Capital Structure

Chapter 15 & 16

Copyright © 2010 by the McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin

Capital Structure and the Pie

The value of a firm is defined to be the sum of the

value of the firm’s debt and the firm’s equity.

V = D + E

• If the goal of the firm’s

management is to make the

firm as valuable as possible,

then the firm should pick the

debt-equity ratio that makes

the pie as big as possible.

Value of the Firm

D E

Capital Structure

Capital structure refers to the mix of long term debt and

equity maintained by the firm.

Leverage - The use of debt in the company leverage results

from the use of fixed cost to magnify returns to the firm’s

owners

� increased leverage raises risk/return

� decreased leverage lowers risk/return

Management can control leverage in the capital structure, and

in turn affect firm value

Stockholder Interests

Is there a ratio of debt-to-equity that maximizes the shareholder’s value?

As it turns out, changes in capital structure benefit the stockholders if and only if the value of the firm increases.

Managers should choose the capital structure that they believe will have the highest firm value, because the capital structure will be most beneficial to firm’s stockholders.

What is leverage ?

Business Risk

arises as a result of

Operating Leverage

Financial Risk

arises as a result of

Financial Leverage

Analytical income statement

Operating

Leverage

Financial Total

Leverage Leverage

Sales- Cost of sales

Gross ProfitOperating ExpEBIT (Operating income)

- InterestNPBT

- TaxNPAT

- Preference Dividend- Earnings available for OS

- EPS

Business risk Financial risk

The variability or

uncertainty of a firm’s

operating income (EBIT)

Affected by:• Sales volume variability• Competition• Cost variability• Product diversification• Product demand• Operating leverage

The variability of a

firm’s earnings per

share and the

increased probability

of insolvency

when a firm uses

financial leverage.

Operating leverage

The responsiveness of the firm’s earnings before interest and taxes to changes in salesRevenue.

A firm with relatively high fixed operating costs will

experience more variation in operating income if

sales change

The use of fixed operating costs as opposed to

variable operating costs

Financial leverage

The use of fixed-cost sources of finance rather

than variable-cost sources to finance a portion of

the firm’s assets.

Fixed-cost sources

• Debt

• Preference shares

Variable-cost sources

• Ordinary shares

EBIT-EPS

Example: Our firm has

• 800,000 ordinary shares on issue,

• no debt,

• and a tax rate of 30%.

We need

$8,000,000 to finance a new project and are

considering 2 options:

1. Sell 200,000 new ordinary shares at $40 per share

2. Borrow $8,000,000 by issuing 10% bonds

Which is the best option?

EBIT-EPS

Assume EBIT to be $2,000,000

EBIT – Interest= EBT– Tax (30%)= Net incomeNo shares issuedEPS

Shares2,000,000

02,000,000

600,0001,400,0001,000,000

$1.40

Debt2,000,000

800,0001,200,000

360,000840,000800,000

$1. 05

EBIT-EPS

Assume EBIT to be $4,000,000

EBIT – Interest= EBT– Tax (30%)= Net incomeNo shares issuedEPS

Shares4,000,000

04,000,0001,200,0002,800,0001,000,000

$2.80

Debt4,000,000

800,0003,200,000

960,0002,240,000

800,000$2.80

EBIT-EPS

Assume EBIT to be $5,000,000

EBIT – Interest= EBT– Tax (30%)= Net incomeNo shares issuedEPS

Shares5,000,000

05,000,0001,500,0003,500,0001,000,000

$3.50

Debt5,000,000

800,0004,200,0001,260,0002,940,000

800,000$3.68

EBIT-EPS

EBIT$2,000,000

Ordinaryshare

financing

EBIT$4,000,000

Debtfinancing

EBIT$5,000,000

???

Conclusion so far

Higher level of debt increases EPS at higher

level of Earnings.

Debt is beneficial for stockholders

But debt is risky in a recession.

Which Capital structure is better ?

Break-even EBIT

EBIT

EPS

$2m $5m$3m $4m0

1

2

3

Sharefinancing

DebtfinancingFor EBIT up to

$4 million, share financing is best

For EBIT above $4 million, debt financing is best

MM Proposition 1 (no tax)

According to M & M, in a perfect market, no combination of capital structure will affect the firm’s value.

The value of a levered firm is the same as the value of an unlevered firm.

MM Proposition I (No Taxes)

…suggests that capital structure is irrelevant in determining the value of the firm:

Value of levered firm is the same as value of unlevered firm.

VL = VU

Total Cash Flow to Investors

The levered firm pays less in taxes than does the all-equity firm.

Thus, the sum of the debt plus the equity of the levered firm is

greater than the equity of the unlevered firm.

This is how cutting the pie differently can make the pie “larger.”

-the government takes a smaller slice of the pie!

E G D G

D

All-equity firm Levered firm

With Taxes….

In a world of taxes, the value of the firm increases

with leverage.

VL = VU + TC B

Modigliani and Miller (MM) showed that the value of an unlevered firm (one with no debt) was the same as a levered firm (Text: Extreme Position 1). That is

VL = VU

but that when tax was introduced, it had the effect of increasing the value of the firm by the tax saving (in perpetuity). That is

VL = VU + TCD

where TCD is the corporate tax rate debt

Who saves more Tax?

Unlevered

(No Debt)

Levered

(Debt)

Revenue 100 100

COGS 60 60

Gross Profit 40 40

Interest - 10

Net Profit 40 30

Less Tax (30%)

12 9

Profit AT 28 21

Total Cash Flow to Investors

The levered firm pays less in taxes than does the all-equity firm.

Thus, the sum of the debt plus the equity of the levered firm is

greater than the equity of the unlevered firm.

This is how cutting the pie differently can make the pie “larger.”

-the government takes a smaller slice of the pie!

S G S G

B

All-equity firm Levered firm

DEF is currently an unlevered firm. The company expects to generate $153.85 in earnings before interest and tax (EBIT) in perpetuity. The corporate tax rate is 35%. All earnings are paid out as dividends.

Unlevered

NoDebt($)

Value of equity 500.00

Value of debt 0.00

Value of firm 500.00

EBIT 153.85

Interest (10%) 0.00

Taxable income 153.85

Tax (35%) -53.85

Net income 100.00

KE 0.2000

Workings

Value of Company without Debt

value of debt = 0

value of the firm = value of equity + Debt (0)

= $ 500 + $ 0

= $ 500

500$0.20

$100

K

incomeNet V

UE,

E ===

The firm is considering a capital restructure to allow $200 of debt. Its cost of debt capital is 10%. Unlevered firms in the same industry have a cost of equity capital of 20%. What will the new value of the firm?

Levered FirmVL = Debt + equity = $ 500 + 0.35 ( 200) = $ 570

Value of equity = Value of firm – Value of Debt= $ 570 - $ 200 = $ 370

The EBIT of the levered firm is the same as that of the unlevered firm as the operations of the firm have not changed. However, the firm now has to pay $20 in interest payments [$200(0.10)] which reduces the taxable income, the tax payable and the amount available to shareholders. But the implication here is that the debt has been used to retire equity (the operating cash flow has not changed, only how the assets are financed) there are fewer shares over which to distribute the income.

Unlevered

($)

Levered

($)

Value of equity 500.00 370.00

Value of debt 0.00 200.00

Value of firm 500.00 570.00

EBIT 153.85 153.85

Interest (10%) 0.00 -20.00

Taxable income 153.85 133.85

Tax (35%) -53.85 -46.85

Net income 100.00 87.00

KE 0.2000 0.2351

%51.23370$

$87

equity of value

incomeNet K LE, ===

Example

1. Alpha is an unlevered firm in which shareholders require a return of 15% after-tax. Alpha is valued at $100,000 and corporate taxes are 40%.

1. What are the perpetual earnings before interest and taxes in Alpha?

2. What is the value of Alpha if it issues $80,000 in perpetual debt at 10% interest?

3. What return will shareholders require in Alpha after it becomes levered?

4. What is the weighted average cost of capital in Alpha if it is unlevered?

5. What is the weighted average cost of capital in Alpha after it issues the debt?

Unlevered Levered

MV Equity

MV Debt

MV Firm

EBIT

Interest at 10%

EBT

Tax at 40%

NOI

RE

( )

( )

%98.10

000,510$

000,100$30.0108.0

000,510$

000,410$1229.0

V

Dtc1R

V

ERWACC DE

=

−+=

−+=

Question

Beta Ltd is an unlevered firm whose net cash flows are constant in perpetuity.

What is the after tax return Beta's shareholders require if Beta is valued at $480 ,000 with annual net cash flows before tax of $80,000, when the corporate tax rate is 30%?

Beta has decided to issue $100,000 in perpetual debt at 10% interest. What will be the debt adjusted value of Beta after it issues the new debt?

What return will shareholders require in Beta after it becomes levered?

What is Beta's weighted average cost of capital before the issue of debt?

What is Beta's weighted average cost of capital following the issue of debt?

where: KE,L = cost of equity for levered firm

KE,U = cost of equity for unlevered firm

KD = cost of debt

T = Tax rate

)K(KEquity

DebtKK DUE,UE,LE, −+=

T)-)(1K(KEquity

DebtKK DUE,UE,LE, −+=

Before Tax

After Tax

Alpha and Omega are identical firms in every way except Alpha has debt in its capital structure. Both firms have earnings before interest and tax (EBIT) of $450,000 and a tax rate of 30%.

i. The market value of Alpha’s debt is $300,000 issued at a cost of 12%. The required rate of return on its equity is 18%. What is the market value of its equity?

ii. What is the market value of Alpha?

iii. As Omega has no debt in its capital structure (unlevered), what is the market value of Omega?

iv. What is the required rate of return on Omega’s equity?