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Q: Finance/Captial Structure ( Answered 4 out of 5 stars,   0 Comments )
Question  
Subject: Finance/Captial Structure
Category: Business and Money > Finance
Asked by: 081705md-ga
List Price: $10.00
Posted: 17 Jul 2005 14:48 PDT
Expires: 16 Aug 2005 14:48 PDT
Question ID: 544606
Acetate, Inc has equity with a market value of $20 million and debt
with a market value of $10 million. The cost of the debt is 14 percent
per annum. Tresury bills that mature in one year yield 8 percent per
annum, and the expected return on the market portfolio over the next
year is 18 percent. The beta of Acetate's equity is 09. The firm pays
no taxes.

a. What is Acetate's debt-equity ratio?
b. What is the firms weighted average cost of capital
c. What is the cost of capital for an otherwise identical all-equity firm?

Request for Question Clarification by omnivorous-ga on 17 Jul 2005 16:05 PDT
MD --

This question's pretty straightforward -- except for the firm's beta. 
Is it 0.9?  (A beta of .09 would be extraordinarily low, while a beta
of 9.0 would be extraordinarily high.)

Best regards,

Omnivorous-GA

Clarification of Question by 081705md-ga on 17 Jul 2005 16:36 PDT
Hello omnivorous,

The firm's beta is 0.9. 

Thank you!!
Answer  
Subject: Re: Finance/Captial Structure
Answered By: omnivorous-ga on 18 Jul 2005 03:53 PDT
Rated:4 out of 5 stars
 
081705MD ?

Implicit in this question is an understanding the Capital Asset Pricing Model, 
developed in the 1960s by William F. Sharpe and the cornerstone of
corporate finance.  It assumes that the minimum return is for
government-backed securities (Treasury bills in the U.S. and gilts in
the U.K.); that there is a market risk for stocks; and that there is a
company-specific risk that can be measured by the beta.

Sharpe was awarded the Nobel Prize for the work in 1990:
NobelPrize.org
?THIS YEAR'S LAUREATES ARE PIONEERS IN THE THEORY OF FINANCIAL
ECONOMICS AND CORPORATE FINANCE,? (Oct. 16, 1990)
http://nobelprize.org/economics/laureates/1990/press.html

---

Now to answer your questions:

A.	Debt-equity ratio is $10M/$20M = 0.5 

When we get to a weighted-average cost-of-capital, we?ll use slightly
different numbers.  Equity to total valuation (E/VL) is $20M/$30M or
66.7% and debt to total valuation is $10M/$30M or 33.3%.

B.  WACC

In order to get the weighted-average cost-of-capital, we first have to
figure out the return expected on equity (also called the return to
the corporation, Rc).


CAPM MODEL
============

The CAPM model says that the return to investors (and to the
corporation, Rc) has to be equal to:
?	the risk-free rate
?	PLUS a premium for stocks as a whole that is higher than the
risk-free rate.  This market return premium is (rM ? rf)
?	And the market return should be multiplied by the risk factor for
the individual company, termed the ?beta of the corporation? (c)


Expressed as a formula, it?s:

Rc = rf + c(rM - rf)

Where,  

Rc is the company's expected return on capital 
rf is the risk-free return rate, usually a long-term U.S. Treasury bill rate 
rM is the expected return on the entire market of all investments. 
Most measures use a common broad index, most often the S&P500 over the
past 5 or 10 years
c is the company's Beta, based on its covariance with the market.


Rc for Acetate, Inc. is:

8% + 0.9 * (18% - 8%) = 8% + 9% = 17%

A couple of notes here:
*  as expected, with a beta lower than 1, this firm has a lower cost
of equity than the overall market
*  this problem is only unusual in predicting future market returns. 
Rc is normally calculated on past market returns.

Now on to the WACC --


WEIGHTED-AVERAGE COST OF CAPITAL
=================================

The full weighted-average cost-of-capital (WACC) for a firm is given by:

WACC = Rc (E/VL) + rD(1-t)(D/VL)

where,
Rc: return on equity
E/VL: proportion of equity in total firm value
rD: debt or bond percentages
t: tax rate (expressed as a decimal; 40% = 0.40)
D/VL: proportion of debt in total firm value

There are no taxes here, so WACC simplifies to:

WACC = Rc (E/VL) + rD (D/VL)

WACC = 17% (.667) + 14% (.333) = 11.34% + 4.66% = 16%


C. ALL EQUITY FIRM

We?ve actually figured out the cost-of-capital already for an all
equity firm ? Rc = 17%.  Except in extreme cases, the level of
leverage makes no difference in the cost of equity.

While this wasn?t in the scope of your question, it may interest you
to know that the latter point was proven by Franco Modigliani and
Merton Miller, who are also Nobel Prize winners.  Merton Miller, who
taught at the University of Chicago?s Graduate School of Business when
I was there, explains the irrelevance of borrowing in the capital
structure this way, "Say you have a pizza, and it is divided into four
slices. If you cut it into eight slices, you still have the same
amount of pizza. We proved that! Rigorously!"

Arnold Kling -- AP Economics
"Corporate Finance: Leverage and the Modigliani-Miller Theorem" (undated)
http://arnoldkling.com/econ/saving/corpfin.html



Google search strategy:
CAPM + beta + WACC
?Capital asset pricing model? + beta

Best regards,

Omnivorous-GA
081705md-ga rated this answer:4 out of 5 stars

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