4.10. Steps in applying CAPM – an example

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From the course by Moscow Institute of Physics and Technology

Principles of Corporate Finance – A Tale of Value

6 ratings

Moscow Institute of Physics and Technology

Principles of Corporate Finance – A Tale of Value

6 ratings

Course 2 of 5 in the Specialization Understanding Modern Finance

The study of Corporate Finance seems to be a very generic part of business education. Still, it either falls in the trap of intimidating formulas or is superficially journalistic. Both extremes preclude the understanding of the core finance ideas, concepts, and models. This Course is an attempt to avoid the above extremes. We discuss the core basis and mechanisms of modern corporate finance in a learner-friendly way. We will analyze the market’s most fundamental problems, realize the intrinsic interests and preferences of investors, reveal the true meaning of specific financial terms, and uncover important issues that are so often ignored in choosing and valuing investment projects. The learners will gain insight into the essence of corporate finance. They will be able to use the obtained knowledge and skills to successfully advance in their career at a financial institution, as well as in the area of financial management at non-financial businesses.

From the lesson

Risk and Return – From Basics to Reality

In Week 4 we study risk and return. We present a stochastic mathematical model of risk and apply it to find the returns and standard deviations of portfolios of assets. We discuss diversification and the role of special portfolios – the riskless portfolio and the market portfolio – in approaching asset risk. We demonstrate how any asset contributes to the market risk and introduce the β coefficient. Then we derive the capital asset pricing model (CAPM) and study how it is used on examples. We discuss the application of the company cost of capital (CCC) rule to choosing investment projects. Then we use CAPM to determine the cost of capital – first, for an equity-financed company and then in the general case with debt and equity. We present the weighted average cost of capital (WACC) formula and discuss it. Finally, on an example we study the steps in applying CAPM.

4.1. Mathematics of risk8:36

4.2. The expected return and the standard deviation for a portfolio of securities. Some empirical evidence9:56

4.3. Diversification. “Special” portfolios6:58

4.4. Contribution to the portfolio risk. β6:22

4.5. Efficient portfolios. The market portfolio’s efficiency7:21

4.6. Capital asset pricing model (CAPM). Examples9:59

4.7. The company cost of capital (CCC) rule10:03

4.8. Applying CAPM – a no debt case4:05

4.9. Applying CAPM – the general case. WACC13:14

4.10. Steps in applying CAPM – an example15:40

4.11. Conclusions. The roadmap to determining WACC. Some objections to using normal distributions7:42

Meet the Instructors

Konstantin Kontor
Director and Professor of Finance and Strategy
American Institute of Business and Economics (AIBEc)

Now let's discuss the following example, that is,

again, provided as one of the problems in Billie and Myers.

And this is not a very advanced thing.

But that will provide you with some ideas how exactly

to go step by step through this path in the use weighted average cost of capital.

So we study the following example.

There is a company, and the company has three divisions.

So this is a division, so this will be food.

The other will be electronics, and the third will be chemicals.

Well, these divisions on the,

Market balance sheets of the company via percentage of market value is different.

And this is 50%, this is 30%

And clearly this is 20%.

So with the asset side, we are done.

Now this whole company, the company as a whole,

has the corresponding capital the structure.

So this is debt, and this is equity.

And debt to equity ratio is 0.5,

and then beta of debt is 0.1.

So the depth is of low risk, but not riskless.

And then finally, what else, I will put it here, that the tax rate is 30%.

So, this is the company, and what we have to do,

we have to find the weighted average cost of capital.

And we have to find beta of equity.

And there are two more things that are given here.

This is about the market,

we can say that rf is 4% and rm is 12%.

You know that these are important inputs for capital pricing model.

Now, so we're given this, and the question is, is this enough?

Well not quite, because the question is what do we know?

We know something about the debt, which is great.

But we do not know anything about

the betas or returns for these kinds of businesses.

Because this company is private.

And even if it was traded, for example, so

we are now, by recognizing these divisions,

are in the position not to fall in the trap of

company cost of capital rule, well quotedly.

We recognize that the risks associated with these

lines of businesses is somewhat different.

And, therefore, our general idea is the following.

We have to look at the market and find some competitors to

these divisions that are publicly traded.

And because they are publicly traded, then, for these competitors, we will know

their returns on equity and also that is observed in the market.

And by knowing their capital structure, we will have the ability to recalculate that

to find the corresponding expected return on their assets.

So the procedure will go like this.

First of all, we have to get some more data for competitors.

And let's say we will find one competitor in the food industry,

the other in the electricity industry, the third in the chemical industry.

And, again, for simplicity in this example, we will assume that

these competitors will be concentrated only in these industries.

So basically this is not a division of any other company.

It can also be done, but it's going to be a little more cumbersome.

So we will just assume that we'll find these sort of clear competitors.

And then knowing their data, we will come up with the betas of the food industry,

betas of the electricity industry, beta of the chemical industry.

That will be our first big step.

Now if we did so, then the next step we will be able to calculate

the beta of assets for the whole company.

Because here on the asset side,

this is just a portfolio of three businesses with different risks.

Then knowing the beta of assets here,

we will use the weighted average cost of capital approach.

Or we will use CAPM to recalculate that, and we'll get to beta of equity.

And if we do all that,

we will come up with WACC.

And now I will reproduce another table that contains this data for competitors.

So again this is competitors.

And for them what we know is this is for the beta equity,

this is observed in the market.

Then beta debt, and then debt to equity.

So this is the information that we will take.

And again, this will be United Food,

General Electronics and

Associated Chemicals, no ingenuity.

Now, the data is like this for United Foods.

This is, 0.6,

this is 0, and this is 0.25.

For electricity this is 1.2,

this is 0.2, and this is 1.

And for chemicals this is 1.8,

this is 0.4, and this is 2.

So these are the inputs.

Now in order to use that properly we will recalculate them in,

Some other parameters that we can see here.

Again, these parameters will be D over V.

E over V, and then finally beta of assets.

Well, now I will start to put what we do and

this, so this is all the data.

Now step 1, We,

Find beta assets, because we know beta equity, we know beta debt.

Now we use the formula that beta assets,

Is equal to D over V times beta

D + E over V times beta, and

that's for all these companies.

So see when all these, I will calculate them right there.

And that's why I will know beta assets.

All right, let's fill the formulas here.

So this is going to be, I will start below,

0.67, this is 0.33.

Now this will be 0.5 and 0.5, and

this will get 0.2 and 0.8.

And therefore we can do all these calculations, and

we will find that this is 0.48.

This is 0.70, and this is 0.87.

What I did under step 1, I just took these things and

I took these from this part of the formula, great.

So far, so good, we ended up with these numbers.

Now, what can we do with that?

These numbers, we will use and

feed the formula for the portfolio of assets of our company.

Remember, that consists of 50% of food, 30% of electronics, and 20% of chemicals.

So we will go ahead with step 2.

We take and we find that the beta assets,

This is for our company, And this would be equal to 0.62.

So all of it at this step 2, we already found a very important thing.

So now we have the market value balance sheet for this company.

And on the left side we put this weighted average, weight of 0.62.

Well, so far so good, let's proceed.

Then equipped with all that, we can take step 3.

And we say that now beta

equity is beta assets + D over E.

This is for our company, which is 0.5.

And here we come, beta assets- beta debt.

So this is 0.62, this is 0.5, this is,

again, this is 0.1, so this is 0.52.

So we end up with this beta equity, which is equal to 0.88.

Now, we're almost there,

we take step 4 and

now we use CAPM.

So we know that R for

the firm is equal to RF + beta for

assets of this firm times RM- RF,

where this is the market.

Well we know this is 12, this is 4.

And we recalculate that and get that this is 9%.

Then the next thing is that we take our equity,

which is, in this case, again, we use the same formula.

This will be RF + beta equity RM- RF, and

that will be about 11%.

And then our D will be 4.8%.

This is a little bit higher than RF, the RF was 4, because beta of debt is 0.1.

And finally, we arrive at

step 5 to find weighted

average cost of capital.

That is going to be 0.33 R- D.

This is the weight of debt + 0.67 times RE,

and that is about 8.5%, so we are all set.

Now, I would like to draw your attention to this procedure of what we do.

Again, we started out by finding

some proxy for our division,

that is publicly traded, for

which we know beta equity or R equity.

And then from that, we calculated that

using the capital structure to get the beta of assets for this kind of business.

Then, that was step 1, step 2 was then we took all of these

betas that we calculated from the competitors or proxies.

And then we put them in the portfolio of our own assets.

And then we ended up with the calculation on the left side.

And then we proceeded with all these steps 3, 4 and 5 to deal with our equity.

Now our equity may not be traded.

But here we see all the expected parameters that we have to use here.

Maybe we are doing this valuation in the hope of being able to go public.

Or we may say that this is the correct WACC for us.

So if, for example, we would like to add another project,

then this is the good WACC for across the board expansion.

But if, for example, we would add a fourth division that will be different

In terms of its business risk, then we would have to find a fourth competitor and

would redo this whole procedure of all these 5 steps once again.

So we found weighted average cost of capital is good for

across the board expansion in which any additional project looks

as the whole company, but at a smaller scale.

So these calculations, they are extremely straightforward.

But believe me they do take time.

And in what we have in our assignments there are some examples of that.

So the only way for

you to really feel that is to try to work on these assignments.

So we're almost done in this week and in the next final episode we just wrap up

go back to where we started and we'll emphasize where we are now and

what else Do we need to discuss the in the remaining weeks of this course.

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