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:
?THIS YEAR'S LAUREATES ARE PIONEERS IN THE THEORY OF FINANCIAL
ECONOMICS AND CORPORATE FINANCE,? (Oct. 16, 1990)
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%.
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).
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? (ßc)
Expressed as a formula, it?s:
Rc = rf + ßc(rM - rf)
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
ßc 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)
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)
Google search strategy:
CAPM + beta + WACC
?Capital asset pricing model? + beta