AFM 371 Winter 2008Chapter 16 - Capital Structure: Basic Concepts

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Outline

Background

Capital Structure in Perfect Capital Markets

Examples

Leverage and Shareholder Returns

Corporate Taxes

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Background

capital structure is the firm’s mix of financing instrumentswe will consider a highly simplified context with only straightdebt and common shareslet B denote the market value of the firm’s debt and let Sdenote the market value of the firm’s equityfirm value V = B + Sthe pie:

B

S

two questions:

1. What happens to the cost of various sources of funds if thefirm changes its capital structure?

2. Is there an optimal capital structure?

Background 3 / 24

Cost of Capital Review

the cost of equity rS is the expected return on the firm’scommon shares

in the CAPM rS = rf + β [E (rM)− rf ]

note that this return can be in the form of dividends, capitalgains, or both

the cost of debt rB is the expected return on the firm’s debt,i.e. the rate of interest paid

the weighted average cost of capital is given by

rWACC =S

B + S× rS +

B

B + S× rB

note that we are ignoring (for now) the tax deductibility ofinterest payments

read over chapters 11 and 13 to review these concepts

Background 4 / 24

The Objective of Management

since management is (in principle) controlled by theshareholders, we normally assume that management seeks tomaximize the value of the firm’s equity

however, as long as there are no costs of bankruptcy,maximizing equity value S is equivalent to maximizing firmvalue V

example:

a firm has 10,000 shares; share price is $25debt has a market value of $100,000firm value V = B + S = $100,000 + $25× $10,000 = $350,000suppose the firm borrows another $50,000 and pays itimmediately as a special dividendthe value of debt increases to $150,000, but how areshareholders affected?

Background 5 / 24

The Objective of Management Cont’d

consider three possible outcomes:

V ↑ $380,000 V → $350,000 V ↓ $320,000S $230,000 $200,000 $170,000Dividend $50,000 $50,000 $50,000Capital gain/loss -$20,000 -$50,000 -$80,000Net gain/loss $30,000 $0 -$30,000

the change in capital structure benefits the shareholders if andonly if the value of the firm increases

managers should choose the capital structure that they believewill have the highest firm value (i.e. make the pie as big aspossible)

Background 6 / 24

Perfect Capital Markets

we will begin by assuming perfect capital markets:

information is free and available to everyone on an equal basisno transaction costsno taxesno costs of bankruptcy

we will also assume (for simplicity) that all cash flows areperpetuities (just to make the calculations easier)

two famous names: Modigliani and Miller (MM)

MM Proposition I (No Taxes): The market value of any firmis independent of its capital structure

let VU be the value of an “unlevered” firm (i.e. all equityfinancing) and let VL be the value of an otherwise identical“levered” firm (i.e. some debt financing)

MM Proposition I (No Taxes) then simply says VU = VL

Capital Structure in Perfect Capital Markets 7 / 24

Proof of MM Proposition I (No Taxes)

let X be the identical income stream generated by each firm(i.e. U and L); VU = SU be the value of the unlevered firm;and VL = SL + BL be the value of the levered firm

consider an investor who owns some fraction α (e.g. 5%) ofthe shares of U:

Investment Returnα of U’s equity αSU = αVU αX

this investor can get the same return by investing in L:

Investment Returnα of L’s equity αSL = α(VL − BL) α(X − rBL)α of L’s bonds αBL αrBL

αVL αX

if VU > VL the investor would not buy any shares in U sincethe same return is available on a smaller investment in L

Capital Structure in Perfect Capital Markets 8 / 24

Proof of MM Proposition I (No Taxes) Cont’d

consider an investor who owns α of L’s equity:

Investment Returnα of L’s equity αSL = α(VL − BL) α(X − rBL)

this investor can get the same return by investing in U andborrowing on personal account:

Investment Returnα of U’s equity αSU = αVU αXBorrow αBL -αBL -αrBL

α(VU − BL) α(X − rBL)

if VL > VU the investor would not buy any shares in L sincethe same return is available on a smaller investment in U

we have shown that no-one would buy shares in U if VU > VL

and that no-one would buy shares in L if VL > VU

therefore VU = VL is the only solution consistent with marketequilibrium

Capital Structure in Perfect Capital Markets 9 / 24

Some Observations

MM’s result is based on a no-arbitrage argument: if twoinvestments give the same future returns, they must cost thesame today

a key (implicit) assumption is that individuals can borrow ascheaply as corporations

one way to do this is through buying stock on marginwith a margin purchase, the broker lends the investor a portionof the cost (e.g. to buy $10,000 of stock on 40% margin, putup $6,000 of your own money and borrow $4,000 from thebroker)since the broker holds the stock as collateral, brokers generallycharge relatively low rates of interestfirms, on the other hand, often borrow using illiquid assets ascollateral (and get charged higher rates)

the same arguments apply to more complicated capitalstructures

the same arguments apply if cash flows are not perpetuities

Capital Structure in Perfect Capital Markets 10 / 24

Example #1

given VU = $100M, X = $10M, r = 5%, BL = $50M, thenMM Proposition I ⇒ SL = $50Msuppose SL = $40M:

suppose SL = $60M:

Examples 11 / 24

Example #2

suppose a firm has the following all equity capital structure:

Original Capital Structure: All EquityNumber of shares 1,000Share price $10Market value of shares $10,000

operating income differs across economic states as follows:

ExpectedState 1 2 3 4 5 ValueProbability 0.20 0.20 0.20 0.20 0.20Operating income $500 $750 $1,500 $2,250 $2,500 $1,500EPS $0.50 $0.75 $1.50 $2.25 $2.50 $1.50ROE 5% 7.5% 15% 22.5% 25% 15%

Examples 12 / 24

Example #2 Cont’d

consider an alternative capital structure with 50% debtfinancing:

Alternative Capital Structure: 50% DebtNumber of shares 500Share price $10Market value of shares $5,000Market value of debt $5,000

assuming an interest rate of 10%:

ExpectedState 1 2 3 4 5 ValueProbability 0.20 0.20 0.20 0.20 0.20Operating income $500 $750 $1,500 $2,250 $2,500 $1,500Interest $500 $500 $500 $500 $500 $500Equity earnings $0 $250 $1,000 $1,750 $2,000 $1,000EPS $0.00 $0.50 $2.00 $3.50 $4.00 $2.00ROE 0% 5% 20% 35% 40% 20%

Examples 13 / 24

Example #2 Cont’d

graphing EPS vs. operating income:

0

0.00

500 750 1500 2250 2500

0.50

0.75

1.50

2.00

2.25

2.50

3.50

4.00

EPS

Operating income

50% debt

All equity

Examples 14 / 24

Example #2 Cont’d

since the expected ROE is higher under 50% debt, should thefirm switch to this capital structure?not only have expected returns increased, but so has riskthe MM argument is that is doesn’t matter, because investorscan effectively create the payoffs from the alternative capitalstructure themselves (“homemade leverage”)assume the firm stays with the original all equity capitalstructure but a particular investor prefers the alternativesuppose the investor buys 10 shares (at a cost of $100), butfinances this by investing $50 and borrowing $50:

EPS $0.50 $0.75 $1.50 $2.25 $2.50Earnings (10 shares) $5.00 $7.50 $15.00 $22.50 $25.00Interest (10% on $50) -$5.00 -$5.00 -$5.00 -$5.00 -$5.00Dollar returns $0.00 $2.50 $10.00 $17.50 $20.00Percentage returns 0% 5% 20% 35% 40%(on $50 invested)

Examples 15 / 24

How Does Leverage Affect Shareholder Returns?

note that from the previous example that leverage increasesthe expected returns and risk for equity, even if there is nochance of bankruptcyrecall the weighted average cost of capital formula

rWACC =S

B + S× rS +

B

B + S× rB

MM Proposition I implies that the weighted average cost ofcapital is constant (i.e. independent of capital structure)in the previous example:

Leverage and Shareholder Returns 16 / 24

MM Proposition II (No Taxes)

define

r0 = cost of capital for all equity firm

=expected earnings for all equity firm

value of equity

since r0 = rWACC, we have

r0 =S

B + S× rS +

B

B + S× rB

this can be rearranged to yield MM Proposition II (No Taxes):

rS = r0 +B

S(r0 − rB)

Leverage and Shareholder Returns 17 / 24

MM Proposition II (No Taxes) Cont’d

graphing MM Proposition II:

B/S

Cos

tof

capital

(%)

r0

rWACC

rB

rS

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Corporate Taxes

so far we have ignored corporate taxes, but the taxdeductibility of interest payments gives a big advantage todebt financing

let TC be the corporate tax rate, and recall from chapter 13that

rWACC =S

B + S× rS +

B

B + S× rB × (1− TC )

a levered firm makes interest payments of rB × B, andtherefore has its corporate taxes reducted by rB × B × TC

(the tax shield from debt)

in an all equity firm, the after tax cash flow to theshareholders is EBIT× (1− TC )

in a levered firm, the total after tax cash flow to theshareholders and bondholders is EBIT× (1− TC ) + TC rBB

Corporate Taxes 19 / 24

MM Proposition I (Corporate Taxes)

the value of an all equity (unlevered) firm is the present valueof the after tax cash flow to the shareholders

VU =EBIT× (1− TC )

r0

MM Proposition I (Corporate Taxes):

VL = VU + PV(debt tax shield)

assuming the amount borrowed is constant over time, we cancalculate the present value of the debt tax shield bydiscounting the cash flow at the rate of interest to get:

VL =EBIT× (1− TC )

r0+

TC rBB

rB= VU + TCB

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Example #3

an investment project costs $100,000 and produces EBIT of$20,000 per year forever, TC = 36%.

financing choices: U: all equity; L: $40,000 debt, rB = 5%,r0 = 10%

U LEBIT $20,000 $20,000Interest 0 2,000EBT 20,000 18,000Tax 7,200 6,480Net income 12,800 11,520Total cash paid to investors $12,800 $13,520

suppose the firm chooses U and issues 10,000 shares. It wouldhave the following market value balance sheet:

Physical assets $128,000 Equity $128,000(10,000 shares)

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Example #3 Cont’d

now the firm announces it will switch to L by issuing $40,000of debt and repurchasing shares

in an efficient market, the stock price will react immediatelyto this announcement

the firm value will rise by the present value of the tax shield,so the market value balance sheet becomes

Physical assets $128,000 Equity(10,000 shares)

the firm then issues the debt and carries out the repurchase:

Physical assets $128,000 Debt $40,000Equity

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MM Proposition II (Corporate Taxes)

how does leverage affect rS and rWACC?

MM Proposition II (Corporate Taxes):

rS = r0 +B

S× (1− TC )× (r0 − rB)

Corporate Taxes 23 / 24

MM Proposition II (Corporate Taxes) Cont’d

graphing MM Proposition II:

B/S

Cos

tof

capital

(%)

r0rWACC = (S/V )rS + (B/V )(1− TC )rB

rB

rS = r0 + (B/S)(r0 − rB)

rS − r0 + (B/S)(1− TC )(r0 − rB)

Corporate Taxes 24 / 24