Adv. Finance – Weekly MeetingsMeeting 1 – Year 15-16

Weekly Meeting I

Finance

1

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

2

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

3

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

5

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

6

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

9

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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Convertible bond

Bond with warrants

Common hybrid (debt and equity composed) instruments

13

Discount rate

Interest rate

Cost of capital

Some lingo

14

• 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

21

Past

Present

Future

Representation

22

0

(1 )t

CF

r 0CF 0 *(1 )tCF r

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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We wish you Success!

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