Part 2 – Lesson 5

### Market Cap is the Sum of the Present Value of all Future Values

In Part 2, Lesson 4, we showed you how to calculate market cap, which is simply the stock price of the company multiplied by the diluted share count of the common equity.  This gives us the market cap, or said differently, it is the current market value of the total equity of the company.  The market cap is how much someone would have to pay to own the entire equity of the company.

But what does the market cap represent?

The market cap of a company represents the present value of all future free cash flow of the company.

Please refer to Part 1, Lesson 12 for a detailed explanation of free cash flow.  As a summary, the free cash flow of a company is the net cash flow after deducting interest expense, taxes, and capital expenditure needs.  It is the cash flow that is available to the equity holders of the business.

Free Cash Flow = EBITDA – Interest Expense – Taxes – Capex

When we take the present value of all future years’ free cash flow, the net result of this calculation is the market cap of the company.  To understand this better, let’s discuss the concept of present value.

### Present Value and Future Value

It is sometimes easier to understand present value by first understanding future value.  Future value is simply the value of a sum of money at some point in the future.  For example, if you had \$100 today and invested it in a security that earned a 5% return, how much money would you have in one year?  You’d have \$105, so the future value is \$105.

Let’s now work backwards to understand present value.  Imagine you want to have \$105 in one year and you’re able to invest it in a security that gives you 5% return.  How much would you have to invest today to have \$105 in one year?  We would get the answer by dividing \$105 by (1 + rate).

Present Value = Future Value / (1 + Rate)
Present Value = \$105 / (1 + .05) = \$105/1.05 = \$100

The present value in this example is \$100.  You can see that present value is essentially future value working in reverse.  Let’s now add in more years to the example and calculate future value:

 Present Value Year 0 \$100.00 x 1.05 (we use 1 + the rate) Year 1 \$105.00 x 1.05 (we use 1 + the rate) Year 2 \$110.25 x 1.05 (we use 1 + the rate) Year 3 \$115.76

To calculate the future value at the end of each year, we simply take the prior year value and multiply by 1.05.  By the end of the year 3, our future value is \$115.76.  You will notice that the year 2 return of 5% is multiplied to the total of the initial investment plus the year 1 return.  This creates a situation where we earn \$5 in year 1, but \$5.25 in year 2.  This concept is referred to as “compounding” because prior years’ returns help to compound the growth of your overall investment.

Now, imagine we wanted to calculate the future value in 20 years.  It would be cumbersome to manually multiply 1.05 so many times to arrive at the future cash flow, so we can use the below formula:

Future Value = Present Value * (1 + Rate)^Time

It is helpful to use a calculator or Excel here.  Let’s work through our previous example by using this formula.

Future Value = \$100 * (1 + .05)^3
Future Value = \$100 * (1.05)^3
Future Value = \$100 * 1.157625
Future Value = \$115.76

The formula accurately calculates the future value at the end of year 3 of \$115.76 using 3 years of 5% returns as the inputs.  Now, let’s look at the formula for calculating present value, which simply re-arranges the formula for future value:

Present Value = Future Value / (1 + Rate)^Time

Let’s use our future value of \$115.76, rate of 5%, and time of 3 years to calculate present value:

Present Value = \$115.76 / (1 + .05)^3
Present Value = \$115.76 / (1.05)^3
Present Value = \$115.76  / 1.157625
Present Value = \$100

Let’s run through a few more examples to make sure we have the hang of it:

• Calculate the future value of an investment in 7 years assuming a current value of \$450 and using a 6% rate of return

1. Future Value = \$450 * (1.06)^7
2. Future Value = \$676.63
• Calculate the future value of an investment in 30 years assuming a current value of \$50,000 and using a 10% rate of return

1. Future Value = \$50,000 * (1.10)^30
2. Future Value = \$872,470
3. Pretty impressive to see how much your investment can grow through the power of compounding!
• Calculate the present value of an investment worth \$5,000,000 in 40 years assuming a rate of 9%

1. Present Value = \$5,000,000 / (1.09)^40
2. Present Value = \$159,188
3. This is an interesting example to show how much an individual would need to invest today if they wish to have a certain amount in the future. It again shows the power of compounding.  It is not an easy task to save \$159,188, but if an investor can do so at a young age and invest these funds at a 9% annual return, this investor can accumulate significant wealth over a few decades.
• Calculate the present value of an investment worth \$900 in 5 years assuming a rate of 12%

1. Present Value = \$900 / (1.12)^5
2. Present Value = \$510.68

### Discount Rate

In example 4 above, we discounted a \$900 cash flow received 5 years in the future by a discount rate of 12%.  The discount rate of 12% can be thought of as an expected or required rate of return.  The required rate of return is the minimum return expected by an investor to entice them to invest in a project.  This minimum rate of return compensates an investor for the risk he/she is taking with the investment.  Therefore, we use the required rate of return as the rate by which we discount future cash flows to determine what we are willing to pay for that cash flow today (present value).

The required rate of return for a project or stream of cash flows is dependent on several factors.  We name a few of these factors below (which is not an exhaustive list):

1. Volatility of the cash flow stream
2. Expected growth rate of the cash flows
3. Quality of the business/assets generating those cash flows
4. Quality of the management team responsible for generating those cash flows
5. Customer concentration
6. Geographic source of those cash flows
7. Amount of financial leverage (debt) deployed in the generation of those cash flows
8. Competitive environment
9. Uniqueness of product or service

All these factors are used so we can triangulate upon a single measurement: risk

When evaluating a stock, the higher the inherent risk, then, the higher the required rate of return.  In other words, for companies that are perceived to be riskier, equity investors will require a high rate of return in order to compensate them for taking on more risk.  Therefore, risky companies = high discount rates.

On the other end of the spectrum, for companies that are perceived to have less risk, investors will require a lower return given the lower risk profile.  Therefore, safe companies = low discount rates.

Let’s consider a few factors named above and how these items affect risk:

 Factor Discount Rate Impact High volatility of cash flow Increases discount rate High growth rate of expected cash flow Reduces discount rate High quality of assets Reduces discount rate High quality of management Reduces discount rate High customer concentration Increases discount rate Exposure to high risk geographies Increases discount rate High financial leverage (debt) Increases discount rate Highly competitive environment Increases discount rate High differentiation of product or service Reduces discount rate

Let’s now compare two companies across a few of these factors:

 Company A Company B High volatility of cash flow Low volatility of cash flow Low growth rate of expected cash flow High growth rate of expected cash flow Low quality of assets – older assets High quality of assets – newer assets Management team has poor track record Management team has excellent track record 5 very large customers make up 100% of sales 5000 customers 50% of revenue from countries with unstable governments 100% of revenue from developed nations Large amount of financial leverage deployed No outstanding debt Competition is fierce leading to low margins Oligopoly business with high margins Commodity product Differentiated product

If both Company A and Company B offered a 10% rate of return, which company would you choose to invest in?  Company B is the clear choice if we are receiving the same return.  Company B is a much safer investment on every metric we have evaluated it on.  It has a higher growth rate of cash flow with newer assets and a high-quality management team in an oligopolistic industry.  For equal return, we should always choose the investment with lower risk.

Now, what if we said that Company A offered a 12% return and company B offered an 8% return?  The choice between these two investments has become a bit more interesting, and here is where the art of investing and individual risk tolerance start to come into focus.  Based on our personal risk preferences, only earning a 4% higher return for a substantially riskier investment, doesn’t feel like enough compensation.  In other words, the reward doesn’t properly compensate for the additional risk.  However, another investor with higher risk tolerance may view this situation differently and be more interested in Company A at a 12% return.

Now, let’s change the dynamic again and assume that Company A offers a 30% return and Company B offers a 2% return.  In this case, the return of Company A starts to look quite interesting.  In 3 years, an investor can earn back their entire investment in Company A.  Whereas, Company B is suddenly looking much more expensive.  Although Company B does appear to be a very high-quality company, only earning a 2% return doesn’t seem that compelling.

This dynamic is playing out constantly in the equity markets.  Every stock price you see in the market is the culmination of thousands of investors making a collective determination as to the appropriate discount rate to apply to that company’s future cash flows.

Let’s now assume that Company A and Company B will both earn cash flow of \$100 in one year.  We will use a high discount rate of 15% for Company A and a lower discount rate of 8% for Company B.  Let’s calculate the present value for Company A’s cash flow and Company B’s cash flow:

Company A Present Value = \$100 / (1 + 15%)^1
Company A Present Value = \$100 / 1.15
Company A Present Value = \$86.96

Company B Present Value = \$100 / (1 + 8%)^1
Company B Present Value = \$100 / 1.08
Company B Present Value = \$92.59

In this example, an investor is willing to pay a higher present value for Company B’s cash flow vs. Company A even though both companies will earn the same amount of cash flow in one year.  This is due to the lower discount rate being applied to the Company B cash flow.  Since stock prices are simply the present value of all future cash flow, we would conclude that the Company B stock price has a higher value than Company A.

Lower Discount Rate = Higher Present Value

Higher Discount Rate = Lower Present Value

### Why do stock prices suddenly plunge 20% (or more) in a single day?

When a stock price suddenly plunges, it is often because investors have suddenly started to demand a higher return (discount rate) as compensation for higher risk that wasn’t previously contemplated.

For example, in our above example, Company B operated in an oligopolistic industry with little competition.  If one day, we wake up and a new competitor has emerged with strong financial backing that has an aggressive plan to steal market share from Company B, then, this introduces significant uncertainty to the future cash flows of Company B.

As such, investors are likely to “re-price” the risk associated with Company B.  If investors were previously comfortable earning an 8% return, now, investors may demand a 12% return to be comfortable taking the risk of a new competitor having entered the market.

While the difference between 8% and 12% discount rates may not sound like much at first, the impact to the present value (stock price) is dramatic since all future cash flows will be discounted at a higher rate.  And in the public markets, this re-pricing of risk can happen in a single day.

Alternatively (or in conjunction), if the future cash flow estimates of a company are revised lower after a significant event (such as an earnings call), then, this can also lead to dramatic drops in the present value of the company.

For example, let’s imagine that in conjunction with the news of a new competitor for Company B, our estimate of future cash flow is no longer \$100.  Now, we expect the future cash flow to be \$90 due to market share loss.  The new present value will be calculated using the lower future value and the higher discount rate.  Discounting this \$90 cash flow by 12% would yield a \$80.36 present value, which is a big change from the \$92.59 present value we calculated earlier.

In the financial markets, investor assumptions around future estimates and discount rates can change rapidly, leading to sharp decreases or increases in the stock price (present value).

### Calculating the stock price of Company B

Let’s now calculate a theoretical stock price for Company B.  As our first step, let’s imagine that Company B will only generate one cash flow 3 years from now of \$100.  Let’s use a discount rate of 10% for Company B.  In other words, an equity investor will require a 10% return to be interested in buying the stock of Company B.

What is the stock price today?

 Present Value Year 1 Cash Flow Year 2 Cash Flow Year 3 Cash Flow ?? 0 0 \$100

Let’s use the formula we learned earlier in the lesson:

Present Value = \$100 / (1 + .10)^3
Present Value = \$100 / (1.10)^3
Present Value = \$100 / 1.331
Present Value = \$75.13

In this example, an investor would be willing to pay \$75.13 for one share of Company B today, which assumes receipt of \$100 of cash flow in 3 years, which would imply a 10% annual rate of return.

However, most companies will have multiple years of cash flow.  How do we calculate the stock price of Company B if we expect to receive cash flow in Year 1, Year 2, and Year 3?  Let’s assume that one share of Company B is expected to earn the following cash flow stream:

 Present Value Year 1 Cash Flow Year 2 Cash Flow Year 3 Cash Flow ?? \$50 \$60 \$100

Let’s use our present value formula to manually calculate the answer:

Year 1 Present Value = \$50 / (1 + .10)^1
Year 1 Present Value = \$50 / (1.10)^1
Year 1 Present Value = \$50 / 1.10
Year 1 Present Value = \$45.45

Year 2 Present Value = \$60 / (1 + .10)^2
Year 2 Present Value = \$60 / (1.10)^2
Year 2 Present Value = \$60 / 1.21
Year 2 Present Value = \$49.59

Year 3 Present Value = \$100 / (1 + .10)^3
Year 3 Present Value = \$100 / (1.10)^3
Year 3 Present Value = \$100 / 1.331
Year 3 Present Value = \$75.13

The current stock price is the sum of the present value of all future cash flows.  In this case, the investor expects to earn 3 years of cash flows, so we will sum the Year 1 present value, Year 2 present value, and Year 3 present value.

Sum of Present Values (Stock Price) = \$45.45 + \$49.59 + \$75.13
Stock Price = \$170.17

Below is a table of how the stock price would change at various discount rates:

 Discount Rate Stock Price of Company B 8% \$177.12 10% \$170.17 12% \$163.65

You can see from this table that if investors were to re-price risk higher (by increasing the discount rate) due to unforeseen negative circumstances, this would lead to a lower stock price.  Alternatively, if investors felt more positive about Company B due to unforeseen positive circumstances, the lowering of the discount rate to 8% would result in a higher stock price for Company B.

While it is easy enough to manually calculate the present value of future cash flows when there are only three cash flows to worry about, the process becomes much more tedious when we must calculate multiple years of cash flow.  This is where the use of Microsoft Excel becomes important.

### Simple Discounted Cash Flow Valuation of Company B

When using Excel, we will use the Net Present Value formula to calculate the present value of a stream of future cash flows.  A few things to note about the Net Present Value formula:

1. The formula will be typed in Excel as =NPV(discount rate, range of cash flows).
2. The NPV formula assumes that each cash flow is received at the end of the year. In other words, the NPV formula will discount the first cash flow number by a full 12 months.
3. The NPV formula can discount a stream of cash flows of both negative and positive values.

This valuation methodology, where we discount the future cash flows of a company, is known as a “Discounted Cash Flow (DCF)” valuation.  Below is a simple DCF of Company B using the NPV formula in Excel: And here is the Excel output showing the embedded formulas: 