review: risk, return, capital structure valuation fin 615 winter a 2005 ross school of business...
TRANSCRIPT
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
Princeton Spring 2004 Sugato Bhattacharyya
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)
Princeton Spring 2004 Sugato Bhattacharyya
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
Princeton Spring 2004 Sugato Bhattacharyya
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%
Princeton Spring 2004 Sugato Bhattacharyya
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
Princeton Spring 2004 Sugato Bhattacharyya
Schematically..
# of Securitiesin Portfolio
Undiversifiable Risk
1 15
1,00030
Risk ofPortfolio
Princeton Spring 2004 Sugato Bhattacharyya
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
Princeton Spring 2004 Sugato Bhattacharyya
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.
Princeton Spring 2004 Sugato Bhattacharyya
CAPM contd
2m
miim2m
mii
r,rovC
The beta gives a measure of how sensitive the stock price is to economy-wide factors.
Princeton Spring 2004 Sugato Bhattacharyya
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 ~
Princeton Spring 2004 Sugato Bhattacharyya
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
Princeton Spring 2004 Sugato Bhattacharyya
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
Princeton Spring 2004 Sugato Bhattacharyya
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
Princeton Spring 2004 Sugato Bhattacharyya
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?
Princeton Spring 2004 Sugato Bhattacharyya
Definitions of Means
Arithmetic Mean of Returns:
Geometric Mean of Returns
N
iirN
r1
1
1)1(
1
1
NN
iirr
Princeton Spring 2004 Sugato Bhattacharyya
Playing with Equations
fmif
10
fmif0
01
fmifi
r)(r1
)(
r)(r)(
r)(r)(
rE
PEP
rEP
PPE
rErE
Princeton Spring 2004 Sugato Bhattacharyya
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
Princeton Spring 2004 Sugato Bhattacharyya
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)
Princeton Spring 2004 Sugato Bhattacharyya
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
Princeton Spring 2004 Sugato Bhattacharyya
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
Princeton Spring 2004 Sugato Bhattacharyya
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
Princeton Spring 2004 Sugato Bhattacharyya
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.
Princeton Spring 2004 Sugato Bhattacharyya
In perfect capital markets,
capital structure is irrelevant to firm value
VL = VU
Debtlevel
Leveraged Firm value, VL
VU VL
Modigliani-Miller: Proposition I
Princeton Spring 2004 Sugato Bhattacharyya
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
Princeton Spring 2004 Sugato Bhattacharyya
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.
Princeton Spring 2004 Sugato Bhattacharyya
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.
Princeton Spring 2004 Sugato Bhattacharyya
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
Princeton Spring 2004 Sugato Bhattacharyya
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)
Princeton Spring 2004 Sugato Bhattacharyya
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
Princeton Spring 2004 Sugato Bhattacharyya
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
Princeton Spring 2004 Sugato Bhattacharyya
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
Princeton Spring 2004 Sugato Bhattacharyya
M&M Proposition II: Graphically
Rate of return (%)
EL
rA WACC
DLrf
rE
rD
Debt is riskyDebt is not risky
Princeton Spring 2004 Sugato Bhattacharyya
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
Princeton Spring 2004 Sugato Bhattacharyya
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
Princeton Spring 2004 Sugato Bhattacharyya
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”
Princeton Spring 2004 Sugato Bhattacharyya
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
Princeton Spring 2004 Sugato Bhattacharyya
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
Princeton Spring 2004 Sugato Bhattacharyya
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
Princeton Spring 2004 Sugato Bhattacharyya
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.
Princeton Spring 2004 Sugato Bhattacharyya
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
Princeton Spring 2004 Sugato Bhattacharyya
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(
Princeton Spring 2004 Sugato Bhattacharyya
Value of Levered Firm contd.
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(
Princeton Spring 2004 Sugato Bhattacharyya
Value of Levered Firm contd.
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(
Princeton Spring 2004 Sugato Bhattacharyya
Value of Levered Firm contd.
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
Princeton Spring 2004 Sugato Bhattacharyya
Value of Levered Firm contd.
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
Princeton Spring 2004 Sugato Bhattacharyya
Value of Levered Firm contd.
Thus, we have established the following relationship
Value of a Levered Firm
= Value of the Unlevered Firm + PV of Interest Tax Shields
Princeton Spring 2004 Sugato Bhattacharyya
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
Princeton Spring 2004 Sugato Bhattacharyya
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
Princeton Spring 2004 Sugato Bhattacharyya
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.
Princeton Spring 2004 Sugato Bhattacharyya
Leverage and Personal Taxes
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
Princeton Spring 2004 Sugato Bhattacharyya
Leverage and Personal Taxes
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
Princeton Spring 2004 Sugato Bhattacharyya
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?
Princeton Spring 2004 Sugato Bhattacharyya
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?
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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
Princeton Spring 2004 Sugato Bhattacharyya
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.
Princeton Spring 2004 Sugato Bhattacharyya
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
Princeton Spring 2004 Sugato Bhattacharyya
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”
Princeton Spring 2004 Sugato Bhattacharyya
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
Princeton Spring 2004 Sugato Bhattacharyya
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
Princeton Spring 2004 Sugato Bhattacharyya
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
Princeton Spring 2004 Sugato Bhattacharyya
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?
Princeton Spring 2004 Sugato Bhattacharyya
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
Princeton Spring 2004 Sugato Bhattacharyya
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?
Princeton Spring 2004 Sugato Bhattacharyya
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
Princeton Spring 2004 Sugato Bhattacharyya
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?
Princeton Spring 2004 Sugato Bhattacharyya
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?
Princeton Spring 2004 Sugato Bhattacharyya
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