Problem 15.6
15.6 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?sweighted
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)?

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Request for Question Clarification by scriptor-ga on 08 Aug 2005 18:08 PDT

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Scriptor

Hi!!

for answer this question properly we must take into account 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*(rA - rD)

where:
rE is the cost of equity
rD is the cost of debt
rA is the cost of capital for an all-equity firm
If rWACC is a firm?s weighted average cost of capital, then, 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 overall
cost of capital be?

We know that Rayburn is an all-equity firm, then the value of the firm?s assets
equals the value of its equity. MM-Proposition 1 establish that the
value of a firm will not change due to a change of the capital
structure, and the overall cost of capital will remain unchanged.
Therefore, the Rayburn?s overall cost of capital will remain at 18%.

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

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

Before the debt issue and the repurchase of stocks:
V = value of firm = firm's equity worth = $2 million 

Before the debt issue and the repurchase of stocks, V remains constant, then:
V = E + D = $2 million ==>
==> E = V - D = $2,000,000 - $400,000 = $1,600,000

rD = cost of debt = 10%

MM-Proposition 2 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. Use your answer to (b) to compute Rayburn?s weighted average cost
of capital after the repurchase. Is this answer consistent with (a)?

rWACC = 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 is consistent with the fact that in a world with no taxes,
rWACC for a levered firm is equal to rA.


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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