Rayburn Manufactoring, Inc, is currently an all equity firm that pays
no taxes.  The market value of the firm is 2\$2 million.  The cost of
unlevered equity is 18% per annum.  Rayburn plans to issue $400,000 in
debt and use the proceeds to repurchase stock.  The cost of debt per
annum is 10%.

what is the firms' weighted average of capital(WACC)after the stock purchases?
After repurchase what is the cost of equity?
What is WACC after repurchase of stock?

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Request for Question Clarification by omnivorous-ga on 02 Sep 2005 17:31 PDT

Munster --

You should probably clarify that market value, due to an apparent typo:
$2 1/2 million?
$2 million?

Best regards,

Omnivorous-GA

Hi!!

I will answer this question assuming a firm's market value of $2
million. If it is not the correct figure, just let me know and I will
use the correct number. Note that the method used to answer this works
for whatever firm's market value that you need to use.


This problem is based on the Modigliani-Miller Propositions without Taxes:

Main assumptions:
? No taxes
? No transaction costs
? Individuals and corporations borrow at same rate

Results:
Proposition I:
VL = VU    (Value of levered firm equals value of unlevered firm)
The cost of capital does not change if the capital structure changes.


Proposition II:
rE = rA + D/E*(r0 - rD)

rE is the cost of equity
rD is the cost of debt
rA is the cost of capital for an all-equity firm
rWACC is a firm?s weighted average cost of capital. In a world with no
taxes, rWACC for a levered firm is equal to rA.



What is the firm's weighted average of capital (WACC) after the stock purchases?


Rayburn manufacturing is an all-equity firm, then the value of the
firm?s assets equals the value of its equity. The MM-Proposition I
establishes that the value of a firm will not change due to a capital
structure change, and the overall cost of capital will remain
unchanged. Therefore, the Rayburn?s overall cost of capital will be
18%. Since the WACC is the overall cost of capital, then we conclude
that the Rayburn's WACC is 18% for all cases.

                           -------------------

After repurchase what is the cost of equity?


Recall the variables:
rA = expected return on assets (cost of capital)
E = market value of equity
D = market value of debt
rD = cost of debt (= 10%)
V = value of firm ; since the initial firm's equity worth is $2
million, when the capital structure changes, V remains constant, so
with the new capital structure:
$2 million  = E + D ==> 
==> E = $2 million - D = $2,000,000 - $400,000 = $1,600,000

MM-Proposition II states that the cost of equity rE is:

rE = rA + (rA-rD)*D/E =
   = 0.18 + (0.18-0.10)*(400,000/1,600,000) = 
   = 0.20
The cost of equity will be 20%.

                           -------------------

What is WACC after repurchase of stock?

This question was answered in the first part of this answer, but I
guess that here you want to check the first question's theoretical
answer with the common way used to calculate the WACC, so here is such
answer:

WACC = rD*D/V + rE*E/V =
     = 10% * 400,000/2,000,000 + 20% * 1,600,000/2,000,000 =
     = 10% * 0.2 + 20% * 0.8 =
     = 2% + 16% =
     = 18%

This result confirms the theoretical result of the MM Proposition I:
The cost of capital does not change if the capital structure changes.

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For additional reference on this topic please visit the following page:
"WWWFinance-Capital Structure and Payout Policies: Campbell R. Harvey":
http://www.duke.edu/~charvey/Classes/ba350/capstruc/capstruc.htm

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I hope that this helps you. Before rate this answer, if you find
something unclear, feel free to request for a clarification.


Regards,
livioflores-ga

Thanks for your in depth answer.  I was on the right track--just
unable to complete all the calculations.  Thanks again