Lecture9 - capital structure theory

# 14 mm1 with no taxes to prove mm1 with no taxes

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Unformatted text preview: se debt because is perpetual. If it is not, then you would need to carefully calculate the corresponding tax shields. 14 MM1 With No Taxes To prove MM1 with no taxes, simply set TC = 0 in all of To the steps above. The proof is identical! The You will conclude that: VU = VL (MM1 with no taxes) You 15 The Two MM2 Propositions MM Proposition 2 without taxes: When TC = 0, then rS = r0 = WACC When WACC is independent of capital structure! WACC MM Proposition 2 with taxes: When TC > 0, then rS = r0 + (r0-rB)(B/S)(1-TC) More debt increases the required return on equity! More Prove MM2 with taxes (without is just a special case) 16 Proof of MM2 With Taxes Start with MM1: VL = VU + TCB = S + B. The levered firm’s B. market value balance sheet is: market Assets VU Liabs.&Equity B TC B S Note that for a perpetuity: r PV = C (from PV = C/r) Note The expected annual cash flow from the left-hand side of the balance sheet is: r0 VU + TC B rB of The expected annual cash flow to bondholders and shareholders together is: rS S + rB B shareholders 17 Proof of MM2 With Taxes Because all cash flows are paid out as dividends in our nogrowth perpetuity model, the cash flows going into the firm growth equal those going to stakeholders. Hence: r0 V U + TC B r B = r S S + r B B But VL = S + B = VU + TC B , so VU = S + B - TC B Plugging into previous equation and rearranging gives: Plugging rS = r0 + (r0-rB)(B/S)(1-TC) (MM2 with taxes) 18 Proof of MM2 Without Taxes Simply repeat the previous proof setting TC =0, and you will get will rS = r0 + (r0-rB)(B/S) (MM2 with no taxes) 19 Implication for Equity Risk Assets = \$10,000 ; Return on debt = 10% ; No taxes Let ROA and Capital Structure Vary State ROA (%) Earnings Interest NI ROE (%) All-equity firm: S=10,000 & B=0 A B C D 0 0 5 500 10 1000 15 1500 0 0 0 500 0 1000 0 1500 0 5 10 15 20 E 20 2000 0 2000 20 Implication for Equity Risk Levered firm (D/V=.5): S=5,000 & B=5,000 A B C D State ROA (%) Earnings Interest NI ROE (%) 0 0 5 500 10 1000 15 1500 500 -500 500 0 500 500 500 1000 -10 0 10 20 E 20 2000 500 1500 30 Debt increases the sensitivity of ROE to changes in earnings. This is the idea of financial leverage. Financial leverage typically increases expected ROE, but also increases the riskiness of these returns. 21 Implications of MM2 for WACC As we on Lecture 5 (p. 12-13), plugging the formula for As MM2 into the WACC formula you get: S + B (1 − T ) WACC = r0 S+B Increasing debt lowers WACC (see Lecture 5) Increasing Without taxes: WACC = r0 Increasing debt does not affect WACC Increa...
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## This document was uploaded on 03/09/2014 for the course COMM 371 at UBC.

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