review: risk, return, capital structure valuation fin 615 winter a 2005 ross school of business...

Review:Risk,

Return,Capital

Structure

Valuation

Fin 615

Winter A 2005

Ross School of BusinessUniversity of Michigan

© Sugato Bhattacharyya. Please do not distribute without written permission.

Princeton Spring 2004 Sugato Bhattacharyya

Recap

Up to now, we have primarily dealt with the case of certain cash flows

But, we have started talking about uncertain cash flows and risk

From basic Micro principles, we have seen that an expected payoff-variance representation may characterize risk and risk-return trade-offs


Opportunity Cost

Certainty: Best alternative matched on maturity period – explicitly or implicitly

Our Aim: Best alternative matched on maturity period AND riskiness

To do that, we have to define Risk Measure(s) properly AND figure out the Market Price of Risk (expected return per unit of risk-measure)


Mean-Variance

Higher Mean is Better Lower Variance is Better Returns can be used as measures Investors are non-satiated Investors are risk-averse

Investors must expect higher returns on a portfolio with higher variance


Evidence

Portfolio Average Return

Standard Deviation

Small Stocks 17.5% 35.3%

Common Stocks 12.4% 20.8%

Corporate Bonds 5.7% 8.6%

Government Bonds

5.1% 8.5%

T-Bills 3.9% 3.4%


Diversification

The empirical evidence shown pertained to portfolios. What about individual securities?

Principle: Rational, risk-averse investors will diversify to reduce risk

Diversification serves to “wipe out” risk, provided component securities in portfolio don’t “move together” much


Schematically..

# of Securitiesin Portfolio

Undiversifiable Risk

1 15

1,00030

Risk ofPortfolio


Implication

Because investors dislike variance, they diversify

Because they diversify, variance of individual securities is not the relevant measure of risk for them

What matters is how much variance each security contributes to the whole portfolio


CAPM

With symmetric information, everybody should hold the same risky portfolio

the Market Portfolio Therefore, the relevant measure of risk

is the covariance with the market portfolio.

This measure, standardized by the variance of the market portfolio, is denoted by beta.


CAPM contd

2m

miim2m

mii

r,rovC

The beta gives a measure of how sensitive the stock price is to economy-wide factors.


The Market Model

Alternative Interpretation:

If the market portfolio can represent the economy-wide risk, then we can use it to write down the Market Model:

i i i m i~r ~r ~


Firm-specific Risk

The larger is the more important is firm-specific risk in the actual realized price of the security.

Total risk of a security may be decomposed into “priced” and “non-priced” risk as

2

2222 mii


Systematic vs. Idiosyncratic

Two stocks with same total risk may have very different levels of priced risk

Two stocks with same level of priced risk may have very different levels of total risk


CAPM

The CAPM shows that, for a properly defined risk measure, the relationship between risk and (expected) return is linear:

fmifi rrrr

The relationship is also called the Security Market Line


Implementing the CAPM

What to take as the Market Portfolio?• A diversified stock portfolio?

What to take as the Risk-free Rate?• How to account for term-structure?

How to get Expected Return on Market Portfolio?• Use historical record? If so, how long?• Should one use Arithmetic or Geometric

Mean?


Definitions of Means

Arithmetic Mean of Returns:

Geometric Mean of Returns

N

iirN

r1

1

1)1(

1

1

NN

iirr


Playing with Equations

fmif

10

fmif0

01

fmifi

r)(r1

)(

r)(r)(

r)(r)(

rE

PEP

rEP

PPE

rErE


Playing with Equations - 2

f

fm21

1

0

fm21

0f

0

01

fm20

01

f0

01

fm2f0

01

fmifi

r1

r)()~,

~(

)(

r)()~,

~(1

r)(

r)(

)~,~

(

r)(

r)(),(

r)(

r)(r)(

rErPCov

PE

P

rErPCov

PP

PPE

rE

rPPP

Cov

P

PPE

rErrCov

P

PPE

rErE

m

m

m

m

m

m

m

mi

CEQ


Introduction

A firm's Capital Structure refers to the mix of the firm’s liabilities.

We will start with the most basic question of capital structure: the mix between debt and equity.

General lessons will apply to more complex capital structures.

To say a firm is Financially Leveraged just means that the firm uses debt in its capital structure. (The British term is Gearing)


A Levered Firm

Three concepts:• Value of the Firm (Enterprise Value)• Value of Equity• Value of Debt

=

Firm ValueEquity Value Debt Value

D + E V

Note: A “$500 M Firm” does not refer to any of these


Leverage: Classical View

Debt is senior to Equity. Hence it is less risky (less sensitive to

shocks to the firm’s prospects) Hence, the expected return of debt is

less than that of equity Conclusion: Issuing cheaper debt

should increase the value of the Firm Caveat: Issuing too much debt makes

it likely for the firm to default


Leverage: Classical View

Thus, according the classical view, there should be some kind of optimal capital structure which trades off• The cheaper cost of debt with• The costs associated with default

This classical view is often seen in the pronouncements of less financially sophisticated executives


Benchmark Scenario

Perfect Capital Markets

1. no taxes;2. no bankruptcy costs;3. no transaction costs (buying, selling or issuing

securities) or bid-ask spreads;4. equal access to the markets (symmetric information,

size is irrelevant, same borrowing and lending rates to all, etc..);

5. Competitive security markets. Firms are price takers.


In perfect capital markets,

capital structure is irrelevant to firm value

VL = VU

Debtlevel

Leveraged Firm value, VL

VU VL

Modigliani-Miller: Proposition I


The Pizza Hut Intuition:

Since production decisions are fixed, the total cash flow is unchanged; Capital Structures are merely different ways of splitting the same total.

Firm Value Equity Value Debt Value Equity Value Debt Value

$100

$40 $6

0$80

$20

M&M Proposition I


The Portfolio Argument:

Owning 10% shares in unlevered firm gives you same cash flows as owning 10% of debt and 10% of equity in levered firm with same gross cash flows.

M&M Proposition I

0.1 x Profit 0.1 x Interest+ 0.1 x (Profit – Interest)= 0.1 x Profit

vs.


The Home-made Leverage Argument:

All players face the same interest rate Holding 10% of equity in levered firm gives you

same cash flows as borrowing 10% of its debt and buying 10% of equity of the unlevered firm

M&M Proposition I

0.1 x (Profit – Interest)- 0.1 x Interest+ 0.1 x Profit = 0.1 x Profit

vs.


Value of the Firm

For a perpetual firm with constant expected cash flows, Value must be the constant expected cash flows of the firm divided by some required rate of return:

where E(Ra) is the required (expected) rate of

return on the assets of the firm.

)aE(R

E(X)

UV

LV


Debt and Cost of Capital

Since VL = VU, it must be that E(Ra) remains constant as the capital structure changes.

But, the required rate of return to holding the levered firm’s securities must be:

where E(Rd) is the required rate of return on debt and E(RL

e) is the required rate of return on the levered equity of the firm.

)LeE(R

DLELE

)dE(RDLE

D

Weighted AverageCost of Capital

(WACC)


Debt and Cost of Capital

WACC

=

= )LeE(R

DLELE

)dE(RDLE

D

)aE(R

The Weighted Average Cost of Capitalis invariant to changes in Capital Structure


Modigliani-Miller Proposition II

If WACC doesn’t change, what does?

Proposition II (no taxes)

The expected rate of return on equity of a levered firm increases in proportion to the debt-equity ratio (D/E), expressed in market values:

)dE(R)aE(R

LE

D)aE(R)

LeE(R


Proof of Prop II

)d

E(R-)a

E(RL

E

D)

aE(R

)d

E(RL

E

D-

LE

D)

aE(R)

aE(R)L

eE(R

)d

E(RL

E

D-

LE

DL

E)

aE(R)L

eE(R

)d

E(RD

LE

D-)

aE(R)L

eE(R

DL

EL

E

)Le

E(RD

LE

LE

)d

E(RD

LE

D)

aE(R


M&M Proposition II: Graphically

Rate of return (%)

EL

rA WACC

DLrf

rE

rD

Debt is riskyDebt is not risky


When we use the SML to estimate the systematic risk of a stock, the estimated beta reflects not only the risk of the assets in the firm (its business risk), but also the financial risk (or the risk associated with the use of debt by the firm).

Thus, the risk of equity consists of both business risk and financial risk.

Business Risk and Financial Risk


The Business Risk of a Firm is, presumably, inherent to its type of business.

The Financial Risk of the Firm’s Equity is, ultimately, a decision variable at the management’s discretion.

The formula in MM Prop II allows us to disentangle these two sources of risk.

Business Risk and Financial Risk


Bottom Line

Should the firm issue “Cheaper Debt”?

Issuing Cheaper Debt does increase the Expected Cash Flows to Equity (and EPS)

But it also increases its Riskiness

MM Prop I says “it’s all a wash”


Possible Departures

In the real-world, we have corporate taxes; interest on debt is tax advantaged

In the real-world, we have personal taxation of income; income from holding debt is tax disadvantaged

In the real-world, costs of bankruptcy are not zero

In the real-world, managers may not maximize value of the firm

In the real-world, investment policy may be impossible to decouple from capital structure


Corporate Taxes

If interest payments are tax-advantaged, and debt and equity are both on the SML, then debt is, indeed, “cheaper” from the firm’s point of view

This may give rise to a preference for debt in capital structure


Intuition # 1

As debt increases, the government share of the given pie decreases. The figures below assume pre-tax value of $100;

thus, with tc = 34%, VU = $66 (first figure on left).

Shareholders Government

Debtholders

$34

$66

Shareholders Debtholders

Government

$50

$17$33

Shareholders Debtholders

Government

$80

$7$13

VU = $66 VL = $50 + $33 = $83

VL = $80 + $13.2 = $93.2


Intuition # 2

Investors cannot get a tax break on personal borrowing and, therefore, are willing to pay a premium for firms to take leverage on their behalf.

Comparable to the growth of auto leasing after 1986 tax reform act when non-mortgage interest deductions were eliminated.


Value of Levered Firm

Consider an infinitely lived firm with a particular investment policy

Each year, its before tax and interest cash flows are denoted by with a mean value of

We will sometimes call this figure Earnings before Interest and Taxes (EBIT) and assume away, for now, issues of Depreciation, Changes in Working Capital, Investment etc

X~

X


Value of Levered Firm contd.

If this firm is financed entirely by equity, its expected after-tax cash flows each period would be

What would be the value today of this firm? We know that we can use two lessons:

• The perpetuity valuation formula• The opportunity cost argument

Xt)1(



Utilizing these lessons, we can write

Where value is calculated at time 0 and the discount rate corresponds to the expected return associated with an investment of equal level of riskiness

au r

XtV

)1(



Now, assume that this firm has, instead debt of Face Value F and coupon rate c. Also assume that the interest on the debt is always fully deductible for taxes (that is, there’s enough cash flows always)

Then, value of its equity can be written as:

er

cFXtE

))(1(



Also, the value of its bonds can be written as:

Finally, the total cash flows to all security holders can be written as:

What is the value of this set of perpetual cash flows?

tcFXt

cFcFXtTCF

)1(

))(1(

dr

cFD



To get the value, remember that each set of cash flows has to be discounted at its own appropriate risk-adjusted discount rate

Clearly, the discount rate for the first set is the one we used for the all-equity firm, while the discount rate for the second set is that for debt cash flows

Then, discounting and adding values would give us the following relationship

tDVV UL



Thus, we have established the following relationship

Value of a Levered Firm

= Value of the Unlevered Firm + PV of Interest Tax Shields


Lesson

With tax deductibility of interest (and our various assumptions up to this point), it is always advantageous to have debt

So, how much debt maximizes the value of the firm?

Answer: As much as the firm’s cash flows can support for tax deductibility


Reality Check

But, we don’t see most firms borrowing to the hilt. And we do see firms paying considerable federal taxes.

So, what gives? Maybe

• Personal tax disadvantages of debt negate the corporate tax advantage

• Maybe costs associated with default act as a brake against too much leverage


Leverage and Personal Taxes

Suppose income from debt is taxed at a rate tp, the ordinary income rate and that from equity is taxed at a rate tpE

Note that, due to differential rates of taxation, the second rate is likely to be smaller than the first rate. That is, debt is tax disadvantaged from the personal taxes point of view.



Then, total cash flow to security holders is:

)1(

)1)(1(1)1()1)(1(

)1)(1()1()1)(1(

)1())(1)(1(

p

pEppE

pEppE

ppE

t

ttcFtXtt

tttcFXtt

cFtcFXttTCF

CF from Unlevered Firm CF from Debt



Translating into Values, we now have:

Bottom Line: With reasonable parameters, the tax advantage to debt stays, but is reduced in magnitude

BM estimate marginal value to be to be 13%, about a third of the value we’d get without considering personal taxes.

Dt

ttVV

p

pEUL

)1(

)1)(1(1


What Limits Leverage?

Companies do not seem to want to borrow according to the theories we have developed up to now.

In fact, there are corporations like Microsoft and Pfizer who do not borrow at all (essentially)

Are all corporations leaving money on the table or are there costs to borrowing that we haven’t dealt with?


Bankruptcy

Classical View: Borrowing too much risks bankruptcy; therefore limit borrowing

But if default brings about either restructuring or liquidation, only ownership pattern changes; value doesn’t

So, why should prospect of Bankruptcy matter in leverage decisions?


Bankruptcy Costs

There are costs associated with being bankrupt that are dissipative

Direct Bankruptcy Costs: Payments to third parties

- Lawyers

- Consultants

Dead-weight costs

- "wasted" time and effort


Bankruptcy Costs

If there are significant costs associated with going bankrupt, then the expected costs go up with leverage

When firms are making their leverage decision, they should take into account the increase in expected bankruptcy costs as leverage increases

Then, we have a tradeoff.


Tax Benefits vs. Expected Costs of Leverage

Debt

Mar

ket V

alue

of

The

Fir

m

Value ofunlevered

firm

PV of interesttax shields

Expected bankruptcy costs

Value of levered firm

Optimal amount of debt

Maximum value of firm


Direct Costs of Bankruptcy

Estimates are of the order of 3% of total book value of assets before entering bankruptcy

Comparing with the tax benefits of debt, these don’t seem high

Especially when the probability of bankruptcy is taken into account

Conclusion: There must be other costs associated with “Financial Distress”


Costs of Financial Distress

Indirect Bankruptcy Costs impaired ability to conduct business

suppliers may demand cash payment

customers may be cautious

Value may be sacrificed by a firm about to default. This dissipation of value would be anticipated and hurt firm value when debt is increased


Agency Costs

When we incorporate the fact that managers act in the interest of stockholders, we encounter situations in which such interest may conflict with firm value maximization

Such situations may arise when a firm is highly leveraged


Risk Shifting

Suppose that you have debt due of $100 tomorrow but your assets are worth $50 today

Assume that default triggers liquidation and the proceeds are distributed by APR

Ignore, for simplicity, the time value of money, direct costs of bankruptcy and risk aversion


Risk Shifting

In this situation, if default occurs, the stockholders anticipate getting $0

Suppose they can take the firm’s assets, liquidate and get $50 today with which they go to Las Vegas and take the following gamble:

-$50

$200

$0

0.1

0.9

Expected Value = $ 20

Will they play this game?


Risk Shifting Contd.

Clearly, they have nothing to lose. Thus, they are willing to take on a

negative NPV project, provided it is risky enough (total risk)

If this is anticipated by debt holders, then they will charge more for debt upfront if the firm attempts to lever up

This will reduce the attractiveness of debt and act as a brake


Underinvestment

Now, consider the same situation as before and say a project opportunity arises that involves an investment of $10 that will, for sure, give a payback of $30.

Clearly, this is positive NPV Will shareholders be willing to

contribute to take on this investment?


Underinvestment

If they do, they are out of $10 but are sure of not getting back anything – all the money goes to debtholders

Thus, they pass up on positive NPV projects if they are not risky enough

Such opportunity costs would also be anticipated by debtholders ex ante and limit the attractiveness of leverage


More Agency Costs of Debt

Would you fly an airline which is in financial distress? Why not?

Would you buy a car from a company that is likely to go bankrupt?

Would you put your money in a bank that is about to go under if it promises to pay you a high interest rate?


Agency Advantage of Debt?

Are there any advantages to debt beside tax deductibility?

Debt may reduce overinvestment incentives on the part of a manager who is not acting in the shareholder interest

High debt obligations may limit wasteful investment.

LBOs?


Commitment Advantage of Debt

Consider a steel plant with high sunk costs and low variable costs

If equity financed, its subject to hold-up by unionized workers who might bargain for higher wages once investment is sunk

Debt may act as a commitment device to limit such bargaining power

review: risk, return, capital structure valuation fin 615 winter a 2005 ross school of business...

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