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 CurrentProposed Assets$20,000$20,000 Debt$0$8,000 Equity$20,000$12,000 Debt/Equity Interest raten/a8% Shares 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 Interest000 Net income$1,000$2,000$3,000 EPS$2.50$5.00$7.50 ROA5%10%15% ROE5%10%15%

EPS and ROE under Proposed Capital Structure Shares Outstanding = 240 Bust Normal Boom EBIT$1,000$2,000$3,000 Interest Net income$360$1,360$2,360 EPS$1.50$5.67$9.83 ROA5%10%15% ROE3%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 =  EPS = 4 per share, in either structure

Financial Leverage and EPS (2.00) ,0002,0003,000 EBIT EPS Debt 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 NormalBoom 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 = = Boom NormalBust 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: V L = V U  P2: Leverage increases the risk and return to stockholders (formula to follow)

Proposition II of M-M  r B is the interest rate  r s is the return on (levered) equity r 0 is the return on unlevered equity  B is value of debt  S L is value of levered equity  r s = r 0 + (B / S L ) (r 0 - r B )

Quick derivation of MM II  Uses MM I. Value unchanged.  Uses cash flow constraint.

ValueRandom cash flow Aa Bb V a+b a+b

V a+b = A + B No arbitrage pricing. Suppose V a+b not equal to A + B. Suppose V a+b > A + B. The potential arbitrage is to buy a and b separately and then sell a+b as a unit. Gain = V a+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

ValueRandom cash flow SharesSLSL sLsL BondsBb Unlevered firmSUSU s U = s L + b For instance, capital structure Conclusion: S U = S L + B

Problem: market rate of return on levered shares  Increased risk of levered shares.  Solution using definition of rates of return and MM I.

MM I Cash flows

MM I Expected cash flows (*)

Weighted average cost of capital  A reorganization of MM 2 with no taxes.  Go back to equation (*) in the derivation, divide by S L + B

MM Proposition II no tax Debt-to-equity ratio (B/S) Cost of capital: r (%). r0r0 rSrS r WACC rBrB

Exam review  What is the weighted average cost of capital?

Answer  Give the definitions and the formula.  r B = bond rate  r S = expected return on shares  B = market value of bonds  S = market value of shares  T C = corporate tax rate

Conclusion  WACC = (S/(S+B))r S + (B/(S+B))(1-T C )r B