying decision on just one formula. Important though it may be.

Last week we discussed the intrinsic value formula that was created by Benjamin Graham. This was a much easier, simpler way to calculate an intrinsic value of a company. The look at discounted cash flows will give us another tool in our effort to find the most accurate intrinsic value of a company we are looking to buy.

There are many different variations of formulas to arrive at an intrinsic value. The Ben Graham formula is one of them and today’s formula, the discounted cash flow is considered a variation of that effort as well.

These are the two most commonly used formulas, but there are others that we may discuss further down the road.

Ok, let’s start.

**6 Steps to Find an Intrinsic Value of a Stock Utilizing a Discounted Cash Flow Formula**

There are six steps along this path to find the intrinsic value of a company using the discounted cash flow formula. We will take a look at each one and break them down so you can follow along.

For this example, we are going to use a company that we analyzed last week so we can compare our results later.

Gamestop (GME)

The steps we will use will be as follows.

- Locate all the required financial data
- Calculate the discount rate and use it to discount the future value of the business
- Perform a discounted free cash flow (DCF) analysis
- Calculate the company’s net present value (NPV)
- Calculate the company’s terminal value (TV)
- Combine the net present value and the terminal value and come up with the company’s intrinsic value

Sounds simple huh? It is and you can do this. I will be here to help you along the way.

**Step 1: Find all the necessary financial information**

Before we dive into this we are going to need to locate all the necessary numbers to fill into our formulas as we go along. And then it’s just a matter of plugging them in.

For our calculations, there are 14 financial figures we are going to need to assemble before we can calculate our intrinsic value.

**Current Share Price: Simple, find the current market price of the company**

**Shares Outstanding**: Again, pretty simple. Find the total number of shares that are issued and currently held by the company’s shareholders.

**Free Cash Flow:**This number represents the company’s capacity for generating free cash flow, which can be used for future expansion, paying down debt, and increasing shareholder value with buybacks or dividends.

**Long-term Growth Rate:**the expected rate at which the company will grow

**Business Tax Rate:**the business income tax paid to the government.

**Business Interest Rate:**the effective rate that the company is charged for its loans and any borrowing.

**Terminal Growth Rate:**The rate that the company is expected to grow at after our cash flow projection period. We’ll use the country’s GDP growth rate as the Terminal Growth Rate

**Market Value of Debt:**the total dollar market value of a company’s short-term and long-term debt.

**Market Value of Equity:**otherwise known as the market cap. The total dollar market value of a company’s outstanding shares.

**Stock Beta:**Beta is a measure of how much the price of a company’s stock tends to fluctuate

**Risk-Free Rate:**the minimum rate of return that investors expect to earn from an investment without any risks. We’ll use a return of the 10-year Government Bond as a Risk-Free Rate.

**Market Risk Premium:**the rate of return over the Risk-Free Rate required by investors. For calculating the discount rate, you use the market risk premium data from NYU Stern School of Business.

**Total Business Debt:**total liabilities of the company

**Total Business Cash:**the total cash and cash equivalents of the company.

**Step 2: Calculate the Discount Rate (WACC)**

This is the most crucial part of our of discounted cash flow analysis. If this point is not done correctly it will throw off the future calculations and lead to an incorrect intrinsic value, which will lead to a possible purchase of an overvalued company. Leading to losses in your investments.

The key to this calculation is not assuming the same discount rate for every stock. You need to calculate the rate for each individual company or you could end up in a world of hurt.

To calculate the discount rate we are going to need five numbers:

- Interest Rate
- Tax Rate
- Risk-Free Rate
- Stock Beta
- Market Risk Premium

The interest rate can be found by looking at the company’s 10-k to gather some information.

- Company’s interest expense, which can be found on income statement
- Time period that income statement covers, which would 12 months in this case
- The principal balance of the company’s debt, which can be found on the balance sheet. Make sure you add up long-term, short-term and current long-term debt.

Now with all of that info, we can calculate the interest rate. The formula goes like this.

**Interest rate = ( interest expense / principal balance of debt) X 100**

So plugging in the numbers.

Interest Rate = (23.4 / 459.5) X 100

Interest Rate = 5.09%

Next, we need to find the tax rate for the company. The current corporate tax rate is 35% but few companies rarely pay this much. Especially if they earn the majority of their income overseas, then the rate will be much lower.

For our purposes today, we will need to find the income tax expense and the earnings before taxes (EBT).

Income tax expense and earnings before taxes can be found on the income statement.

Simply divide income tax expense by the earnings before taxes and you will arrive at your tax rate.

222.4/625.22 = 35.57% Yikes!

Next, we will need to find the risk-free rate and to do this we can look at our link from above and find that number.

Next, we will need the stock beta. This measures the volatility of a stock. The easiest way to find this is to go to any financial website and look for it there. In this case, I went to gurufocus to find the numbers. Great website by the way.

The beta is 1.21

Lastly, we need the market risk premium, which can be found using the link above.

The market risk premium is 5.69

Now that we have those numbers we next need to find the market weighted average of both the debt and equity. We need to do this because we are discounting cash flows.

First, let’s tackle the equity.

To find the company’s market value we are going to use the current share price and the number of shares outstanding.

MV = $24.71 X 101.87 million shares outstanding $2,822 billion

Next, we need to find the Book Value per share (BVPS), which is $20.71

We will take that number by the shares outstanding and get 2,109 billion.

Now we subtract the MV from the BVPS and get the market value of the equity.

2.822 billion – 2.109 billion = $713 million

Next up is the weighted average of the debt. To do this we will use numbers already gathered.

We will add up the book value of the debt and the market value of the equity.

$713 (MVe) + $459.5 (BVd) = $1.172.5

Now to find the weighted average of the debt we will take the total debt of the company and divide it by the market value of the debt and equity.

So.

$459.5 / $1172.5 = 39.18% (Wd)

Next will be the weighted average of the equity which would be the market value of equity divided by the market value of the debt and equity.

$713 / $1172.5 = 60.81% (We)

Before we figure out the discount rate of the weighted averages of debt and equity we need to calculate the cost of equity (Re) and cost of debt (Rd)

**Cost of debt = interest rate X (1 – Tax Rate)**

Rd = 5.09% X ( 1 – 35.57%)

Rd = 3.27%

**Cost of equity = Risk-Free Rate + Stock Beta X Market Risk Premium**

Re = 2.45% + 1.21 X 5.69%

Re = 9.33%

Ok, now that we have all those numbers we can calculate our discount rate that we will use to help us discount our cash flows.

The formula for our discount rate is as follows:

**Discount Rate (WACC) = (We X Re) + (Wd X Rd)**

Therefore plugging the numbers in we get.

Discount Rate = (60.81% X 9.33%) + (39.18% X 3.27%)

**Discount Rate = 6.95%**

Congratulations! That wasn’t that hard, was it? Trust me, the more that you do this the better you will get at it.

**Step 3: Calculate the Discounted Cash Flows (DCF)**

Now that we have the discount rate we are going to use it to do a discounted cash flow analysis.

This will involve 3 steps:

- Project the Future Free Cash Flow (FFCF) of our company
- Calculate the Discount Factor (DF)
- Calculate the Discounted Free Cash Flow (DFCF) of our company

**Calculate the Discounted Cash Flow (DCF)**

- We will estimate the future free cash flow of the business for the next ten years

Formula

**Projected Cash Flow = Cash Flow X (1 + Long-Term Growth Rate)n**

N = number of years

Use the discount rate to find the discount factor using this formula

**Discount Factor = 1 / (1 + Discount Rate)n**

N = number of years

So combining these elements we arrive at our formula for Discounted Cash Flow

**Discounted Cash Flow (DCF) = Projected Cash Flow X Discount Factor**

Looking at the cash flow statement we see that Gamestop had a trailing twelve-month free cash flow of $451 million with a analysts growth rate of the free cash flow of 7.8% for 10 years. And our discount rate that we calculated will be 6.95%

First, we will calculate the projected free cash flows for the next ten years.

So year 1 will be $451 X (1 + .078) = $486.18

And year 2 will be $486.18 X (1 + .078) = $524.10 and so for the next 10 years.

Step 1: Calculate Projected Free Cash Flows | ||||||||||||

Year 0 | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | Year 6 | Year 7 | Year 8 | Year 9 | Year 10 | ||

Projected Free Cash Flow | 451 | 486.18 | 524.1 | 564.98 | 609.05 | 656.56 | 707.77 | 762.97 | 822.48 | 886.64 | 955.8 | |

Discount Factor | ||||||||||||

Discounted Free Cash Flow | ||||||||||||

Assume a Free Cash Flow growth of 11.20% and discount rate of 6.95% |

Next we will calculate the discount factor that we will use to discount our future cash flows.

To calculate the discount factor we will use the formula from above.

Discount factor of year one will be:

1 / (1 + .0695) = .935

Year two will be .935 / (1 + .0695) = .874 and we will follow this thru for ten years.

Step 2: Discount Factors | ||||||||||||

Year 0 | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | Year 6 | Year 7 | Year 8 | Year 9 | Year 10 | ||

Projected Free Cash Flow | 451 | 486.18 | 524.1 | 564.98 | 609.05 | 656.56 | 707.77 | 762.97 | 822.48 | 886.64 | 955.8 | |

Discount Factor | 0.935 | 0.874 | 0.817 | 0.764 | 0.714 | 0.668 | 0.624 | 0.584 | 0.546 | 0.511 | ||

Discounted Free Cash Flow | ||||||||||||

Assume a Free Cash Flow growth of 11.20% and discount rate of 6.95% |

Now we can discount our future cash flows. This is very simple, we multiply our projected free cash flow by our discount factor to achieve our number.

DCF = 501.51 X .602 which will be $301.91 and so on for the following ten years.

Step 3: Calculate Discounted Cash Flows | ||||||||||||

Year 0 | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | Year 6 | Year 7 | Year 8 | Year 9 | Year 10 | ||

Projected Free Cash Flow | 451 | 486.18 | 524.1 | 564.98 | 609.05 | 656.56 | 707.77 | 762.97 | 822.48 | 886.64 | 955.8 | |

Discount Factor | 0.935 | 0.874 | 0.817 | 0.764 | 0.714 | 0.668 | 0.624 | 0.584 | 0.546 | 0.511 | ||

Discounted Free Cash Flow | $454.58 | $458.06 | $461.59 | $465.31 | $468.78 | $472.79 | $476.09 | $480.33 | $484.11 | 488.41 | ||

Assume a Fr |

**Step 4: Calculate the Net Present Value (NPV)**

Next, we will calculate the net present value of our discounted future free cash flows. To do this we simply add up the discounted cash flows for years 1 thru 10. Finally some easy math huh!

So for our example, the number will be billion $4710.06

**Step 5: Calculate Perpetuity Value (Terminal Value)**

Because our company is going to grow into the future we need to discount those cash flows for the future. But because we can’t calculate those forever. That would be no fun.

The terminal value model will represent all future cash flows for a company.

This value will be discounted back to end of the projected year or in this case year 10. We will use our discount rate to help us with this.

Our formula for the Discounted Terminal Value is:

**TV = Year 10 Discounted Cash flow X (1 + Perpetuity Growth Rate) /**

**Discount rate – Perpetuity Growth Rate**

The Perpetuity Growth Rate is the rate that the company will grow. We will use the GDP as that number because as nice as it would be. To expect the company to grow beyond the GDP is unrealistic. And this is a more conservative number which is what we want.

Current GDP is 2.6%

Because we have used projected cash flows we need to discount these cash flows to get a present value of our Terminal Value.

The formula for that would be:

**DTV = Terminal Value (TV) X Year 10-Discount Factor**

So let’s calculate our Discounted Terminal Value

First using the formula for Terminal value

TV = $488.41 X (1 + .03) / .0695 – .03

TV = $12735.75

So now discounting the Terminal Value

DTV = $12735.75 X .511

DTV = $6507.97

**Step 6: Calculate the intrinsic value**

We are finally here. This is where we put all of our numbers together and arrive at the intrinsic value of Gamestop.

After calculating the present value and the terminal value we simply add those together to arrive at our intrinsic value of our company. We are not quite at a price per share yet, but we are close.

**Intrinsic Value = Net Present Value (NPV) + Discounted Terminal Value (DTV)**

Intrinsic Value = $4710.06 + $6507.97

Intrinsic Value = $11218.03

To find the intrinsic value per share we use this formula:

**Intrinsic Value Per Share = Intrinsic Value + Cash – Debt / Total Shares Outstanding**

IVPS = $11218.03 + $450.40 – 2253.90 / 101.87

**Intrinsic Value per Share = $92.42**

Congratulations! You just calculated your first discounted cash flow analysis to find the intrinsic value of a company.

That wasn’t that hard, was it? It just requires a little patience and some pretty basic math. Because there are so many different calculations and inputs of specific numbers you can see how if you make an error at any one point it could cause a misleading evaluation.

** Final Thoughts**

As we looked thru the process of working out the discounted cash flow analysis of Gamestop we found that the company’s intrinsic value was $92.72.

Which when you compare that to the current market price of $24.98. This would give us a margin of safety of 73%. Now that is what I called undervalued.

This illustrates how a formula can give us a number and we have to decide how accurate it is and decide whether or not to pursue this opportunity.

This also should illustrate that it is foolhardy to buy a stock based on one formula or variable. Do I think Gamestop is undervalued? I do, but I am not convinced it is this undervalued. A 73% margin of safety would be miraculous. Is it possible? Of course, but not likely.

Last week we valued the same company using the modified Benjamin Graham formula. And the number we came up for that one was $60.09, which would have given us a margin of safety of 58%. Which is still pretty high but more in line.

What does all this tell us? I think it is telling us that Gamestop is currently selling below its intrinsic value and it would be worth our time to look more deeply into this opportunity.

Why would it be undervalued?

There is a whole list of reasons why this could be. It could be that the earnings growth hasn’t been there. It could be a that retail is taken a beating the last few years. It could be that it just isn’t followed that closely and people aren’t aware of it’s potential.

These are just some of the reasons why a company may be undervalued. Our job is to determine as accurate an intrinsic value that we can so we can assign a price to this company before we buy it.

That is how you make money in the stock market. By finding good companies that priced below their value.

This has been a learning process for me too. And I enjoyed it thoroughly. I am kind of a math geek and I love stats and figuring things out so this was right up my alley. I didn’t find the math that difficult and it was just a matter of determining where to find the correct information.

Once you have those variables nailed down it is just a matter of following the formulas and plugging in the numbers.

If you want to learn more about this kind of calculations I would strongly recommend you check out the work of Aswath Damodaran. He is a professor and NYU Stern Business School. He is considered the undisputed king of discounted cash flows and his writings have been guiding people for decades.

I took his valuation class thru iTunes University a few years ago and it blew me away. Frankly, it was over my head at the time but I wanted to wade into the deep water. I would strongly suggest you take a look at it, and it’s FREE!

He also has a great blog called Musings on Markets which is a must read.

I hope you have enjoyed this post and you didn’t get too overwhelmed by all the formulas and math.

I would love to hear your take on these intrinsic value formulas we have done the last couple of weeks. Please let me know in the comments your thoughts.

As always, thank you for taking the time to read this post.

Until next time.

Take care,

Dave