Capital Structure

Basic concepts: no taxes

Chapter 15 Capital Structure: Basic Concepts

Capital-structure and pie theory

No-arbitrage pricing.

Example: shares for debt

Value

Required return on the levered firm.

Financial Leverage, EPS, and ROE

Current Proposed

Assets $20,000 $20,000

Debt $0 $8,000

Equity $20,000 $12,000

Debt/Equity 0.00 0.67

Interest rate n/a 8%

Shares 400 240

Share price $50 $50

Comments

Straight swap of equity for debt Market prices unchanged Real asset unchanged

Financial leverage and risk

Three states: bust, normal, boom. Probabilities not explicit. Look at each state separately.

EPS, ROE, Current Structure

Shares Outstanding = 400

Bust Normal Boom

EBIT $1,000 $2,000 $3,000

Interest 0 0 0

Net income $1,000 $2,000 $3,000

EPS $2.50 $5.00 $7.50

ROA 5% 10% 15%

ROE 5% 10% 15%

EPS and ROE under Proposed Capital Structure

Shares Outstanding = 240

Bust Normal Boom

EBIT $1,000 $2,000 $3,000

Interest 640 640 640

Net income $360 $1,360 $2,360

EPS $1.50 $5.67 $9.83

ROA 5% 10% 15%

ROE 3% 11% 20%

Find the point of equal EPS

For understanding the situation, not because it is a key to anything.

Let x = EBIT Solve x/400 = (x - 640)/240 Solution x = 1600. EPS = 4 per share, in either structure

Financial Leverage and EPS

(2.00)

0.00

2.00

4.00

6.00

8.00

10.00

12.00

1,000 2,000 3,000EBIT

EP

SDebt

No Debt

Break-even Point

Modigliani-Miller (MM) Model

Perpetual Cash Flows (convenient) Firms and investors can borrow and

lend at the same rate (convenient) Only value matters No transaction costs (convenient) No taxes

Homemade is a big concept

What financial managers do in the firm…

can be duplicated by investors in the market …

if they want to. Implication: financial managers can’t

raise value by restructuring.

Homemade leverage

Instead of the firm swapping equity for debt.

The investor does it himself, by borrowing.

It works out just as well.

Borrow $8000, buy the unlevered firm for $20,000

Bust Normal Boom

Earnings $1000 $2000 $3000

Interest at 8% $640 $640 $640

Net Profits $360 $1360 $2360

ROE (on $12K) 3% 11% 20%

Same as owning the levered firm

Okay, don’t buy the whole firm

Buy 10%, forty shares for $2000. Borrow $800. Total cost $1200 Same as having 10% of the levered

firm, that is, 24 shares at $50 per share.

Homemade annihilation of leverage

Idea. Form a portfolio. Part lending… part the levered firm. Portfolio has the action of the unlevered

firm. A levered firm is a portfolio.

Buy the levered firm (240 shares) and lend 8000

Cost of Portfolio = 12000 + 8000 = 20000

Boom Normal Bust

EPS $1.50 $5.67 $9.83

Earnings $360 $1360 $2360

Interest at (8%) $640 $640 $640

Net cash flow $1000 $2000 $3000

ROE 5% 10% 15%

(Net cash flow / $2,000)

The firm is a veil

A way for shareholders to hold a portfolio.

The MM Propositions I & II (No Taxes)

P1: Value is unaffected by leverage P1: VL = VU

P2: Leverage increases the risk and return to stockholders(formula to follow)

Proposition II of M-M

rB is the interest rate

rs is the return on (levered) equity r0 is the return on unlevered equity

B is value of debt SL is value of levered equity

rs = r0 + (B / SL) (r0 - rB)

Quick derivation of MM II

Uses MM I. Value unchanged. Uses cash flow constraint.

Value Random cash flow

A a

B b

Va+b a+b

Va+b = A + B

No arbitrage pricing.

Suppose Va+b not equal to A + B.

Suppose Va+b > A + B.

The potential arbitrage is to buy a and b separately and then sell a+b as a unit.

Gain = Va+b - A – B, which is > 0.

Position a + b – (a+b) = 0 is riskless

Complete markets

Cash flows a and b must be tradable.

e.g., not gambling debts

e.g., not insurance contracts

Value Random cash flow

Shares SL sL

Bonds B b

Unlevered firm SU sU = sL + b

For instance, capital structure

Conclusion: SU= SL + B

Problem: market rate of return on levered shares

Increased risk of levered shares. Solution using definition of rates of

return and MM I.

BSS LU

bss LU

MM I

Cash flows

bsEsE LU )()(

bb

s

Ls

U

r

br

r

sEr

r

sEr

)()(

00

BrSrSr bLsU 0

BSS LU

BrSrSr BLSU 0

MM I

Expectedcash flows

BrSrBSr BLSL )(0

BrBSrSr BLLS )(0

(*)

BrBSrSr BLLS )(0

BrrSrSr BLLS )( 00

LBS S

Brrrr )( 00

Weighted average cost of capital

A reorganization of MM 2 with no taxes. Go back to equation (*) in the

derivation, divide by SL + B

MM Proposition II no tax

Debt-to-equityratio (B/S)

Cost of capital: r(%)

.r0

rS

rWACC

rB

LBS S

Brrrr )( 00

Exam review

What is the weighted average cost of capital?

Answer

Give the definitions and the formula. rB = bond rate

rS = expected return on shares

B = market value of bonds S = market value of shares TC = corporate tax rate

Conclusion

WACC =(S/(S+B))rS + (B/(S+B))(1-TC)rB