1 CapStructure 1

LECTURE 1 FNGB 7422 PROF. HOVAKIMIAN CHAPTER 16 FALL 2011

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CAPITAL STRUCTURE 1

Required end-of-chapter problems

Chapter 16: 1,2,4,6,8,9,12-19,21,23

1. Value of the firm is the sum of the market values of debt and equity:

V = B + S

The firm’s capital structure is described by the relative proportions of B and S.

- Unlevered firm

- Financial leverage

Why would capital structure matter?

Value of the firm = PV(CF)

If the capital structure of a firm consists of only debt and common equity,

discount rate (cost of capital) = SCBWACC RV

StR

V

BR )1(

Consider a firm, whose cost of debt (10%) is lower than its cost of equity (20%). One may suggest that the firm can issue more debt and repurchase equity reducing its overall cost of capital. Is such reasoning correct?

Not necessarily. Increases in the firm’s leverage will increase the riskiness of debt (higher probability of default) and of equity (more volatile equity values).


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2. Sources of Risk Faced by Stockholders

Business risk: Risk (uncertainty) in firm’s operating income.

Depends upon

Demand Variability

Sales Price Variability

Input Price Variability

Ability to Adjust Output prices for Changes in Input Prices

Does not depend upon the capital structure.

Financial Risk: Debt magnifies the risk to shareholders.


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3. Modigliani and Miller (MM) propositions with no taxes (tc = 0)

Example 1. Consider the following firm, which is all equity financed.

# shares 100,000

price/share $10

market value of shares $1,000,000

State of Economy Recession Normal Boom

EBIT 75,000 125,000 150,000

Net Income

EPS

Return on equity

Expected outcome

Example 2. Suppose, the firm from Example 1 issues $500,000 of debt at an interest rate of 10% and uses the proceeds to repurchase 50,000 shares at $10 each.

After Restructuring

# shares

price/share

market value of shares

market value of debt


EBIT 75.000 125,000 150,000

Interest

Net Income

EPS

Return on equity

Expected outcome


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Which capital structure is better? EPS, $

2.00

1.75

EPS2 1.50

EPS1 1.25

1.0

.75

.50

.25

50 75 100 125 150 EBIT, $000

expected op. income (EBIT)

Let us find the break-even level of EBIT:


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Based on Examples 1 and 2 the change in capital structure:

did not affect

- the operating cash flows of the firm (we will see later that this may not always be the case)

- since cash flows did not change, their volatility (business risk) did not change either.

did affect

- the cash flows to equityholders

- the volatility of cash flows to equityholders, i.e. the cost of equity

Question 1: Which of the two capital structures maximizes the value of the firm?

Since cash flows on the firm level did not change, the question is essentially which capital structure minimizes the WACC.

Since the volatility of the operating cash flows (and, therefore, the asset beta) did not change either, the WACC and, therefore, the value of the firm did not change.

Question 2: Which of the two capital structures maximizes the value of the equity?

Here, both the expected cash flows to equityholders and the cost of equity increased.

Because these two effects are offsetting, we cannot, at this point, say whether the value of equity increased, decreased, or stayed the same.


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Lessons from the above examples

The effect of financial leverage depends on EBIT. When EBIT is high, leverage is beneficial.

When the expected EBIT exceeds the break-even point, leverage increases the expected returns to shareholders.

Even though the expected returns increase, the shareholders may not be better off because the riskiness of the returns also increases.

debt ratio financial risk

market value of a firm and of its equity may not be affected by changes in the firm’s capital structure.

Modigliani and Miller (MM or M&M) argue that a firm cannot change its value by altering its capital structure.

MM proposition I (with no taxes):

The value of a firm is unaffected by its capital structure, i.e., capital structure does not matter.

VL = VU

MV of firm, V B

The following example illustrates their point.


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Example 3. Consider the firm from Example 1. An investor can create her own "homemade" leverage. Say, you have $1,000 to buy 100 shares at $10 each. You can borrow another $1,000 at 10%. You can now buy 200 shares.

Your return on investment can be found as follows.


EPS $0.75 $1.25 $1.50

Earnings for 200 shares

Less: interest on $1,000 at 10%

Net earnings

Return on investment ($1,000)

This return is the same as in Example 2.

Thus, investors can create their own leverage if they want to. They don't have to wait for the managers to do that.

Similarly, investors can "undo" the leverage created by the managers.

Example 4. Consider the firm from Example 2. An investor can undo the firm's leverage in the following way. Say, you have $2,000 invested in the firm. You sell 100 shares at $10 each. You invest the proceeds of $1,000 in bonds at 10%.

Your return on investment can be found as follows.


EPS $0.50 $1.50 $2.00

Earnings for 100 shares

Plus: interest on $1,000 at 10%

Total earnings

Return on investment ($2,000)

This return is the same as in Example 1.

Since investors can create "homemade" leverage and undo the firm's leverage, then the firm's leverage does not matter.


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MM proposition II (with no taxes):

The required rate of return on equity increases as the firm’s debt-equity ratio increases.

Please recall that:

SBwacc RSB

SR

SB

BRR

0

)( 00 BS RRS

BRR (Proposition II, no taxes)

The cost of equity consists of two components:

R0, is the required return on assets and reflects the business risk of the firm. This is the cost of equity (cost of capital) of an unlevered firm. For an unlevered firm, 0RRWACC .

)( 0 BRRS

B reflects the financial risk of the firm.

Because levered equity is riskier, it should have greater expected return as compensation.

MM Proposition II when all debt is risk free:


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Summary of MM Propositions I and II with no taxes

Required Assumptions:

1. No taxes

2. No transactions costs.

3. Individuals and corporations borrow at the same rate.

4. No costs of bankruptcy and financial distress.

5. No conflicts of interest between the firm’s securityholders or between the managers and the securityholders (no agency costs).

6. The firm’s financing decisions do not affect its investment decisions.

Proposition I: VL = VU

Through homemade leverage individuals can either duplicate or undo the effects of corporate leverage.

Proposition II: )( 00 BS RRS

BRR

The cost of equity rises with leverage because the risk to equity rises with leverage.


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4. MM Propositions I and II with corporate taxes (tC>0)

interest is tax deductible

dividends and retained earnings are not tax advantage of debt

annual tax shield = tC (RB B)

assuming tax shield is a perpetuity:

PV tax shield = Annual Tax shield / RB = [tC (RB B)]/RB = tCB

MM proposition I with corporate taxes

The value of levered firm = value of unlevered firm + PV of tax shield

VL = B

BCC

R

BRt

R

tEBIT

0

)1(= VU + tCB

VL VU B


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MM Proposition II with taxes

)1)(( 00 CBS tRRS

BRR

Example 5. Consider an all-equity financed firm, that generates annually $125,000 in operating income in perpetuity and pays 40% income tax. There are 100,000 shares outstanding. The cost of equity is 12.5%. What will happen to the value of the firm and to its share price if the firm raises $500,000 of debt (at 10% interest) and uses this money to repurchase some of its outstanding shares?

No Debt Debt of 500,000 @ 10%

EBIT 125,000 125,000 - Interest

EBT 40% - taxes

NI EPS

Debtholders get Equityholders get

Total


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Unlevered firm:

MV of firm = MV of equity =

Price per share, P =

Levered firm:

debt tax shield =

PV tax shield =

MV of levered firm =

MV of debt =

MV of equity =

Find the new share price.

Price per share, P =

Number of shares repurchased =

New number of shares outstanding =

Check: MV of equity =

The new cost of equity:

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