Adv. Finance Weekly Meetings - Success Formula · PDF fileCh15 & Ch20 3. More advanced slides...
Transcript of Adv. Finance Weekly Meetings - Success Formula · PDF fileCh15 & Ch20 3. More advanced slides...
Introduction What can you expect from the following meetings
Four types of
firms
• Ownership
• Liability
Conflicts of
InterestFocus on corporations
Further topics
• Time value of money
• Net Present Value (NPV)
• Interest rates: Effective Annual Rate (EAR), Annual Percentage Rate (APR)
• Annuities and Perpetuities
Agenda
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Program outline
Session Task(s) Topic(s) Chapter(s)
1 1-4 Corporation, Financial decision making,
Time Value of Money, Interest rate
Ch1, Ch3, Ch4, Ch5
2 5-8 Financial Statement Analysis,
Bond Valuation
Investment Decision rules
Ch2, Ch6, Ch7
3 8-11 Capital budgeting
Valuing Stocks
Ch8 & Ch9
4 12 &13 Capital Markets and Pricing of Risk
Optimal Portfolio Choices
Ch10 & Ch11
5 14 Estimate Cost of Capital
Investor Behavior and Capital Market
Efficiency
M&M
Ch12, Ch13, Ch14
6 15 Debt and taxes
Options
Ch15 & Ch20
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More advanced slides
M.Sc. in Corporate Finance & Banking as tutor
Potential side track depending on the students’ questions and any current news
Challenging atmosphere: challenge yourself and most important challenge your tutor with your questions!
Different between Finance and advance finance
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Sole Proprietorships Partnerships
Corporations (limited liability companies)
• Ownership: One owner
• Liability: Owners has unlimited personal
liability
• Ownership: Divided among the partners
• Liability: All partner have unlimited
personal liability
Special case: Limited Partnerships
• General Partners has unlimited personal
liability; Limited partners‘ liability is
limited to their investment
• Ownership: Stockholders
• Liability: Corporations are separate legal entities; Owners are not liable
Generate the largest percentage of revenue and second least common form
The different types of firms
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Types of firms – Sole proprietorship
Characteristics Size
Advantages
Owned & run by one person
One or few employees
No separation between owner and firm
Most frequent type of company
Low revenue generation
• Easy to set up
• Relatively low cost to operate
• Owner has unlimited liability for firm‘s debt
• Existence of company limited to life of
owner
As company is increasing and ease of
borrowing increases sole proprietorship tend to
switch type of firm
Disadvantages
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Types of firms – Partnership
Characteristics Size
Advantages and Disadvantages
Identical to sole proprietorship except of
having more than one owner
All partners are liable for firm’s debt
Popular for firms with high reputation needs
(lawyer, accounting etc.)
Least common form of company
Low revenue generation
+ Easy to set up
+ Relatively low cost to operate
+ One partner can be withdrawn or liquidation
through buyout
- Partner has unlimited liability for firm‘s debt
General partner:
liable for firm‘s debt
Managing authority
Limited partner:
Limited liability (private assets cannot be
seized)
No managing authority
E.g. Private Equity, Venture Capitalist
Limited partnership
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Types of firms – Corporation
Characteristics Characteristics
Corporation
Private
Shares not
traded in stock
markets
e.g. GmbH (Ger);
SARL (Fr)
Public
Can betraded in
publicstock
markets
e.g. AG (Ger); SA(Fr)
• Entity separated from owner
• Owners are not personally liable
• No limitation on number of owners
(shareholders)
Second least frequent type of company
Highest revenue generation
+ Public companies can raise more easily
money via stock market (issuing shares)
- Higher cost compared to sole proprietorship
or partnership
- Double taxation - Profit taxation
- Income taxation (dividends)
- Special case (S-shares only once taxed)
Advantages and Disadvantages
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Stakeholders
Conflict of interest
Conflicts of Interest in Corporations
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Employees ManagersBoard of directors
Shareholders
The different owners of a corporation are likely to have different interests and goal.
• Common goal: Increasing the value of their ownership, hence raising share price
A conflict of interest might arise between owners and managers
• Owners elect board of director and tie managers‘ compensation to performance
• Managers are risk averse and therefore require higher compensation if it‘s tied to performance
• Threat of hostile takeover
Further conflicts of interest exist between different stakeholders, e.g. employees and shareholders
Primary and secondary markets
How it works
Primary market: Market where corporations sell stocks to investors
- IPO: Initial public offerings (first sale of stocks)
- SEO: Seasonal equity offering (following sale of stocks)
SEO are faster to do than IPO since the company is already listed
Secondary market: Trade of already issued stocks between investors without direct involvment of
the corporation (no change of book equity)
Primary market:
Corporation through investment banks decide a share price and the banks sell the newly created
shares to investors directly
Secondary market:
Market makers (dealers) sell and buy already issued stocks in the market
Post a ask price (buy price) and a bid/offer price (sale price)
Create liquidity in the market
Bid-ask spread (dealer spread): difference between sale and buy price (compensation for market
maker)
Stock market
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Stock exchange:
Physical places where marketmakers operate at one place (e.g. New York Stock Exchange (NYSE))
one share has only one marketmakers
Over the counter (OTC) markets(dealer market):
Collection of dealers or marketmakers connected by phone or
computer
Less rules and unregulated assetscan be traded
share can have multiple marketmakers that compete against each
other
Market forms
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Debt Equity
Contractual agreement
Legal obligation to repay
Interest payment required
No upside
Less risk, less reward
Loan (from one individual) or bond (from market participants)
Legal ownership of a company
No legal repayment
No dividends required
Upside available
More risk, more reward
Shares
Debt vs Equity
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• Bid and ask price in different market are the same no arbitrage should exist
Competitive markets
• Risk-less profit
• e.g. buying an asset with the certainty to resell it for more right away
Arbitrage
• An asset should be priced at the same price in different markets (incl. transaction costs)
• One of the most important finance concepts for valuation purpose
• Holds within the boundaries of transaction costs
Law of one price
Financial market concepts
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Example
Coffee in Brazil 150$ per pound
Coffee in Europe 190$ per pound
Risk free profit of 40$ per pound
(assuming no transaction cost)
Idea
Law of one
price
If the same good has two different prices in two different markets an investor
could create a profit without any form of risk.
The market would regulate the price
No arbitrage condition
If equivalent investment opportunities trade simultaneously in different
competitive markets, then they must trade for the same price in both markets
Idea that the same goods should have the same value across various
markets
Arbitrage - Example
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Interest rates
Risk free rate Risk
Expected return
Risk free rate (𝑟𝑓) :
Rate at which we can borrow and lend without
any risk
Caused by uncertainty of possible outcomes
Simplified: More than one outcome is possible
Example:
Option 1: Pay 1000 and get 1100 after one year
Option 2: Get either 750€ in bad times (50%) or
get 1450€ in good times
𝑟𝑓 = 6%
Expected value: Sum of Probability * Outcome
Option 1: 1100/1.06= 1038
Option 2: 0.5*750 + 0.5*1450 = 1100
PV= 1100/1.06 = 1038
Investor would not be willing to pay this
amount due to the additional risk
Investors tend to be risk averse
Risk averse: Investor would be willing to pay
more money for safer investments (risk seeking
is the inverse)
The weight potential losses (loosing 350€ in
bad times) more than potential gains (winning
350€ in good times)
Prospect theory
Interest rate of a security: 𝑟𝑠= 𝑟𝑓 + risk
premium
Risk averse vs risk seeking
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APR and EAR
APR and EAR EAR
Annual percentage rate (APR) = the rate
without the compounding effect
In general terms you should use the discount
rate including compounding as the investor is
entitled to the compounding effect
EAR > APR (holds true if and only if the return
is positive and that there is a compounding
effect)
Effective annual rate (EAR) = the rate with the
compounding effect
1 + 𝐸𝐴𝑅 = (1 +𝐴𝑃𝑅
𝑘)𝑘
A investment pays an annual interest of 4%
paid quarterly, what is the Effective annual
rate and the annual percentage
Rate
Example
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1 + 𝐸𝐴𝑅 = (1 +4%
4)4
Continously
compounding
When reducing the frequency of payment to infinity within one year.
Formula:
𝑒𝑟 − 1
Permanent payment of the interest rate
Real interest
rate
After tax
interest rate
Real interest rates is the nominal interest rate adjusted for inflation
Formula:
𝑟 = 𝑖 − 𝜋
More precise when making a financial decision
Only an approximation
In case cash flows of investment are taxed.
Formula:
𝑟 − (𝑡 𝑥 𝑟) = 𝑟(1 − 𝑡)
Taxes reduce the amount of interest the investor can keep
Forms of the interest rate
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Situation
Representation
Since money you can invest or earn interest on money that you own today compared to money that
you would own tomorrow, $100 today is worth more than $100 tomorrow. The difference is called
the time value of money.
We need to discount future cashflows with the interest rate at which we can invest or borrow.
Time value of money
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January 1, 2014
$100
June 1, 2014
$110
December 31, 2014
$115
1. Comparison
Compare only cash flows at the same point in time
100€ now ≠ 100€ in one year
2. Compounding
3. Discounting
To calculate the value of the cash flow in the future
Compounding: interest on interest payment
FV= C(1+r)*(1+r)*... , where C=Cash flow
To move cash flows back in time
Discounting: used to calculate the Present Value (PV)
PV= FV/(1+r)
Time value of money – 3 rules
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Characteristics Assume we receive a payment of $1000 in 2 years (n = 2).
The risk free interest rate at which we can borrow and invest is 10% (r = 0.10)
Time value of
money
Impact of
interest rates
1. What is this payment worth in terms of dollars today?
2. What is this payment worth in dollars in 3 years?
1. $1000 / (1 + 0.10)2 = $826.45
2. $1000 * (1 + 0.10) = $826.45 * (1 + 0.10)3 = 1100
How would the value of the payment in terms of dollars today change if the
interest rate rose from 10% to 12%?
$1000 / (1 + 0.12)2 = $797.19
The value of the payment in terms of dollars today would decrease.
How do we value future cashflows?
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Net present value
NPV Decision rule:
NPV = Net Present Value
The NPV of an investment is the equivalent of the cash you would receive/pay today. Therefore as
long as the NPV is positive the investment should be pursued.
Calculation: Subtract the present value of an investment‘s costs from the present value of its
benefits.
NPV = PV(Benefits) – PV(Costs)
When you have to choose between different investment alternatives and they are mutually
exclusive, choose the one with the highest NPV.
When you have to choose different investment alternatives and they are not mutually exclusive,
choose the all options with a positive NPV.
What is the NPV?
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Characteristics
An investor has two mutually exclusive investment opportunities:
1: Invest $100 today, get $140 in two years.
2: Invest $100 today, get $65 in one year and $65 after two years.
The interest rate is 8%.
NPV
Timing of
payments
What is the NPV of the two investment opportunities?
1: -$100 + $140 / 1.082 = $20.03
2: -$100 + $65 / 1.08 + $65 / 1.082 = $15.91
The investor should choose investment opportunity 1.
The investor will need to make a payment of $50 in one year and therefore
prefers to receive cash earlier in time. Is this circumstance changing the
optimal investment decision, hence is the timing of payments important?
No, the investor should always maximize NPV since he can borrow or lend in
order to shift the payments.
NPV calculation
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Proposition 1 Proposition 2 & 3
Pricing the securities
Price = ?
Payoff next year = 1050
Price = ?
Payoff next year = 0 or 4200
Likelihood: 75/25
OR
Price = ?
Payoff next year = 950 or 1150
Likelihood: 50/50
Knowing that the interest risk free rate is 5%
• What is the price of the first security?
• What is the price of the second security?• Hard to do price isn’t it?
• The market is currently trading the second security at 913.04 and the third at 954.55. Can you make
an arbitrage out of this?
• What is the market implied discount rate in security 2? What about the security risk premium?
• What is the market implied discount rate in security 3? What about the security risk premium
Pricing risk, are you risk averse?
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Proposition 1
Price =𝐹𝑉
1+𝑟 𝑡
Price =10501+0.05 1 = 1000
Proposition 2
Proposition 3
Expected Value= probability x outcome
E(V)= 0.75*0+0.25*4200= 1050
Price =𝐹𝑉
1+𝑟 𝑡 913.04 = 1050
1+𝑟
r=0.15 risk premium=10%
E(V)= 0.5*950+0.5*1150= 1050
Price =𝐹𝑉
1+𝑟 𝑡 954.55 = 1050
1+𝑟
r=0.10 risk premium = 5%
Solution
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How to value a stream of cash flow
Finite life: Annuity Annuity formula
Solve for the annuity
A rather long approach using the previous
method.
Shortcut:
PV (finite stream of cash flows) = annuity
Formula = 𝐴
𝑟∗ (1 −
1
1+𝑟 𝑛)
FV (annuity) = 𝐴
𝑟∗ ( 1 + 𝑟 𝑛 − 1)
1000
0.05∗ 1 −
1
1 + 0.05 5= 4329
In case of a perpetuity it would be impossible
to find the present value of all the individual
payments.
Solution:
Perpetuity formula = 𝐴
𝑟Perpetuity can only be present value
Infinite life: Perpetuity
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Project opportunities
Questions
Project Investment Next year cash flow
Expand the factory 2,500,000 3,000,000
New training program 1,000,000 1,100,000
Open 10 new stores 6,500,000 10,000,000
Knowing you have 10,000,000 in cash and that the risk free rate is 10%.
1. Which projects should you undertake?
2. What is the investment return you would make on those projects?
(ROI=Profit/Initial investment)
3. We revised our investment projection and the investment cost of the 3rd investment is now
8,000,000, which projects should you undertake?
Testing your understanding
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Investment 1𝑁𝑃𝑉 = −2,500,000 +
3,000,000
1.1= 227,272
Return on investment =500,000
2,500,000= 0.2 → 20%
Investment 2𝑁𝑃𝑉 = −1,000,000 +
1,100,000
1.1= 0
Return on investment= 100,000/1,000,000=0.1
Investment 3𝑁𝑃𝑉 = −6,500,000 +
10,000,000
1.1= 2,590,000
Return on investment =3,500,000
6,500,000= 0.538 → 53.85%
Choice
Question 1&2: With the 10,000,000€ in cash, the optimal distribution would
be: 6,500,000€ in Project 3 & 2,500,000 in project 1 and the rest into risk free
bonds
Question 3: 𝑁𝑃𝑉 = −8,000,000 +10,000,000
1.1= 1,090,000
Return on investment =2,000,000
8,000,000= 0.25 → 25%
We invest all in project 3 and 2,000,000 in risk free bonds
Investment choices
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Financial decision making
IRR Growing annuity
Annuity
The interest rate that equates your PV and the
Cash flows (NPV = 0) need to solve for r
Used often in order to get the return on your
investment that would create a break even
investment when the NPV is equal to 0
In case of a growing annuity
Formula need to be adjusted
Can be used to derive all the other formulas
𝐶
𝑟 − 𝑔∗ 1 −
1 + 𝑔
1 + 𝑟
𝑛
Where, C= first payment, g=growth rate,
r=interet rate, n=number of periods
PV(Perpetuity):𝐶
𝑟
PV(growing perpetuity):
𝐶
𝑟 − 𝑔
Perpetuity
PV(Annuity): Formula = 𝐶
𝑟∗ (1 −
1
1+𝑟 𝑛)
FV (annuity) = 𝐶
𝑟∗ ( 1 + 𝑟 𝑛 − 1)
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Parameters
Solution
Investment: 1000
Cash flow year 1 to 5: 0
Cash flow year 6: 300
Cash flow year 7-10: CF(6) growing at 2% per year
Prevailing discount rate: 5%
Find the NPV of this investment
𝑁𝑃𝑉 = −1000 +
3005% − 2%
∗ (1 −1 + 2%1 + 5%
5
)
1 + 5% 5= 57.16
Never forget that the PV(Annuity) formula assumes payment starting the next period
One step further: “Toothbrush”
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