With an all-equity firm, the firm's equity is worth $2 million. The
cost of that equity is 18 percent. The firm pays no taxes. The firm
plans to issue $400,000 in debt and to use the proceeds to repurchase
stock. The cost of debt is 10 percent. After repurchasing the stock,
what will the firm's overall cost of capital be? What will the cost of
equity be? (explain).

hi again!!

what will the firm's overall cost of capital be?

Since the firm is an all-equity firm, the value of the firm?s assets
equals the value of its equity. Under MM-Proposition 1, the value of a
firm will not change due to a capital structure change, and the
overall cost of capital will remain unchanged. Therefore, firm?s
overall cost of capital is 18%.

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What will the cost of equity be?

rA = expected return on assets
V = value of firm = firm's equity worth = $2 million = E + D ==>
==> E = V - D$2,000,000 - $400,000 = $1,600,000

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


According with MM-Proposition 2, the expected return on the 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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I hope that this helps you. Feel free to request for a clarification
if you need it before rate this answer. I will be glad to give you
further assistance on this topic if you need it.

Best regards.
livioflores-ga