Lecture9 - capital structure theory

# Prove mm1 with taxes without is just a special case 8

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Unformatted text preview: hen More debt always increases firm value! Prove MM1 with taxes (without is just a special case) 8 Proof of MM1 is Based on No Arbitrage The strict definition of arbitrage is a strategy that The arbitrage makes a positive amount of money with no risk makes There can’t be strict arbitrage opportunities in There financial market equilibrium. People would replicate such strategies and make infinite profits. replicate In practice, arbitrage means going long and short In similar but not identical assets to make a positive expected return. But there is some risk. 9 Proof of MM1 With Taxes: The Logic We will prove MM1 by contradiction: Show that if it We does not hold, then there are arbitrage opportunities does Form two portfolios with same future cash flows & risk – Portfolio 1 uses the levered firm, and thus inherits the Portfolio leverage of the firm leverage – Portfolio 2 uses the unlevered firm, and adds leverage Portfolio by borrowing on the investor’s account by Arbitrage opportunities will exist unless the two portfolios Arbitrage cost the same. This only happens if MM1 holds. cost 10 Portfolio 1 Composition: a fraction α of equity in the levered Composition: levered firm. firm. Initial cost: αSL Initial – Alpha is % of stock outstanding purchase – C is operating cash flow Returns: perpetual cash flows of α(C-rBBL)(1-TC) Returns: 11 Portfolio 2 Composition: – Invest αVU dollars in the equity of the unlevered firm Invest unlevered – Partially finance by borrowing αBL (1-TC) Partially Initial net cost: αVU - αBL (1-TC) Returns: perpetual cash flows of αC(1-TC) – From the equity: From – From the debt: From - αrBBL(1-TC) – Total perpetual return: α(C- rBBL)(1-TC) Total 12 The Arbitrage Argument The The perpetual cash flows to portfolio 1 are equal to the perpetual returns to portfolio 2. the What happens if VU + TCB > VL = SL + BL ? Buy P1 (levered), sell P2 (unlevered) Cash flow at time zero: Cash = (αVU - αBL(1-TC)) - αSL )) = (αVU - αBL(1-TC) - α(VL-BL) = a (VU + TCB – VL) > 0 CFs in the future: CFs = α(C- rBBL) (1-TC)- α(C- rBBL) (1-TC) = 0 )13 The Arbitrage Argument What happens if VU + TCB < VL ? Arbitrage in the other direction! Sell P1 and buy P2. Arbitrage Since arbitrage opportunities cannot exist: VU + TCB = VL (MM1 with taxes) Note that PV(tax shield)=TCrBB/rB=TCB becau...
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