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Hi again.

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

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

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

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

Â Well, suppose you would like to buy or

Â sell equity of a firm that is not publicly traded.

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

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

Â So, the goal of this session is to try and

Â understand how we can achieve this objective.

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

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

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

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

Â So how does this method work?

Â So you can think of a firm having productive assets

Â that generate future cash flows for this firm.

Â Now, similar a net present value analysis

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

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

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

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

Â debt and we have the market value of equity.

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

Â So what type of cash flows do we need?

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

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

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

Â a explicit forecast horizon of N years.

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

Â depending on the industry.

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

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

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

Â simplifying assumption because these casuals are very difficult to estimate.

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

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

Â Let's call it the rate g.

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And once we make this assumption,

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

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

Â free cash flows that occur beyond the explicit forecast horizon.

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

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

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

Â the growth rate.

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

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

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

Â both equity and debt holders.

Â It also represents the expected returns of investors that are investing

Â in the firm's securities.

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

Â Or more specifically, the price of one share.

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

Â 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.

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

Â divide by the number of shares outstanding, and

Â then we get the price of one share.

Â Now, let's be more specific.

Â Let's look at an example.

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

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

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

Â The weighted average cost of capitalist is 12%.

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

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

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

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

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

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

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

Â So in year 2020.

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

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

Â dollars.

Â Now how do we get the value of one share?

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

Â We divide by 100 million shares and

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

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

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

Â And this is the so-called valuation by multiples.

Â So based on multiples.

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

Â they must have the same price.

Â So what we do is being for

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

Â 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.

Â So the firm has earnings of $10 million US.

Â And we know that comparable e-commerce firms,

Â they have a price earnings ratio of 20.

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

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

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

Â 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.

Â So this firm has an EBITDA of 30.7 million,

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

Â Now comparable firms in the same industry,

Â they have an enterprise value to EBITDA ratio of 7.4.

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

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

Â we can compute the enterprise value of B incorporated.

Â So we multiply 7.4 times the EBITDA of 30.7.

Â This will give us the enterprise value.

Â We subtract the value of debt.

Â We divide by the number of shares outstanding.

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

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

Â based on this multiple approach.

Â So there are other multiples that people are using,

Â the most commonly used multiples are the price earnings ratio.

Â Then the enterprise to EBITDA multiple, and

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

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

Â Now how do we choose a good multiple?

Â Well, we should typically take multiples that are operating in

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

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

Â meaning that they have the same expected growth rate.

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

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

Â