chapter 14 berk and demarzo capital structure in a perfect market

Chapter 14Berk and DeMarzo

Capital Structure in a Perfect Market

Chapter Outline

14.1 Equity Versus Debt Financing

14.2 Modigliani-Miller I: Leverage, Arbitrage, and Firm Value

14.3 Modigliani-Miller II: Leverage, Risk, and the Cost of Capital

14.4 Capital Structure Fallacies

14.5 MM: Beyond the Propositions


• The relative proportion of debt and equity a firm has outstanding is called its capital structure.

• The most common cases:– Financing a Firm with Equity – Financing a Firm with Debt and Equity


• How should we chose between debt and equity?

• Does capital structure matter?

• Why or why not?

• MM gave us the tools to answer these questions.

• MM were the first to use the Law of One Price to prove a theoretical claim.

Table 14.1 The Project Cash Flows

•Since the two states of the economy are equally likely, the expected cash flow is $1,150.

•If the cost-of-capital is 15%, then the NPV of this investment is: -$800 + 1150/1.15 = $200

•Since the PV of the investment is $1150/1.15 = $1000, an entrepreneur can raise $1,000 by selling equity, keeping $200 for herself.

Table 14.2 Cash Flows and Returns for Unlevered Equity

Equity in a firm with no debt is called unlevered equity. Investors are entitled to all cash flows.

Given investors’ initial $1000 investment, the expected return on the unlevered equity is:

0.5 x 40% + 0.5 x -10% = 15%

Table 14.3 Values and Cash Flows for Debt and Equity of the Levered Firm

Will adding leverage affect the value of the firm?

Suppose the risk-free rate is 5%.

Notice that the remaining equity is called levered equity.


• What price should the remaining equity sell for?

• Which is the best capital structure choice for the entrepreneur?

• Can he make more than $200?

• Remember that this is a perfect market.


• The cash flows of the company will be the same.

• The entrepreneur’s financing choice wont effect the likelihood of a weak or strong economy, thus the required return won’t change.

• Thus, the PV will still equal $1000. • And, by the law of one price, no matter how you

cut it, Debt + Equity will equal $1000. • Thus, E = $1000 – $500 = $500


• Before Modigliani and Miller, it was common to believe that:

543$

15.1

375$5.0875$5.0

E

But, this logic overlooks the fact that the leverage increases the risk of the equity of the firm. Therefore, a discount rate of 15% is too low.

Table 14.4 Returns to Equity with and without Leverage

Given an initial investment of $500, equity holders earn a higher return in good times and a lower one in bad times.

Table 14.4 Returns to Equity with and without Leverage

The increased risk is compensated with an increased expected (or required) return: 25% rather than 15%.

Table 14.5 Systemic Risk and Risk Premiums for Debt, Unlevered Equity,

and Levered Equity

Because levered equity has twice the systematic risk as unlevered equity, the risk premium for unlevered equity is twice that of levered equity.

Example 14.1 Leverage and the Equity Cost of Capital


Date 0 Date 1

Strong Weak

Firm 1000 1400 900

Debt 200 210 210

Equity 800 1190 690

Strong Return = (1190/800) – 1 = 48.75%

Weak Return = (690/800) – 1 = – 13.75%

Exp. Return = 0.5(48.75%) + 0.5 (13.75%) = 17.5%

Question 3, P.453

Parametersr 10%rf 5%

Unlevered Date 0 Date 1: prob. Value Date 1: prob. Return Exp ReturnValue 80% 20% 80% 20%

DebtEquity 40 50 20 0,25 -0,5 10%

LeveredDebt 19,05 20 20 0,05 0,05 5%Equity 20,95 30 0 0,43 -1 14,55%Firm 40 50 20

Double-click table to open Excel

14.2 Modigliani-Miller (MM) I: Leverage, Arbitrage, and Firm Value

• This section shows how MM relates to the Law of One Price

• If:1. Investors and firms can trade the same

securities in a competitive market2. There are no taxes or transaction costs3. A firm’s financing decision does not affect the

cash flows from its operations, then:• MM Proposition 1: The total value of a firm is

equal to the market value of the total cash flows generated by its assets and is not affected by its choice of capital structure.

14.2 Modigliani-Miller (MM) I: Leverage, Arbitrage, and Firm Value

• MM argument is an application of the law of one price (LOP).

• The total amount of cash paid out to all the firm’s security holders equals the total cash generate by the firm’s assets.

• By the LOP, the firm’s securities and assets must have the same value.

• As long as the firm’s financing decision does not affect its cash flows from assets, the decision can not affect the value of those assets.

Table 14.6 Replicating Levered Equity Using Homemade Leverage

Suppose an investor wanted to earn a higher expected return, and thus would prefer more leverage. In this case, the investor can build that leverage himself. This is called Homemade Leverage.

Table 14.7 Replicating Unlevered Equity by Holding Debt and Equity

Suppose the entrepreneur used debt, but the equity holder wanted to reduce her risk and expected return.

She could do this by buying debt from the firm, recreating an unlevered payoff.

Example 14.2 Homemade Leverage and Arbitrage

Question 4, p. 453Suppose there are no taxes. Firm ABC has no debt, and firm XYZ has debt of $5000 on which it pays interest of 10% each year. Both companies have identical. Fill in the table below showing the payments debt and equity holders of each firm will receive given each of the two possible levels of free cash flows.

owning 10,00% of the debt and 10,00%50,00 per year 50,00 30,00 or 50,00 80,00 or 100,00

c.

10,00% 30,00 or 50,00

500,00 and buying 10,00%80,00 or 100,00

(50,00 ) per year (50,00 )30,00 or 50,00

Suppose you hold 10% of the equity of XYZ. If you can borrow at 10%, what is an alternative strategy that would provide the same cash flows?

These cash flows could be replicated by

The debt cash flows would beThe equity cash flows would beFor total cash flows of

borrowingYou would receive dividends ofand pay interest offor a total cash flow of

provide cash flows ofequity in XYZ would

These cash flows could be replicated by

Double-click table to open Excel

Table 14.8 The Market Value Balance Sheet of the Firm

Equation 14.1

Example 14.3 Valuing Equity When There Are Multiple

Securities

Table 14.9 Market Value Balance Sheet After Each Stage of Harrison’s Leveraged

Recapitalization ($ million)

Question: What happened to the risk and required return for equity?

14.3 Modifliani-Miller II: Leverage, Risk, and the Cost of Capital

• Why can’t we lower the overall cost-of-capital by choosing a particular capital structure?

• Next, we show that the cost of capital of levered equity is equal to the cost of capital of unlevered equity plus a premium that is proportional to the market value debt-equity ratio.

Equation 14.2MM proposition 1 states that:

•E is the value of levered equity

•D is the value of debt,

•U is the value of unlevered equity

•A is the value of the firm’s assets

In words, we can use homemade leverage to replicate any financing mix.

Equation 14.3

Thus, the realized return to unlevered equity is:

•RE is the realized return to levered equity

•RD is the realized return to debt

•RU is the realized return to unlevered equity.

Equation 14.4

Rearranging Equation 14.3 gives us the return to levered equity.

We see that by increasing leverage (D), we magnify the RE relative to the unlevered case, thus increasing risk. The increase is proportional to the D-E ratio.

Equation 14.5 Cost of Capital of Levered Equity

We can write this relationship in terms of expected returns as well.

MM Proposition II: The cost of capital of levered equity is equal to the cost of capital of unlevered equity plus a premium that is proportional to the market value of the debt-to-equity ratio.

Example 14.4 Computing the Equity Cost of Capital

Capital Budgeting and the WACC

• Suppose you are the CFO of Yahoo. You want to calculate the value of a new project – A social networking website for coal miners.

• You estimate the expected cash flows, but what is the appropriate cost-of-capital?

• One option, find a comparison business whose assets have the same risk.

Equation 14.6

If the comparison business is unlevered then,

You can use the unlevered equity cost of capital to value your project.

But, what if the comparison firm is levered?

Equation 14.7 Weighted Average Cost of Capital (No Taxes)

From the homemade leverage argument, we know that the return on the firm’s assets is not changed by its capital structure (again assuming we are in a no-market-imperfections world).

Thus, the cost-of-capital is the weighted average of the firm’s equity and debt cost-of-capital – WACC.

Equation 14.8

•In a perfect market, a firm’s WACC is independent of capital structure.

•It’s equal to the cost-of-capital of unlevered equity, which equals the expected return on the firm’s assets.

Example: two capital structures

Date 0 Date 1 Date 1 return

Strong Weak Strong Weak Ex. R

E 200 280 180 0.4 -0.1 0.15

Date 0 Date 1 Date 1 return

Strong Weak Strong Weak Ex. R

Firm 200 280 180 0.40 -0.10 0.150

D 80 84 84 0.05 0.05 0.050

E 120 196 96 0.63 -0.20 0.216

What is the WACC of the restructured firm?

Figure 14.1 WACC and Leverage with Perfect Capital Markets

As the fraction of the firm financed with debt increases, both the equity and the debt become riskier and their cost of capital rises. Yet, because more weight is put on the lower-cost debt, the weighted average cost of capital remains constant.

Example 14.5 Reducing Leverage and the Cost of Capital

Example 14.6 WACC with Multiple Securities

Today Strong Weak

Firm 1000 1400 900

Debt 500 525 525

Equity 440 665 375

Warrant 60 210 0

Example 14.6 WACC with Multiple Securities

Equation 14.9

Equation 14.10

Levered beta reflects increased risk introduced by leverage.

Equation 14.11

If the firm’s debt is risk free, then we can write:

We can see explicitly how leverage amplifies the market risk of firm’s equity.

This is one explanation why firms in same industry have different BE.

Example 14.7 Airline Betas

Equation 14.12

Example 14.8 Cash and Beta

14.4 Capital Structure Fallacies

• Leverage and Earnings per Share

• Equity, Issuances, and Dilution

Figure 14.2 LVI Earnings per Share with and without Leverage

The sensitivity of EPS to EBIT is higher for a levered firm than for an unlevered firm. Thus, given assets with the same risk, the EPS of a levered firm is more volatile.

Example 14.9 The MM Propositions and Earnings per Share

14.5 MM: Beyond the Propositions

• Nobel Prize: Franco Modigliani and Merton Miller

chapter 14 berk and demarzo capital structure in a perfect market

Documents

unlevered equity equity

debt equity

equity slide

remaining equity

equity holders

debt financing

levered firm

firm value