Since EL + DL = VL, implying VU = VL. Otherwise, there will be arbitrage opportunity. A firm’s cost of capital-WACC * A firm's cost of capital is the minimum rate of return the firm should expect to earn on its invested funds so that all providers of funds just earn their required rate of return.

* In perfect Capital markets, a firm's cost of capital equals the expected return on its assets, WACC = rA, regardless of the firm's capital structure. Because accorfing to Proposition 1, WACC is independent of Capital structure.

The cost of levered equity Modigliani and Miller's Proposition 2 * The expected rate of return on levered equity is * The risk of the equity increases as the proportion of debt in the capital structure increases, the shareholder then require a premium for compensation, which is the second part of the equation. *

When the debt is riskless, i.e., βD = 0, then Capital structure and E/P (or P/E) ratios For non-growth firms the E/P is equal to the return on equity rE. (For growth firms it is proportional to rE.) Since equity holders require higher rates of return as leverage is increased, the E/P increases with leverage.

Be careful! A high E/P ratio is likely to reflect a higher financial risk, rather than being a bargain. (Also, recall that a high E/P ratio reflects lack of available growth opportunities.) Capital Structure in Imperfect Markets

Capital Structure and Corporate Taxes * The value of an unlevered firm is * Leverage creates tax shield and thus increase the firm value. * The present value of the tax saving is

Use Rd as discount factor because the risk of getting a loan= risk of getting Tax shield. MM Proposition 1 with Taxes * The value of the levered firm equals the value of the unlevered firm plus the present value of the tax savings on interest payments: VL = VU + tCDL. * Proof | Investment | Annual return | Strategy 1 | α*EU | αNOI(1-tc) | | | | Strategy 2 | αEL | α(NOI-rdD)(1-tc) | | α(1-tc)DL | α(1-tc) rdD | Total | α(EL+(1-tc)DL) | αNOI(1-tc) | The law of one price implies that (EL + (1-tC)DL) = VU.

EL + DL = VL, implying VL = VU + tCDL.

The Cost of Equity Capital

Modigliani and Miller Proposition 2 with taxes * The expected rate of return on levered equity is

* Three sources of expected return on equity:

Shareholders' expected return comes from three sources:

i) Return on invested equity funds - they get rA on the invested equity EL - tCDL, ii) Financial risk premium - they get a return of (rA - rD) on the borrowed funds DL, iii) Annual tax savings of tCrDD

The Firm's Cost of Capital - the WACC * A levered firm's cost of capital is given by

* Substitute rE from Proposition 2 to get

Equivalently,

Cash flow from real assets = VL WACC = VU rA

Notes:

i) WACC decreases with leverage. Therefore, firm value increases with leverage (recall VL = VU + tcDL). iii) A lower WACC implies that a marginal negative NPV project can become attractive if it is partially debt financed because of the tax subsidy. βrisk with corporate taxes Proposition 2 implies that the βof the equity increases with debt in the following way

Inverting this formula, we obtain

Note that this formula is not a weighted average of βD and βE, because DL + EL is larger than Vu. Vu =D+E-tc*D!!!!!!

Capital