Need help with the following question:

Rayburn Manufacturing, Inc. is currently an all-equity firm that pays
no taxes. The market value of the firm?s equity is $2 million. The
cost of this unlevered equity is 18 percent per annum. Rayburn plans
to issue $400,000 in debt and use the proceeds to repurchase stock.
The cost of debt is 10 percent per annum.
	a. After Rayburn repurchases the stock, what will the firm?s weighted
average cost of capital be?
	b. After the repurchase, what will the cost of equity be? Explain.
	c. Use your answer to (b) to compute Rayburn?s weighted average cost
of capital after the repurchase. Is this answer consistent with (a)?

Hi lolome!!

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

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.



a. After Rayburn repurchases the stock, what will the firm?s weighted
average cost of capital be?

Since Rayburn manufacturing is an all-equity firm 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%.

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

b.  After the repurchase, what will the cost of equity be?

If you call:
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, then
we have with the new capital structure that:
$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%.

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

c.  Explain your result in (b).

According with MM-Proposition 2, the expected return on a firm?s
equity will rise with the amount of leverage. This rise occurs because
of the risk added by the debt.

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For additional reference see:
"WWWFinance-Capital Structure and Payout Policies: Campbell R. Harvey":
http://www.duke.edu/~charvey/Classes/ba350/capstruc/capstruc.htm


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

Regards.
livioflores-ga

I hope that this helps you. Please do not hesitate to request for a
clarification if you need it. I will be glad to give you further
assistance on this topic if you need it or if you find something
unclear in this answer.

Best regards.
livioflores-ga