We will now talk about a few miscellaneous topics
related to cost of capital estimation. Here are the four items
that we will deal with: estimating beta and determining
project beta, country risk, marginal cost of capital
schedule and flotation costs. First, estimating
beta and determining project beta. A firm's beta is used
to estimate its required return on equity and we
saw this in the CAPM formula where we said that the required
return on equity is equal to the risk-free rate plus
the beta times the expected return on market minus the
risk-free rate. This was also called the equity risk
premium or the market risk premium. The risk-free
rate is based on the economy. The market risk premium
or equity risk premium is also based on a given
economy. The beta is a number that represents the
particular stock and this represents the riskiness
of the stock. Beta is a measure of risk. Riskier
firm's will have higher betas. When we use the term
equity beta then we are talking about the beta
of the stock. This captures both financial risk
as well as business risk. Business risk is the risk
associated with the regular operations of a business
i.e. the risk of sales not being as high as we expected
or the risk of costs being higher than expected. Financial
risk stems from the level of debt that a company has
taken. Beta is estimated by regressing a stock's
return with overall market returns. We will discuss
beta in more detail when we cover portfolio management later
in our course, but very simplistically beta tells
us about how a given stock price varies relative
to the market and since beta deals with variations
relative to the movements of the market,we can calculate
beta by doing a regression of a given stock's returns
with the overall market returns. This might seem
a little complicated but don't worry about it too
much. This is material that you will see at level
two. At times we need to estimate the beta for a company
or project that is not publicly traded. And what
we are going to do in this segment is talk about how
we can calculate the beta for a company or project
that is not publicly traded. So we don't have the
stock price, we cannot compare movements in the
stock price with the market. So what do we do? The
answer is that we use a method called the pure-play
method which will be discussed in detail on the next
slide but first some basic terminology. To use the
pure-play method we have to identify a comparable
company. This comparable company would be a publicly
traded company where we know the stock price and
where we can come up with the beta. We'll see these
terms also; equity beta and levered beta. Equity
beta and levered beta are synonymous. These are the
terms that we actually have been using over here.
When we talk about the beta of a stock we are
really referring to the equity beta or the levered
beta. Levered beta is the beta assuming that
the company has some leverage. So the financial
risk is also incorporated into the beta. Asset beta and
unlevered beta are synonymous, this refers to the risk
associated with purely the assets of a company.
We assume that the company is unlevered and the riskiness
of a company assuming no debt is called asset beta
or unlevered beater. Now, let's understand this
method called the pure play method and we will do
so by discussing an example. AA Corp is a large conglomerate
and wants to determine the equity beta of its food
division. This food division is not publicly traded.
So how will we come up with the beta of the food division?
That's what this slide is all about. This division
has a debt-to-equity ratio of 0.7. This ratio gives
us a sense for how much debt the division has taken
or what is the leverage of this division. The tax
rate is 40%. A comparable publicly traded food company
has an equity beta of 1.2 and a debt to equity ratio
of 0.5. Not explicitly stated here but let's assume
that the tax rate is also 40%. What is the equity beta
of AA's food division? There are three steps that
you need to follow. The first step is identify
a comparable publicly traded company and estimate
its beta. This is an important step in the real
world. But in the exam world, this information will
typically be given to you as it has been given over
here. We are told that this comparable company has
an equity beta of 1.2. So step one is done for you.
Then you determine the comparable's asset beta,
which is also the unlevered beta. First I'll tell you
conceptually what we are doing over here. We know
that the equity beta of the company is 1.2. This
is a number that incorporates the fact that the company
has debt. What we need to ask is what is the asset beta or
what is the beta of this comparable company
if it had no debt and we come up with that number, the
asset beta or the unlevered beta using this formula
and this is a formula you need to memorize. The asset
beta is equal to the equity beta, which is 1.2.
multiplied by 1 / 1 + 1 - the tax rate that is 0.6 multiplied by the debt to equity
ratio. This is the debt to equity ratio of the comparable
company, which is 0.5. When you do the calculation,
you should come up with 0.92. This is the asset beta of
the comparable. It represents the riskiness assuming
there is no debt. We can assume that the food division
of AA Corp. has the same business risk as the business
risk of the comparable. We can therefore say that
the asset beta of the food division is also 0.92.
But now we need to account for the fact that the food
division has a debt-to-equity ratio of 0.7. We need
to calculate the equity beta or the levered beta
and the formula is given over here. The levered beta
is equal to the asset beta, which is 0.92 * 1 + the tax rate or 1 - the tax rate
which is 0.6 times the debt to equity ratio, which
is 0.7. You do the calculation and you should get
1.3 and it should make sense that the equity or levered
beta for the food division is higher than the equity
beta of the comparable because the food division
has more debt. It has a higher debt-to-equity ratio,
more debt means more risk and more risk means that it
should have a higher beta. While not explicitly
asked in this question, but you can now use this beta
number to calculate the required return for the
food division and you would use CAPM for that. You could
use the required return is equal to the risk-free
rate plus the beta which is 1.3 * the equity risk
premium. Now, I want you to do examples 9, 10, and 11.
Some of these are a little long but if you have understood
the concepts discussed here, you should be able
to do the examples. Next item, country risk. For companies
in developing countries we need to add a country
risk premium to CAPM, most of the discussion so
far has been from the perspective of an investor
in a developed-market. If you are a US-based investor
and you are investing in an American company, then
you can simply use the capital asset pricing model
which we have discussed, required return is equal
to risk-free rate + beta into equity risk premium.
You use this to come up with your required return.
But what if you are investing in a developing country
like India, then there is risk involved associated
with the developing country and you need to add a
premium for that risk. That is called the country risk
premium. Notice that the formula that we have here
is very similar to the regular CAPM and formula. The
only difference is this country risk premium. Just
to give you a simple example now. If you are a US based
investor, you would use the US-based risk-free rate. Let's
say that is 3%. And then let's say that the beta of
a given stock is 1.5. You would have the expected
return on the market minus the risk-free rate. Let's
say that this premium is 6% and let's say that the
country risk premium associated with India is 3%. You
would plug that number in and do your calculations.
Don't get too hung up on this, the high-level concept
is what is needed over here. I think the probability
of being tested on this is relatively low. The next
question is how do we calculate the country risk
premium? The country risk premium is given by the
sovereign yield spread * something which I will
talk about in a moment. But first let's understand
the sovereign yield spread. The sovereign yield spread
is a measure of the riskiness of a given country. Sovereign
means national or country, yield spread means the differences
between two yields. So let's understand the definition,
sovereign yield spread is equal to the developing
country government bond yield. Let's say our developing
country is India. And India has issued government bonds
denominated in US Dollars and let's say that the
yield on those bonds is 7%. We are looking at the spread.
So this needs to be a difference. We then subtract
the yield on the developed country bond. Let's
say a comparable maturity US bond issued by the US
government has a yield of 3% then the sovereign yield
spread is 7 - 3 which is 4%. This 4% gives us a measure of the
risk associated with investing in India. But notice the 4% is purely based on
investing in the government bond market. What if
we are investing in the stock market? We then need
to account for the risk associated with the stock
market and that's where this next term comes in.
This next term is equal to the annualized standard
deviation of the equity index of the developing
country. So let's take... let's continue with our India
example and we take a major equity index in India
and look at the standard deviation of returns of that
index. So standard deviation of the equity index
in India, divided by the annualized standard deviation of
the sovereign bond market in terms of the developed-market
country. So you divide by the standard deviation
of the bond market. This would be the bond market
in India. This term tells us about the relative riskiness
of the stock market. When you combine the two the
riskiness of the bond market in India and the riskiness
of the stock market we come up with the country
risk premium. Just as a disclaimer here this method
is not a method that you will see in every single textbook.
When you study country risk premium from different
books you might see slightly different formulas.
Don't worry about it too much in terms of your CFA
level 1 exam this is what you need to use and again
understanding the concept is more important than
understanding the details that we have discussed
over here. To understand this concept a little better
make sure you do example 12.