jayaraj,
First, I'll give you a general overview of how we use betas in
Corporate Finance. Then I'll specialize to the specific question that
you raise.
The beta of a firm typically refers to the equity beta - that is the
relationship between the return on shareholder equity and the market
return. We will call this beta, B_E (for "Beta Equity").
However if there is debt associated with the firm, then the beta of
the entire firm is not the same as the equity beta. Consider this
simple balance sheet :
ASSETS | LIABILITIES
|
Total Assets (A) | Debt (D)
|---------------
| Equity (E)
The beta of debt is typically assumed to be 0 (ie. the debt is not
risky, so it's value does not vary with market returns).
The beta of debt and equity combined, is simply the weighted average
of the equity beta (B_E) and the debt beta (0). Call this combined
beta B_U (for beta-unlevered)
B_U = D/(D+E) * 0 + E/(D+E) * B_E
= B_E * E/(D+E)
But the value of the Assets, A, must equal the combined value of the
liabilities, D+E, so the beta of the assets (call it B_A) must equal
B_U.
Now suppose that we can split the assets into several separate
projects as follows :
ASSETS | LIABILITIES
|
Project 1 (A1) | Debt (D)
|---------------
Project 2 (A2) | Equity (E)
And suppose that the betas of projects 1 and 2 are B_A1 and B_A2,
respectively.
Then we know that the total asset beta, B_A must satisfy the equation
:
B_A = A1/(A1+A2) * B_A1 + A2/(A1+A2) * B_A2
i.e. the total asset beta is just the weighted average of the two
project betas.
The same holds true if we have multiple projects - we just take the
weighted average of each project beta.
So now we can use this information to answer your question.
You have a ceramin coatings division (C) and the rest of the company
(R). We can assume that the value of these divisions are AC and AR,
respectively. We can assume that the betas of these divisions are B_C
and B_R, respectively.
If the ceramin projects have a high growth rate, this means that the
value of assets in this division will grow faster than the remainder
of the company. i.e. the ratio :
AC/(AC+AR) will grow over time, while the ratio
AR/(AC+AR) will diminish over time.
So if we are looking at the beta of the entire company (ignoring the
debt/equity ratio), then we will see :
B_A = AC/(AC+AR) * B_C + AR/(AC+AR) * B_R.
The question tells us that the aggregate risk of the dividion remains
unchanged - so neither B_C or B_R change over time.
Without even placing values on B_C or B_R, we can see that the beta of
the company will grow to reflect B_C more than B_R as the proportion
of the company represented by the ceramin division grows.
If B_C > B_R - ie. if the ceramin division is a high-risk division
relative to the rest of the company, then the corporate beta will
increase over time.
If B_C < B_R, then the corporate beta will decrease over time.
If B_C = B_R, then there will be no change in the beta of the
corporation.
What does this mean for the cost of capital? The cost of capital is
determined by the rate of return on debt and equity in the firm.
WACC = D/(D+E) * rd * (1-T) + E/(D+E) * re
where rd is the rate of return on debt, T is the tax rate (you can
deduct interest payments on debt prior to calculating tax, so you get
a tax break) and re is the rate of return on equity given by :
re = rf + B_E * rp
(where rf is the risk free rate and rp is the risk premium)
As the asset beta increases, the equity beta will increase also.
However as the value of assets increases, the leverage will decrease -
this will cause a partially offsetting effect, however for normal
levels of debt, the equity beta will increase.
As the equity beta increases, re will increase and the WACC will
increase.
Hence the cost of capital will increase too.
Hope this helps, feel free to reply if any of this does not make sense
and I will do my best to clarify.
Regards
calebu2-ga
Search Strategy :
unlevered levered beta
WACC |
Clarification of Answer by
calebu2-ga
on
17 Jan 2003 06:23 PST
Jayaraj,
Don't get confused between the beta of a project and the beta of a
division. Each project should be evaluated by its own riskiness, and
the beta of each division as a weighted average of the project betas
that it comprises.
If by "more risky than average" you mean "more systematic risk" then
the beta of the projects will be higher than the rest of the division
and their growth will cause the aggregate beta for the ceramics
division to increase.
As for how long it will take for the markets to reflect this higher
beta, if you assume "efficient markets" - which is a strong
assumption, then the prices should reflect the change as soon as it
becomes public knowledge.
In reality the speed of market adjustment relies on many factors
including trading volume and liquidity of the company's stock, number
of analysts/specialists following the stock and the quality of the
information disseminated. If the information is made available in a
timely fashion, the market will on average price such information
within 48 hours.
For a more detailed exposition of market reactions to news I recommend
the text "A Random Walk Down Wall Street" by Burton Malkiel. For more
information on corporate betas I recommend chapter 12 of Ross,
Westerfeld and Jaffe's "Corporate Finance" text.
Regards
calebu2-ga
|
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