Topical Issues in Financial Economics
National Research University Higher School of Economics
Maria Shchepeleva
Department of Theoretical Economics
Lecture 1. Introduction and Course Overview
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Roadmap
▪ Course Overview and Organisational Issues
▪ Evolution of Financial Theory
▪ Basic concepts and principles of Finance
▪ Arrow-Debreu Pricing
▪ Revision
⮚ How to measure return
⮚ Present Value/Future Value
⮚ Special Cash Flows
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Course Overview
Date
Lecture
Seminar
11.01
Introduction to the Theory of Finance. Revision of the major
concepts.
18.01
Capital Budgeting & Financing Decisions
Problem Solving (annuity, perpetuity, AD, Capital Budgeting)
25.01
Payout Policy & Valuation
Problem Solving (WACC, Valuation)
01.02
General Principles of asset pricing
Problem Solving (CAPM) + essay (30 min)
08.02
Introduction to Options
Quiz (CAPM; 20 min) + 3 papers
15.02
Options Pricing
Problem Solving (Option Pricing)
22.02
Real Options
Midterm 1
01.03
Introduction to market microstructure
Problem Solving (Real Options) + 2 papers
15.03
Systemic Risk
Quiz (Options; 20 min) + 3 papers
22.03
Efficient Market Hypothesis
Midterm 2
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Grading System
Activity
Score
Presentation in class
20%
Midterm 1
25%
Midterm 2
25%
Class activity
30%
Quizzes
15%
Essay
5%
In-class problem solving
10%
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Literature
▪ Intermediate Financial Theory. Danthine J.-P., Donaldson B. 2001.
▪ Financial Decisions and Markets. Campbell J. 2018.
▪ Asset pricing. Cochrane J. H. 2005.
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Evolution of Financial Economics
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Financial Theory Evolution
PERIOD
EVENTS
FINANCIAL THEORY
The early 20th century
Movement toward corporate consolidation
Focus on capital structure, liquidity issues, preventing the company from bankruptcy
1920-1950
1929 crash
Consolidation process (M&A) intensified
Reinforced interest in capital structure
Focus on internal control procedures
1950-1960
World War II
Fear of post-war recession
Technological development (computing)
Relevance of funding raising, cash-flow management
Corporate Finance: Modigliani and Miller (1958)
Asset pricing: Markowitz (1952), Tobin (1958) Sharpe (1964)
1960-1970
1974 US stock market crash
Global Recession & oil crisis
CAPM first devised in the works of Markowitz and Tobin and further simplified by Sharpe,
Lintner and Mossin (systematic and non-systematic risk)
E.Fama Efficient Market Hypothesis
1980
1990
2000
Financial disintermediation
External debt crisis in developing countries
First Basel accord (Basel I)
Basel I Agreement
Intensification of capital flows, risk of infection
The use of mathematical models expanded
Corporate scandals: Enron, Arthur Anderson,
WorldCom
Concern with reduction of systematic risk and focus on mitigation of clearing risk and credit
risk.
Black & Sholes pricing model (complex derivative strategies for risk limitation)
Wide-spread use of options and futures-based hedging strategies
Greater importance of Corporate Governance and information transparency.
Discussion of corporate ethics as applied to finance
Behavioral Economics
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The Scope of the Theory of Finance
• Capital Budgeting
• Modern Portfolio Theory
• Financing Decisions
• Arbitrage Pricing Theory
• CAPM
• Payout Policy
Corporate
Finance
Asset
Pricing
Efficient
Market
Hypothesis
Risk
Management
& Financial
Stability
• Option Pricing
• Arrow-Debreu Pricing
• Types of financial Crises
• Causes and consequences
of financial crises
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• Macroprudential Policy
Design
8
Asset Pricing Models. Classification
Calculation of risk premium
����
�
(1 + �� + �)�
Equilibrium Approach
Arbitrage Approach
CAPM
CCAPM
APT
���� − Π
�
Calculation of distorted
probabilities
Calculation of the price of
one unit of money from
period to period
(1 + �� )
Martingale Measure
����
�
(1 + �� )
�� ∈Θ�
�( �� )CF(�� )
Arrow-Debreu Pricing
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Arrow-Debreu Pricing
9
Asset Pricing Models. Classification
▪
����
�
▪
(1+�� )
▪
Risk-bearing behaviour needs to be renumerated
▪
Discounting at a rate that is higher than the risk-free rate
▪
Correcting the expected CF to discount at the risk-free rate
▪
Distorting probabilities
▪
Decomposing CF into its state by state elements
This formula can be used when the risk does not matter (when we assume market participants risk-neutral)
����
�
(1+�� )
�� ∈Θ�
����
�
(1+ �� +�)�
���� −Π
�
(1+�� )
�( �� )CF(�� )
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Basic Principles of Finance. Introduction to the state-space model
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Unifying Principles of Finance
▪
▪
▪
Principle 1: There is no such thing as a free lunch in the financial market (The concept of Arbitrage)
Principle 2: Other things equal, individuals/agents (the Concept of Optimization)
⮚ Prefer more money to less (non-satiation);
⮚ Prefer to avoid risk (risk aversion);
⮚ Prefer money now to later (impatience).
Principle 3: Financial market prices shift to equalize supply and demand (the Concept of
Equilibrium)
▪
Principle 4: Financial markets are highly adaptive and competitive
▪
Principle 5: Risk-sharing and financial frictions are key to financial innovation
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Time and Risk: two key elements in finance
▪
The two important characteristics of Finance
⮚ time (time value of money)
⮚ risk (risk premium)
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Framework to think about assets: state space model
▪
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What does define an asset?
▪
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Matrices notation
▪
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We can combine assets to get new assets
▪
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Arrow-Debreu securities
▪
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Complete markets: every AD security exists
▪ If there are S AD securities, one for each state, then the payoff matrix of
these securities is the identity matrix
▪ In this case we can obtain any payoff by combining AD securities. Thus we
say that markets are complete
▪ AD securities do not exist in real world.
▪ Does this mean that markets are incomplete?
▪ Not necessarily. We can construct AD securities from existing assets.
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Market Imperfections
▪
Transaction costs (TCs)
⮚ Missing markets
⮚ Access cost
⮚ Trading cost/liquidity
⮚ Position/trading constraints
▪ Information asymmetry
⮚ Between a firm’s different stakeholders
⮚ Between corporate managers and the financial market
⮚ Between different market participants
▪ Taxes
⮚ Corporate taxes
⮚ Personal taxes
▪
▪
Our analysis always starts with a frictionless market as the benchmark.
Real markets have frictions, which will be considered when needed.
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Unifying Principles of Finance
▪
▪
▪
Principle 1: There is no such thing as a free lunch in the financial market (The concept of Arbitrage)
Principle 2: Other things equal, individuals/agents (the Concept of Optimization)
⮚ Prefer more money to less (non-satiation);
⮚ Prefer to avoid risk (risk aversion);
⮚ Prefer money now to later (impatience).
Principle 3: Financial market prices shift to equalize supply and demand (the Concept of
Equilibrium)
▪
Principle 4: Financial markets are highly adaptive and competitive
▪
Principle 5: Risk-sharing and financial frictions are key to financial innovation
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Arbitrage resembles “free lunch”
▪ An arbitrage opportunity is an investment strategy that
⮚ Never requires a cash outflow now or in the future
⮚ Generates a cash inflow
• In one or more states in the future but not now (arbitrage Type 1)
• Now and possibly in one or more states in future (arbitrage Type 2)
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Assumption of no-arbitrage
▪ Financial theory assumes there are no-arbitrage opportunities
⮚ Any opportunities that arise disappear very quickly
⮚ This assumption should not be taken literally, but as a reasonable
benchmark
▪ The no-arbitrage assumption has powerful implications for relative prices
of assets
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Implications of no-arbitrage
▪
Law of One Price (LOOP): 2 assets or portfolios with the same payoffs in every future
state should have the same price
⮚ If not, buy the cheap one and sell (short) the expensive one. Cash inflow today with
no costs in any future states (Type 2 Arbitrage)
▪
AD securities must have positive state prices.
⮚ If one has a negative price buy it. Cash inflow today and in one future state, with no
costs in other states (Type 2 Arbitrage)
⮚ If one has a zero price, buy it. Cash inflow n one of the future states of the world, with
no costs in any other state (Type 1 arbitrage)
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No-arbitrage gives strong results when markets are complete
▪
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Arbitrage Pricing. Example 2 (a bunch of composite securities)
▪
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Role of optimization and equilibrium
▪ No-arbitrage tells us something about relative prices of assets
▪
It says nothing about absolute prices, e.g., the level of each state price
▪ For that we need two remaining concepts
⮚ Optimization – individuals demand for consumption in each state
⮚ Equilibrium – adjustment of the price to ensure demand is equal supply
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Revision
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Measuring return
▪
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Return: example
▪
▪
Buy a stock at the beginning of the year for $50
At the end of the year it pays $2 dividend
▪
At the end of the year, the ex-dividend price is $55
▪
Gross return (2+55)/50= 1.14
▪
Net return (2+55-50)/50=0.14
▪
Income yield 2/50=0.04=4%
▪
Capital gain (55-50)/50=0.10=10%
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The power of the compound interest (compounding return)
▪
By convention, we always report the return on an annual basis (at an annual rate),
even if the period over which we calculate return is different from a year
▪
This convention facilitates return comparisons
▪
The correct way to do this is to raise the gross return to a power
▪
▪
▪
▪
Example
This quarter a stock has a return of 8%
The gross return this quarter is 1.08
If this same gross return was repeater for four quarters, the return after a year would be
(1.08)^4=1.36
Thus, the annualized return is 1.36 (Not 32% = 4*8%)
▪
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Compounding
Typical quote convention:
▪ Annual Percentage Rate (APR)
10% APR Compounded Annually, Semi-Annually, Quarterly, and Monthly
▪ k period of compounding
▪ Interest per period is APR/�
▪ Actual annual rate differs from APR.
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APR
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Compounding
Example. Bank of America's one-year CD offers 5% APR, with semi-annual
compounding. If you invest $10,000, how much money do you have at the
end of one year? What is the actual annual rate of interest you earn?
▪ Quoted APR of 5% is not the actual annual rate.
▪ It is only used to compute the 6-month interest rate:
(5%)(1) = 2.5%
2
▪ Investing $10,000, at the end of one year you have:
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Example: what annual return doubles your money in 10 years?
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Example: what annual return doubles your money in 10 years?
▪ If an investment doubles your money over a decade, its gross return is 2
▪ The annualized return is 2^ (1/10) = 1.072
▪ The annual return of 7.2% will double your money if it is repeated each
year for ten years
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Measuring portfolio returns
▪
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Leverage and short selling. Portfolio weights can sometimes be
negative
▪
Can portfolio weights be negative?
▪
A negative weight on a money market asset represents borrowing (leverage).
▪
A negative weight on a risky asset, such as stock, represents short selling
▪
A negative weight on any asset corresponds to greater than 100% on other assets,
⮚ Borrow money now and commit to pay in future (we have a riskless debt)
⮚ Borrow the asset now, and commit to return it in the future
because all weights must add to 100%
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Leverage in practice: buying on margin
▪
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Return to buying on margin
▪
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Short selling in practice
▪
How to sell a stock short?
▪
Borrow shares from a large institution
▪
▪
Sell the stock and receive cash
Deposit, say, 102% of the value of stock as cash-collateral in a margin account
▪
Later, buy back the shares and return them to the lender
▪
You profit if the stock price has declined while you were short
▪
In a short sale the order of buying and selling is reversed
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Return to short selling
▪
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Short selling in practice
▪
If the value of the shares goes up, you must increase your posted collateral to maintain the ratio of
102%
▪
If the stock pays dividends, you must pay the corresponding amount to the owner of the shares
▪
The lender can ask for the shared back at any time (this is a call loan of shares, not a time loan)
▪
When you return the shares, you get back your collateral and interest
▪
The interest paid on collateral is slightly lower than the risk-free rate (the difference is the lender’s
fee)
▪
If there is strong shorting demands, the interest rate may be much lower (the stock is on special)
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Present value and discount rate
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Present vs future value
▪ We can bring $ back from the future, discounting at the proper discount rate.
▪ We can also send $ into the future, growing at the proper return rate.
PV vs FV
1.8
1.3
0.8
0
1
10
2
3
4
5
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6
7
8
9
Future value (FV)
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Special cash flows
We will consider special several cash flows
▪ Annuity
▪ Annuity with constant growth
▪ Ordinary annuity and annuity due
▪ Perpetuity
▪ Perpetuity with constant growth
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Special cash flows
Annuity A constant cash flow for T periods (starting in period 1)
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Special cash flows
Example.
▪ An insurance company sells an annuity of $10,000 per year for 20 years.
▪ Suppose �� = 5%.
▪ What should the company sell it for?
PV = 10,000 ×
= 124,622.1
1
×
0.05
1
= 10,000 × 12.46
20
1.05
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Special cash flows
Annuity with constant growth rate g
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Special cash flows
Example. Saving for retirement.
■ Suppose
that
million at
you
age
are
65
now
for
30
and
need
your retirement.
$2
■ At the end of each year, you can save an amount that grows by 5% each
year.
■ How much should you start saving now, assuming that r = 8%?
35
1.05
2,000,000
A
=
0.08 − 0.05
1.08
1−
(1.08)35
2,000,000
35
⇒ A= (1.08)
= 6,472.96
20.898
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Ordinary Annuity
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Annuity Due
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Special cash flows
Perpetuity An annuity with infinite maturity
PV (Perpetuity) = �
�
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Special cash flows
Perpetuity with constant grow g
�
PV (Perpetuity with growth) =
,
� −g
>g
�
Example. Super Growth Inc. will pay an annual dividend next year of $3. The
dividend is expected to grow 5% per year forever. For companies of this risk
class, the expected return is 10%. What should be Super Growth's price per
share?
3
3(1 + 0.05)
PV = 1.10
+
+ 3
0.05)2 1.102 1.10
3
3(1 +
+ ⋯ = 0.10 − 0.05 = 60
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Special cash flows
Example. You just won the lottery and it pays $100,000 a year for 20 years.
Are you a millionaire? Suppose that r = 10%.
PV = 100,000 ×
= 851,356
1
1
1−
= 100,000 × 8.514
20
0.10
1.10
■ What if the payments last for 50 years?
1
1
PV = 100,000 ×
1−
= 100,000 × 9.915
1.1050
0.10
= 991,481
■ How about forever - a perpetuity?
PV = 100,000 = 1,000,000
0.10
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Problems
▪ In order to create an endowment which pays $185000 per year forever, how
much money must be set aside today if the rate of interest is 8%? What if
the first payment won’t be received until 3 years from today?
▪ You are receiving $1000 a year for 3 years and you deposit each annual receipt
into a savings account earning 7% interest. How much money will you have at
the end of 3 years?
▪ Assuming a 10% discount rate, how much would you pay for a 5-year annuity
that begins by making the 1st payment today?
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Delayed Perpetuity
▪
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Topical Issues in Financial Economics
National Research University Higher School of Economics
Maria Shchepeleva
Department of Theoretical Economics
Lecture 2. Capital Budgeting and Capital Structure
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Finance
Finance is a discipline about CFs spread over time and how risky these
CFs are
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Financial system
Capital Providers (Savers)
Capital Users (Firms, Government)
Provide money (financial capital)
Use money to buy real assets
□
□
Real assets are used to produce firms’ products and services
Financial ssets (stocks, bonds) are claims on income generated by real
assets
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Main Decisions in the Corporation
Maximizing Firm Market
Value
Capital
Budgeting
Financing
Decisions
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Payout Policy
62
Balance Sheet of the Firm
Assets
Current Assets
Cash + Mkt. Securities
Accounts receivable
Inventories
Other
Liabilities
Short-term Debt
Accounts payable
Debt Due <1y
Other
LT Investments
Net Fixed Assets
• Tangible assets (PPE)
• Intangible Assets (patents, labels,
brendnames, copymarks)
Long-term Debt
Shareholders’ Equity
Preferred Stock
Common Stock
▪
ASSETS side reflects capital budgeting decisions
▪
LIABILITIES side reflects financing decisions
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Assets
Liabilities
Existing Assets
Short-term Debt
Growth Assets (will generate value in future)
Long-term Debt
Equity
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How could we reconcile interests of different shareholders by
maximising shareholders’ value?
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Income Statement
Sales (Revenue)
-Cost
-Depreciation
EBIT (profits from operations)
Interest
EBT
Taxes
Net Income
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Capital Budgeting
1. Estimate project cash flows (what are the CFs and what is the timing)
2. Discount the cash flows using the appropriate discount rate (r).
3. Apply a decision rule:
▪ NPV
▪ IRR, Modified IRR
▪ Rules of “thumb”
• payback rule, discounted payback rule
6
7
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NPV
IRR
MIRR
Payback period
Discounted
Payback Period
+
-
+
-
+
-
+
-
+
-
NPV
uses
cash flow
Problems
with
scaling
Manager
s&
investors
like
returns
Lending/
borrowing
CFs are
reinveste
d at the
opportuni
ty cost of
capital
The
same as
IRR
Easy to
communi
cate
Does not
consider
CFs after
the
payback
period
Never
accept
negative
NPV
project
The
same as
Payback
period
Compara
ble
across
projects
of
different
sizes
Multiple
rates
Ignores
the time
value of
money
Mutually
exclusive
projects
Equally
weighs
CFs
CFs are
Accept
too many
short-
NPV
uses all
cash
flows of a
project
NPV
discounts
the cash
flows
properly
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d at IRR
Profitability Index
+
Favours
smaller
projects
over
larger
ones
68
Net Present Value
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Why does the NPV Rule work?
▪ The NPV Rule works properly for three reasons:
▪ NPV uses cash flow
▪ Cash flows can’t be manipulated like earnings
▪ NPV uses all cash flows of a project
▪ Some approaches ignore cash flows beyond a certain date
▪ NPV discounts the cash flows properly
▪ Cash flows discounted at the opportunity cost of capital, an economically-meaningful rate,
unlike many other methods
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NPV Profile
• Plot of an investment’s NPV at various discount rates
• Shows ranges of “r” where you would accept, reject, or be indifferent
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NPV profile
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Challenges to the NPV Rule
▪ The Investment Timing Decision
▪ The Choice between Long and Short-Lived Equipment
5
7
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Investment timing
Example
A common example involves a tree farm.
You may defer the harvesting of trees. By doing so, you defer the receipt of the cash flow, yet increase
the cash flow. Assume an opportunity cost of capital of 10%.
Year
Cost
Sales
NPV
NPV
discounted
0
50
70
20
20
1
55
80
25
22.7
2
60
88
28
23.1
3
64
95
31
23.3
4
68
102
34
23.2
5
70
105
35
21.7
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Choice between long and short-term projects (projects with different lives).
Equivalent Annual Annuity
Example
Given the following costs of operating two machines and a 6% cost of capital,
select the lower cost machine using equivalent annual annuity method.
Year
NPV, 6%
Machine
0
1
2
3
F
-15
-4
-4
-4
G
-10
-6
-6
EAA
-25.69
-9.61
-21.00
-11.45
75
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Equivalent Annual Annuity
Equivalent Annual Cost - the cash flow per period with the same present value as the cost of
buying and operating a machine.
Equivalent annual annuity takes the NPV of each project and finds the annuity that will spread
the NPV over the life of the project.
76
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Profitability Index
������������� ����� =
���
������� ����������
The pitfall of Profitability Index: it may favor small projects over larger projects with higher NPVs.
Project
J
PV
4
Investment
3
NPV
1
K
L
M
N
6
10
8
5
5
7
6
4
1
3
2
1
Profitability
Index
1/3 = .33
1/5 = .20
3/7 = .43
2/6 = .33
1/4 = .25
6
6
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Other Investment Criteria. Internal Rate of Return
▪ The most popular alternative to NPV
▪ IRR is the discount rate that causes the NPV of a project to equal zero
��� = �� +
��
�+���
+
��
(�+���)�
+…+
��
(�+���)�
▪ Only real way to calculate IRR: trial and error
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=�
Internal Rate of Return
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IRR Rule
• IRR Rule: accept a project if IRR is greater than the opportunity cost of
capital
• Advantages
• Managers and investors like to look at returns
• Comparable across projects of different sizes
• Useful in preparing analysis for outside investors (sometimes difficult to
figure discount rate to apply NPV rule)
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Pretty good rule, but be careful
Pitfall 1 - Lending or Borrowing?
▪
With some cash the NPV of the project increases as the discount rate increases
▪
This is contrary to the normal relationship between PV and discount rates.
Pitfall 2 - Multiple Rates of Return
▪
Certain cash flows can generate NPV=0 at two different discount rates.
Pitfall 3 - Mutually Exclusive Projects
▪
IRR sometimes ignores the magnitude of the project.
Another Issue
▪
Cash flows assumed to be reinvested at IRR
4
0
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Pitfall 1: Lending or borrowing?
• Consider two investments
4
1
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Pitfall 2: Multiple Rates of Return
▪ When the sign of the cash flows changes more than once, we usually get multiple IRRs
▪ Which one do we use? Problem!
▪ Consider the following project cash flows
▪ Negative cash flows at the end of projects common for investments like nuclear power
plants, coal mines, etc where there is significant clean up cost
C0
Project A -$1000
C1
C2
C3
C4
$600 $800 $900 -$700
4
3
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Multiple Rates of Return
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Mutually exclusive projects
Example
You have two proposals to choice between. The initial proposal has a cash flow that is different
than the revised proposal. Required rate of return is 12.26%. Using IRR, which do you prefer?
Project
Initial Proposal
Revised Proposal
C0
-350
-350
C1
400
16
C2
C3
16
466
IRR
14.29%
12.96%
$
$
NPV@7%
24,000
59,000
When you need to choose between mutually exclusive projects, the decision rule is simple.
Calculate the NPV of each project, and, from those options that have a positive NPV, choose
the one whose NPV is highest.
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Mutually exclusive projects
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Can we salvage IRR for mutually exclusive projects?
▪ We can use IRR to evaluate mutually exclusive projects
▪ Find IRR of “incremental” cash flows
▪ Accept Project A since incremental cash flows have IRR above the opportunity cost of
capital
C0
C1
C2
C3
IRR
NPV @ 10%
Project A
-$9000
$3000
$4000
$5000
14.51%
$789.63
Project B
-$2000
$750
$950
$1150
18.52%
$330.95
B-A
-$7000
$2250
$3050
$3850
13.37%
$458.68
5
3
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So is IRR any good?
▪
We pointed out several pitfalls of using IRR. Does this mean it is not a
good rule for making investment decisions?
▪
▪
No. Used properly, it is a very useful rule
▪
We need to be aware of the potential for poor decisions using IRR
It is a good idea to use NPV to make your decision, and IRR as a
supporting measure to help managers better understand the decision
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Other Investment Criteria. Modified Internal Rate of Return
▪
IRR assumes that all cash flows are reinvested at the IRR until the end of
the project
▪
Reinvestment at the opportunity cost of capital is a better assumption
▪
MIRR fixes this problem, and assumes that all cash flows are reinvested at
the opportunity cost of capital
4
6
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Calculating MIRR
▪
Method
▪
Bring all positive cash flows to the end using the opportunity cost of
capital as the rate
▪
Bring all negative cash flows to the beginning using the opportunity cost
of capital
▪
Find the IRR of the new cash flows, one at the beginning and one at the
end
▪
Easier to see with an example
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7
Multiple Rates of Return
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MIRR Example 2
Cost of Capital: 10%
0
1
-$1000 $300
2
3
4
-$300
$400
$700
-$1000
-$247.9
Now find IRR of these cash flows
$1539.30
$1247.9 =
(1 + MIRR)4
$700
$440
$399.3
$1539.3
MIRR = 5.39%
4
9
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MIRR Rule
▪
Like IRR, accept project if MIRR > opportunity cost of capital
▪
MIRR is a pretty good rule, even better than IRR since it deals with
reinvestment in a more practical way
▪
However, it has the same pitfalls as IRR so be careful where you apply it
5
0
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Other Investment Criteria. Payback Method
▪
Payback Period - time until cash flows recover the initial investment of the
project.
▪
The payback rule specifies that a project can be accepted if its payback
period is less than the specified cutoff period.
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Payback Method
Example
The three project below are available. The company accepts all projects with a 2 year or less
payback period. Show how this decision will impact our decision.
Project
+10000
Payback
NPV, 10%
2
+7249
A
-2000
+1000
+1000
B
-2000
+1000
+1000
2
-264
C
-2000
0
+2000
2
-347
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Problems with payback
▪ Payback does not consider any cash flows that arrive after the payback.
▪ The Payback Rule ignores the time value of money.
▪ It equally weights all the cash flows before the cutoff.
▪ Accept too many short-lived projects!
▪ Why do people use it then ?
▪ IT IS EASY TO COMMUNICATE!
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Other Investment Criteria. Discounted Payback Method
Discounted-payback period: Number of periods before the present value of cash
flows equals or exceeds the initial investment.
Advantage: You will never accept a negative NPV project.
Disadvantage: It does not account the cash flows after the cutoff date.
2
7
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Why does the NPV Rule work?
Source: Graham and Harvey (2001)
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Conclusion
• NPV is Best
• IRR has problems with
• mutually exclusive projects
• project scale issues
• reinvestment at IRR
• If you want to use rates to judge projects use MIRR
• Reinvestment rate assumption is changed to reflect reinvestment at
opportunity cost of capital.
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Financing Decisions. Capital Structure
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Terminology
▪
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101
What is Capital Structure
▪
Capital structure is a way firm finances it’s investment decisions:
⮚ Debt (public or private)
⮚ Equity (common stock/preferred stock)
▪
Does it matter what capital structure we use?
▪
▪
Some say – yes:
Lower cost of debt, tax advantages
▪
▪
Some say – no
Slicing the same pie, assets are worth of what they are worth and financing decisions are
irrelevant
▪
Does it matter? Probably…
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102
Capital Structure Theories
▪ Tradeoff Theory (Modigliani and Miller,1958)
▪ Pecking order (Myers, 1984)
▪ Market Timing (Baker and Wurgler, 2002)
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103
Modigliani & Miller (M&M)
▪ 1956 – a new idea… capital structure is irrelevent
▪ Assume
✔ No taxes
✔ No bankruptcy
✔ No transaction costs
✔ Financing does not impact operations
▪ Proof by arbitrage and law of one price
▪ A later paper by Miller even includes taxes and still finds capital structure
is irrelevant
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104
Pie Reference
E
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105
Basic M&M Proof
▪ Suppose two firms have the exact same operating cash flows
▪ One firm is financed completely by equity (U – unlevered)
▪ One firm is financed partially by equity, partially by debt (L – levered)
▪ They have the same operating cash flows
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106
Proof Cont.
▪
▪
Suppose you buy 10% of the U
Consider an investment in the levered firm where you purchase 10% of the equity and
10% of the debt of firm L
Dollar Investment
Dollar Return
10%*��
0.1*Profit
Unlevered firm. Return
Levered firm. Return
Equity
10%*��
0.1*(Profit-Interest)
Debt
10%*��
0.1*Interest
0.1*�� +0.1*�� = 0.1��
0.1*Profit
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Proof Conclusion
▪
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108
M&M Prop. 1 & 2
▪
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109
Cost of Equity under Prop. 2
▪
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110
M&M Prop. 1 & 2
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111
Risk and Cost of Equity
▪ We saw the cost of equity is increasing in the D/E ratio
▪ Why? Can we put this in the context of risk and return?
▪ Let’s immerse ourselves in the CAPM for a deeper analysis of capital
structure
▪ Let’s take a closer look at the effect of leverage on beta
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112
What’s in a beta?
▪ Business cycle sensitivity (covariance with the market)
▪ Operating leverage (fixed vs variable costs) – business risk, irrelevant of
the capital structure
▪ Financial leverage – financial risk, how leverage will affect return (How
flexible is the cost structure? Can you quickly adapt to changing sales
conditions?)
▪ Leverage acts as an amplifier: increases ROE in good times and
decreases in bad times.
▪ What will increasing leverage do to a company’s equity beta?
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113
Firm beta and equity beta
▪ The firm’s asset beta is a weighted
average of the betas of the firm’s debt
and equity
▪ Same idea as the beta of the portfolio
being the weighted average of betas
of individual stocks
▪ Debt betas of large blue-chip firms
are typically in the 0.1 to 0.3 range
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114
How does leverage affect company’s beta?
▪
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Linking beta and risk (CAPM)
▪
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M&M Prop. 1 & 2 (once again, summary)
▪
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So is capital structure irrelevant?
▪
So far, we have seen that under certain assumptions, capital structure is independent of
firm's value
✔ Tells us not to waste our time considering capital structure
▪
But firms spend a lot of time considering capital structure and definite patterns emerge in
the data
✔ Capital structures are not being randomly determined by the companies
▪
Are CFO wasting their time? Or does it change when we relax assumptions?
▪
Let’s look at the characteristics of debt that may lead us to believe that capital
structure and debt policy matter
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Advantages of Debt
▪ Reduces agency costs (Jensen, 1986)
⮚ Debt creates obligations for a firm
⮚ A portion of cash must go toward repaying the debt
⮚ Management is less likely to overinvest and be an “empire-builder”
▪ Tax shield created by interest expense
⮚ After tax cost of debt is low compared to alternative ways of financing
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The Interest Tax Deduction
▪
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The Interest Tax Deduction
▪
▪
▪
Consider Inc. XYZ which had EBIT of approximately $1.85 billion in 2008
Interest expenses of about $350 mln.
XYZ marginal corporate tax rate is 35%.
With Leverage
Without Leverage
EBIT
$1.85
$1.85
Interest expense
-$350
0
Income Before tax
$1.50
1.85
Taxes (35%)
-525
-640
Net income
975
1.200
With Leverage NI will be smaller.
Do you think this company with leverage looks worse?
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The Interest Tax Deduction
▪ XYZ’s debt obligations reduced the value of its equity.
▪ But the total amount available to all investors was higher with leverage.
With Leverage
Without Leverage
Income available to debt
holders
350
0
Income available to equity
holders
975
1200
Total available to all
investors
1325
1200
Less NI in leverage case does not mean that company generated less money!
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The Interest Tax Deduction
▪ Without leverage, XYZ was able to pay out $1200 mln in total to its
investors
▪ With leverage, Safeway was able to pay out $1325 mln in total to its
investors
▪ Where does the additional of $123 mln com from?
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Interest Tax Shield
▪ How does it affect M&M capital structure?
✔ Is debt policy still irrelevant?
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M&M Prop.1 (With Taxes)
▪
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Value of the levered firm in the presence of corporate taxes
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M&M Prop.2 with Corporate Taxes
▪
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Deriving the cost of Equity
▪
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M&M Prop.2 with Corporate Taxes
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Beta with taxes
▪
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M&M (No Bankruptcy) Summary
▪
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Have we found a money machine?
▪
If we can do this for the first mln in debt financing, what about the tenth mln, the twentieth?
▪
Can we reduce our investment to almost nothing and make all of this cash?
▪
Obviously not… we are not picking up some aspects of reality
⮚ Possibilities
⮚ More complex corporate and personal tax system
⮚ Other costs of debt. Bankruptcy? Agency costs?
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Disadvantages of debt
▪ Lack of future financing flexibility
✔ Debt can lock the firm in a particular capital structure for a long time
✔ Lack of flexibility for using firm cash flows
▪ Agency costs (between lenders and owners)
▪ Bankruptcy costs
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Owner vs Lender Agency Problem
▪
Debt has a senior claim to firm’s CFs, while equity has a residual claim
⮚ Equityholders have incentives to accept riskier projects at the expense of higher
default risks
⮚ Management will generally make decisions which will increase shareholder’s value.
However, when the firm has debt, managers can make decisions which benefit
shareholders but harm the firm’s creditors and lower the total value of the firm.
▪
To combat this debtholders include restrictive covenants on the actions of the company
⮚ Can lead to rejection of positive NPV projects and other losses of value
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Selfish Strategy 1: Take risks
▪
▪
▪
▪
XYZ Inc borrow $100 at 10%.
XYZ can invest in one of two projects that each cost $100.
Project A returns $111 with certainty.
Project B returns $90 with probability 50% and $115 with probability 50%. Which would equityholders
prefer? Bondholders?
✔ With project A bondholders will get paid $110 with certainty & equityholders will get the remaining $1.
✔ With project B debtholders will receive $90 with 50% probability and 110 with 50% probability,
equityholders will receive 0 with 50% and 5 with 50%.
▪
Equityholders would rather choose project B and bondholders will be sad
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Selfish Strategy 1. Take risks (another example) Riskshifting
▪ Low risk project
Probability
Recession
Boom
0,5
0,5
Probability
Recession
Boom
0,5
0,5
Value of the
firm
$100
$200
E
D
0
100
100
100
▪ High risk project
Value of the
firm
$50
$240
E
D
0
140
50
100
Which project returns more to equityholders? Which project has higher NPV?
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Selfish Strategy 2: Underinvestment
▪
▪
A firm has to pay $4000 to debtholders
There is a project which brings $1700, cost = 1000 (positive NPV) equity will be used
to finance it.
Without the
project
With the project
Boom
Recession
Boom
Recession
Firm CF
5000
2400
6700
4100
Debtholders’
claim
4000
2400
4000
4000
Stockholders
claim
1000
0
2700
100
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Agency Costs Translate to Actual Costs
▪ Firms may take actions that will not benefit bondholders… managers and
shareholders have incentive to work for their own interest
▪ Bondholders know this and have a higher required return (remember covenants!)
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Bankruptcy costs of debt
▪ The expected cost has two components
✔ Probability of bankruptcy
✔ Dollar Cost of bankruptcy (direct and indirect costs)
✔ Expected Bankruptcy Cost = Probability of Bankruptcy * Cost of Bankruptcy
✔ All else equal, the greater the bankruptcy cost and/or the probability of
bankruptcy implicit in the operating CFs, the less debt the firm can afford to use
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Probability of bankruptcy
▪ Likelihood firms CFs will be insufficient to meet its promised debt obligations
(interest and principal)
▪ Probability is a function of
⮚ Size of operating CF relative to size of debt obligations
✔ Higher operating CF can support more debt
✔ Higher operating CF implies lower probability of default
⮚ Variance in operating CF
✔ More stable CF implies lower default probability
✔ More volatile CF – higher default probability
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Dollar Costs of Bankruptcy
▪
Direct Costs: Legal and Administrative Costs
⮚ Warner (1977): costs 5,3% of assets at the time of bankruptcy
⮚ Weiss (1989): 3% of book value of assets, 20% of prior year’s equity market value
▪
Indirect costs
⮚ Lost sales, change in customer behavior
⮚ Change in supplier behavior, like requiring up-front cash payments for raw materials
⮚ Difficulty in obtaining new capital (higher cost)
⮚ Note: this can occur even before bankruptcy when the firm is in financial distress
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Bankruptcy Costs of Debt
▪
Implications for optimal Capital Structure
⮚ Firms with more volatile CF should have less debt (Tech & Biotech Firms)
⮚ A firm can have more debt if it can match the CF of debt and investments (commodity
companies)
⮚ Firms protected by an external entity will tend to borrow more (banks – FDIC, Fannie
Mae, Freddie Mac)
⮚ Firms with illiquid assets (R&D) tend to have less debt (assets cannot be easily
separated from business)
⮚ Firms producing assets requiring long-term service and support tend to have less debt
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Bankruptcy Cost
▪ Bankruptcy Cost = Bankruptcy Dollar Cost * Probability of Bankruptcy
▪ The dollar cost of bankruptcy depends largely on firm operations, not so
much on capital structure
▪ The probability of bankruptcy is heavily dependent on capital structure
(higher D/E implies higher probability of default)
▪ Therefore, bankruptcy cost is increasing in D/E
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Traditional view on capital structure
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Pecking Order Theory
▪
Myers & Majluf (1984)
▪
✔
✔
✔
Based on asymmetric information
CFO has more information about his company than investors do
Stock prices change when company make announcements
Inside trading can produce huge gains
▪
✔
✔
✔
Leads to a “pecking order” sources of capital
First use internal funds
Than issue debt.
Issue equity as a last resort
▪
✔
✔
✔
The pecking order theory is at odds with the tradeoff theory
No target D/E ratio
Profitable firms use less debt
Companies like financial flexibility
▪
How does this pecking order arise?
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Sources and uses of business funding
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Advantages of Internal Funds
▪
Internal funds are the dominant source of financing for capital needs
▪
Internal funds are readily available to the financial manager
✔ No public offering or private placement needed
✔ No transaction costs
✔ No questions from outside investors
▪
This seems like a convenient source of capital
▪
If a financial manager thinks the firm has good investment opportunities, this seems like a
likely source of capital
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Asymmetric Information leads to Firm Actions
▪ 2 firms: A and B
▪ Public information and market expectations are identical for both firms
▪ Both stocks currently trade at $100
▪ One of the firms is undervalued, the other one is overvalued (CEO knows
stocks are worth of $80)
▪ Both firms need more capital
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New Information to the Market
▪ Each firm makes an announcement
▪ A is beginning $1mln debt offering
▪ B is planning to issue $1mln in new equity at $100 per share
▪ Which company is actually worse $80 per share?
▪ Which one is worth $120 per share
▪ The market considers the same information… what would the market
reaction be?
▪ Implication: No firm would like to issue equity
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Our Pecking Order
▪ It is suboptimal for any firm to issue equity if it can issue debt because either:
✔ Equity is underpriced and debt is cheaper
✔ Equity is overpriced and equity issuing will signal the market about this
mispricing… stock price will fall to fair value
▪ So debt is above equity in the pecking order
▪ Evidence in real world?
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Stock returns of the companies that announce equity issuance
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The Pecking Order Theory
▪ If external finance is required, issue the safest security first
▪ Debt
▪ Convertible bonds
▪ Equity
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Pecking Order Theory
▪
Firms prefer internal financing
▪
Firms adapt a target dividend payout policy to investment opportunities, while avoiding
sudden changes in dividends
▪
Firms will have very sticky dividend policy. They will not want to change dividends that
much. Because of sticky dividends and changing CFs, sometimes internal funds will not
be enough to cover CAPEX.
✔ If internal funds is more than CAPEX, pay off debt or invest in marketable securities
✔ If it is less, draw down cash balance or sell marketable securities
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Market Timing
▪ Baker and Wurgler (2002) propose a market timing explanation of capital
structure
▪ Managers issue equity when stock is overpriced, debt when stock is
underpriced
▪ Current capital structure is cumulative outcome of past market timing efforts
▪ Mixed evidence for this theory
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Signaling
▪
The firm’s capital structure is optimized when the marginal subsidy to debt equals the marginal cost.
▪
Usually market reacts fairly to the announcement of leverage increase: very often stock prices
increase
▪
Investors view debt as a signal of firm value
⮚ Firms with low anticipated profits will take on a low level of debt
⮚ Firms with high anticipated profits will take on a high level of debt
▪
As a manger that takes on more debt that is optimal
in order to fool investors will pay the
cost of the long
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What do firms actually do?
▪
▪
▪
We spent a lot of time looking at capital structure theories
Tradeoff
Pecking Order
▪
Market timing
▪
What do firms actually do?
▪
How do firms choose leverage targets if they do at all?
▪
How do firms decide between alternative sources of financing?
▪
What other factors appear to be influencing firm financing behavior?
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Additional Factors
▪ In tradeoff theory, we often consider the interest tax shield to be the major
benefit and bankruptcy costs to be the main cost of debt
▪ In practice some other factors appear to influence capital structure
⮚ Firm age
⮚ Industry
⮚ Financial flexibility
⮚ Credit rating
⮚ Cost of adjustment
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Life-cycle of firms
▪ Firms tend to have the same steps in their lives
▪ Young startup stage
▪ High growth stage
▪ Mature growth stage
▪ Decline stage
▪ We tend to see similar financing activities among firms in a particular stage
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Capital Structure in the Life-Cycle
▪ Young firms
⮚ Very low leverage
⮚ Equity from owner or private equity firms
▪
High growth firms
▪
Mature growth firms (high debt capacity, limited investment opportunities)
▪
Decline firms
⮚ Low leverage, but increasing
⮚ Have done an IPO & equity is the main form of financing
⮚ Increasing leverage
⮚ High debt capacity, & debt is used as the main source of new financing
⮚ High leverage, but may be decreasing
⮚ Quality of debt decreasing due to worsening business prospects probably not issuing much new
debt, but debt still used fairly heavily
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Industry Considerations
▪ Firms in an industry are pretty similar
▪ Obviously in a similar business (similar business risk and cash flow volatility)
▪ Often competitors are in the same stage of life-cycle (similar operating
leverage and financial leverage)
▪ Firms in the same industry typically have very similar capital structures
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Regulation
▪
Another consideration for companies is regulation
▪
Financial firms and utilities are regulated
▪
Financial firms often have restrictions on the assets and liabilities they can have
▪
Utilities are often forced to set prices based on costs, influencing their incentives for
⮚ Government want to limit the risk of bankruptcy for financial firms
capital structure determination
⮚ Government wants to limit their monopoly
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Financial Flexibility
▪ Firms appear to make financial decisions that give them financial flexibility
▪ What is financial flexibility
⮚ Ability to raise lots of capital quickly and cheaply
⮚ Ability to alter capital structure relatively easily
✔ Increase or decrease reliance on debt or equity
✔ Change types of debt & equity in capital structure
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Flexibility as a goal
▪ Why is financial flexibility valuable?
▪ Companies don’t know for sure when investment opportunities will come
along
⮚ A new investment opportunity may require a substantial initial investment
⮚ Without any means of raising new capital, the firm may have to reject the new project
⮚ Excess borrowing capacity gives financial flexibility & prevent the firm of turning down
value-adding projects
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Another benefit of flexibility
▪
Financial flexibility also allows the firm to change its capital structure more quickly
▪
If a company’s situation changes, the capital structure may not fit the new conditions
⮚ Business cycle changes
⮚ Competition
⮚ Acquisition target
▪
Flexible firms can alter their capital structures to a new optimum quickly
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How would a firm achieve financial flexibility
▪
Often we are thinking of issuing debt to finance unexpected investment opportunities
▪
Having characteristics that would scare potential lenders away limits our ability to borrow
more money, so it limits our financial flexibility
▪
Don’t want high debt, low CF relative to debt, volatile CF
▪
On the other hand, if a firm could support a lot of debt but currently have small leverage,
lenders are happy to lend to the firm
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Credit Ratings
▪
There is substantial evidence that credit ratings influence capital structure
▪
There are benefits of having a high credit rating
⮚ Increased financial flexibility – many lenders are happy to lend to reliable borrowers
⮚ Lower borrowing costs – high credit rating are associated with much lower credit spreads
▪
The cost of having a high credit rating is that a firm has to maintain low leverage
⮚ May be giving up substantial amounts of investment tax shield
⮚ Leverage below the otherwise optimal level
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Credit Ratings
▪ Companies with high credit ratings are able to borrow more easily
⮚ Firms with high credit ratings do issue more debt relative to equity
⮚ Firms with low credit ratings are able to borrow as much as they like &
tend to try to decrease leverage
▪ Firms close to credit rating changes try to issue less debt
⮚ Close to upgrade issue less debt to receive upgrade
⮚ Close to down grade issue less debt to avoid downgrade
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Theory of Finance
National Research University Higher School of Economics
Maria Shchepeleva
Department of Theoretical Economics
Seminar 1. Corporate Finance Decision Making I
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Business+Financial Risk, assuming debt beta = 0 (it is very common)
▪
Business Risk
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Financial Risk
170
Financial Restructuring
▪
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Financial Restructuring
▪
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Using beta and cost of debt to get WACC for a project
▪ A CFO of Amtrak you are deciding of building an airline division. You
estimate the new division will return 17% (after tax) on invested capital
(t=40%)
Corporate’s
competitors
A
Company Beta
D/E
Unlevered beta
1.010
59.1
0.746
B
0.970
56.3
0.725
C
0.680
47.8
0.528
D
0.650
73.8
0.451
E
0.560
32.5
0.468
Mean
0.584
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Add the financing decision proposed airline division
D/V
D/E
Levered beta
0
0
0,584
10
11,1
0,622
20
25
0,671
30
42,9
0,734
40
66,7
0,817
50
100
0,934
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Cost of Equity
▪
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Cost of debt
▪ We determine an airline with 20% debt will receive a credit rating of A
▪ A rated bonds have currently a required rate of return of 7.74 (YTM) –
google it
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Credit Ratings
Credit rating
Cost of Debt
AAA
7.54
AA
7.65
A
7.74
BBB
8.05
BB
8.94
B
10.38
Cost of debt = risk free rate + default risk premium
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Putting it all together: The Airline Division Decision
▪ Debt 20%
✔ Cost of debt = 0.0774
✔ After-tax cost of debt = cost of debt *(1-t) = 0.0774*0.06 = 0.0464
▪ Equity 80%
✔ R airline division = 0.117
▪ WACC airline division
✔ 0.2*0.0774+0.8*0.117 = 0.103
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