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MM Proposition 1: No taxes

Hi guys, i have a question over the application of MM..

Assuming perfect capital markets; Company A is an all-equity company, with share price at $10. It announces to issue debt of $100m to repurchase shares.

By MM, the share price of Company A after announcement of this debt issuance should remain at $10. And the reason behind this is Value(levered firm) = Value(unlevered firm). 

While i agree that the firm value stays the same, wouldn’t the market of value equity change as a result of the debt issuance (i.e Equity value goes down because debt went up, overall value stays same). So, wouldn’t share price change accordingly?

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Yes, the market value of equity will decrease, by exactly the amount of equity that the company repurchases.

Simplify the complicated side; don't complify the simplicated side.

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Am i right to say there is no change in share price after the announcement but before the actual repurchase?

Share price should decrease by Δ Debt / # common shares outstanding.

This is due to the increased cost of equity, given the formula rEK = r0 + (r0 -rD) * D/E.

The increase of the cost of equity and corresponding decrease in market value of equity (or share price) outweighs exactly the amount of additional debt.