What is a firm's weighted-average cost of capital if the stock has a
beta of 1.25, Treasury bills yield 4%, and the market portfolio offers
an expected return of 15%?  In addition to equity, the firm finances
25% of its assets with debt that has a yield to maturity of 8%.  The
firm is in the 25% marginal tax bracket.

-What's the cost of equity for this firm. 
-What's the after-tax cost of debt for this firm.  
-What's the WACC.  formulas with breif definition 
	
I qould like to see the formula's and some high level work

Hi!!

I will start with the first question:

-What's the cost of equity for this firm?

According to CAPM we have that the Cost of Equity is the Risk-Free
Rate plus Market Risk Premium times Beta. Recalling that the Market
Risk Premium is the difference between the expected return on a market
portfolio and the risk-free rate, we finally get:

rE = rF + rP * BETA 

where:
rE = cost of equity
rF = risk free rate = Treasury-Bill's rate of return
rP = market risk premium = rE - rF 

With this the first question can be answered.

See for additional reference:
"CAPM - Capital Asset Pricing Model":
http://www.valuebasedmanagement.net/methods_capm.html

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-What's the after-tax cost of debt for this firm?

The pre-tax cost of debt is its yield to maturity, of 8% in this case.
But since debt expenses are a deductible expenses, the cost of debt is
computed as an after-tax cost to make it comparable with the cost of
equity (earnings are after-tax as well), therefore debt is discounted
by the tax rate:
After-tax cost of debt  = cost of debt * (1-Tax rate) =
                        = rD * (1-T)
where:
rD = cost of debt = yield to maturity

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-What's the WACC?

Firms take money from two main different sources: debt and equity
(common and preferred). Each source has its own cost, and to find the
cost of capital for a firm we must take into account the capital
structure (the proportion of debt and equity) and the cost of each
component of the capital structure. In order to be able to compare the
cost of equity and the cost of debt we must consider the after-tax
cost of debt. To find the firm's cost of capital we must do a weighted
sum of the cost of each capital component. This is why the cost of
capital is also called Weighted Average Cost of Capital (WACC), and it
is calculated by multiplying the cost of each capital component by its
proportional weight and then sum:

WACC = Wd*rD*(1-T) + We*rE ;

where:
Wd = weight of debt
We = weight of equity
Wd + We = 1
rD = cost of debt 
rE = cost of equity
T = tax rate
NOTE:
The weight of an asset is equal to its proportion in the capital structure.


One thing that is important to recall now is:
Assets = Liabilities + Equity

The above is useful when we read at the statement that "the firm
finances 25% of its assets with debt", thus Wd = 0.25 and We = 0.75

Now you have all the elements needed to answer this last question.


IMPORTANT NOTE:
In the real world we may have two types of equities: common stocks and
preferred stocks. In these cases the WACC's formula is:

WACC = Wd*rD*(1-T) + Ws*rS + Wp*rP;

where:
Wd = weight of debt
Ws = weight of common stocks
Wp = weight of preferred stocks
Wd + Ws + Wp = 1
rD = cost of debt 
rS = cost of common stocks
rP = cost of preferred stocks
T = tax rate


See for additional reference:
"Weighted Average Cost of Capital - WACC":
http://www.investopedia.com/terms/w/wacc.asp

"Weighted average cost of capital - Wikipedia":
http://en.wikipedia.org/wiki/WACC

"Cost of capital - Wikipedia":
http://en.wikipedia.org/wiki/Cost_of_capital

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I hope that this helps you. Feel free to request for a clarification
if you need it before rate this answer.

Regards,
livioflores-ga