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Hi again.

So now that we know how we can value simple investment projects using the net

present value of rule, let's go one step further and

let's try to understand how we can value shareholders equity.

Now, why should we be interested in this type of question?

Well, suppose you would like to buy or

sell equity of a firm that is not publicly traded.

Well, in this case, you have to come up with a valuation of shareholders equity,

at what price you would like to buy or sell this equity.

So, the goal of this session is to try and

understand how we can achieve this objective.

Now in practice, there are two main methods use to value shareholder's equity.

On one hand that's the discounted cash flow evaluation method.

On the other hand, that's the valuation based on comparable firms.

Let's first talk about the discounted cash flow method.

So how does this method work?

So you can think of a firm having productive assets

that generate future cash flows for this firm.

Now, similar a net present value analysis

we need to compute the present value of those future cash flows.

And once we compute all the present values of the future cash flows that the firm

generates, and we sum those present values we get the firm value or enterprise value.

If you're interested in the market value of equity we need to subtract the firms

debt and we have the market value of equity.

Now let's get more specific about those different steps.

So what type of cash flows do we need?

Well we need the so-called free cash flows, these are the cash flows that

are available to all investors of the firm, both debt and equity holders.

And what we need to do is we need to forecast those free cash flows over

a explicit forecast horizon of N years.

Now in practice, this is going to be mostly between four and seven years,

depending on the industry.

Well, what happens beyond the explicit forecast horizon because we know that

forms they're exist for a longer time than just for five years.

Well, for horizons that are further in the future, we need to make

simplifying assumption because these casuals are very difficult to estimate.

And the typical assumption that we would make is that this future cash flow that

are further away in the future, they're growing at a constant rate.

Let's call it the rate g.

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And once we make this assumption,

we can then compute a terminal value with a simple formula.

Also, we call the 'Vn" the terminal value of those

free cash flows that occur beyond the explicit forecast horizon.

And what we do is we take the last forecasted free cash flow,

we gross it up by one period using this constant growth rate.

And then we divide it by the difference between the cost of capital and

the growth rate.

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Now, what type of discount rate do we need in this type of analysis?

Well, we need a so-called, weighted average cost of capital,

which represent the average cost of capital to all investors in the firm,

both equity and debt holders.

It also represents the expected returns of investors that are investing

in the firm's securities.

Once we have those ingredients, we can then easily compute the value of the firm.

Or more specifically, the price of one share.

What we do is we can simply compute the present value of those free cash flows by

discounting those cash flows, and also discounting the terminal value,

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and that will give us the firm value, or enterprise value.

Once we have the enterprise value, we again have to subtract the value of debt,

divide by the number of shares outstanding, and

then we get the price of one share.

Now, let's be more specific.

Let's look at an example.

So we have a firm that generates free cash flows of 100,

110, 120, 127, and 134 in the coming years.

Then beyond this explicit forecast verizon, cash flows will grow at 4%.

The weighted average cost of capitalist is 12%.

The firm has $500 million in debt outstanding and 100 million shares.

So what is going to be the price of one share in this example?

Well, let's implement this discounted cash flow method.

What we do is we take those future cash flows, future free cash flows and

we discount those free cash flows at 12%, which I do in this slide.

And note that the last term, which is the term 1,742,

that is going to be the terminal value at that year.

So in year 2020.

So, we have to discount that terminal value as well.

So, if you do this computation, we get a value of approximately 1.4 billion U.S.

dollars.

Now how do we get the value of one share?

Well we subtract the value of debt which in this case is $500 million.

We divide by 100 million shares and

we get the price of one share which is approximately $9 US.

So we have just implemented the very simple discounted cash flow analysis.

Now, let's look at a second way we can value shareholder's equity.

And this is the so-called valuation by multiples.

So based on multiples.

So the idea of this approach is that assets that generate identical cash flows,

they must have the same price.

So what we do is being for

the price of the company we're interested in based on the price or

based on the value of comparable firms that we observe in the market.

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Suppose that we want to value a privately held company, A.com.

So the firm has earnings of $10 million US.

And we know that comparable e-commerce firms,

they have a price earnings ratio of 20.

Now what is going to be the value of equity of A.com?

Well, we just take the firms earnings which is $10 million,

we multiply it times the price earnings ratio and we get $200 million.

So the firms equities is going to be $200 million.

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Let's look at an example, now we have again privately held firm B Inc.

So this firm has an EBITDA of 30.7 million,

it has 5.4 million shares outstanding, and debt of 125 million.

Now comparable firms in the same industry,

they have an enterprise value to EBITDA ratio of 7.4.

So what is going to be the price of one share for B incorporated?

Well, what we can do is we can using the multiple of 7.4,

we can compute the enterprise value of B incorporated.

So we multiply 7.4 times the EBITDA of 30.7.

This will give us the enterprise value.

We subtract the value of debt.

We divide by the number of shares outstanding.

And we get a price which is going to be 18.92 dollars in this example.

So again, we have very easily computed the value of one share, and

based on this multiple approach.

So there are other multiples that people are using,

the most commonly used multiples are the price earnings ratio.

Then the enterprise to EBITDA multiple, and

enterprise value to our EBIT multiple, enterprise value to sales, etc.

Depending on the industries people have come up with many more multiples.

Now how do we choose a good multiple?

Well, we should typically take multiples that are operating in

the same industry in order to make sure that I have a similar operating risk.

And we should also try to take firms that are in the similar stage of development,

meaning that they have the same expected growth rate.

In addition, if you want to use the price earnings ratio,

we should also make sure that the firms have a similar financial risk.