# Example5 value of firm in perfect capital markets

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EXAMPLE 5Value of Firm in Perfect Capital MarketsCompany A has 25% debt and 75% equity in its capital structure. Managementdecides to increase leverage, so it issues more debt and buys back companystock. As a result, the new capital structure is 50% debt and 50% equity. Whichof the following statements is true in perfect capital markets?APost refinancing, the company is worth more because leverage hasincreased.Post refinancing, the company is worth less because there is a greaterchance of bankruptcy.Solution:Neither answer is correct. In perfect capital markets, a change in capital structurehas no impact on the value of the company.B(2)(3)
EXAMPLE 6Effect of Leverage on Equity BetaThe Chang Shou Noodle Company is financed with 10% debt and 90% equity.1If the asset beta is 0.8 and the beta of the debt is 0.2, what is the equitybeta?2How does the equity beta change if management increases leverage to30% debt?
Modigliani–Miller Propositions51Solution:We use Equation 3 to solve this problem.1Prior to the change in capital structure, the equity beta isβe= 0.8 + (0.8 – 0.2)(10/90) = 0.87.2After the capital structure change, the equity beta is higher because moredebt increases the risk to equityholders. The new equity beta isβe= 0.8 + (0.8 – 0.2)(30/70) = 1.06.3.3MM Propositions with Taxes: Taxes, Cost of Capital, andValue of the CompanyNow let’s explore what happens when we take a more realistic assumption, that ofcorporate taxes.In most countries, interest paid on debt is deductible from income for tax purposes.In other words, debt provides a tax shield for companies that are earning profits. Themoney saved in taxes enhances the value of the company. Ignoring other realities, suchas the costs of financial distress and bankruptcy, the value of the company increaseswith increasing levels of debt. The actual cost of debt is reduced by the amount ofthe tax benefit:After-tax cost of debt = Before-tax cost of debt × (1 − Marginal tax rate).Modigliani and Miller show that in the presence of corporate taxes (but not per-sonal taxes), the value of the levered company is greater than that of the all-equitycompany by an amount equal to the tax rate multiplied by the value of the debt, alsotermed thedebt tax shield.MM Proposition I with corporate taxes:The market value of a levered company is equal to the valueof an unlevered company plus the value of the debt tax shield.VL=VU+tD,wheretis the marginal tax rate andtDis the debt tax shield. When there are corporatetaxes, a profitable company can increase its value by using debt financing.If the value of the company (V) increases as it uses more debt, the weighted averagecost of capital must decrease as it uses more debt:rDVrtEVrwaccde=-()+1Ifr0represents the cost of equity for an all-equity company, Modigliani and Milleralso show that the cost of equity for the same company with debt is:r r r rtDEed= +-()-()001which leads us to MM Proposition II with corporate taxes:MM Proposition II with corporate taxes:The cost of equity is a linear function of the company’s debt-to-equityratio with an adjustment for the tax rate.

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Term
Spring
Professor
hooreman
Tags
target capital structure, Franco Modigliani