Foster MBA 2010 Finance Jump Start - Gilbert - Day 1 with notes and answers

8/7/2019 Foster MBA 2010 Finance Jump Start - Gilbert - Day 1 with notes and answers

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MBA Jump Start

Finance - Day 1

Thomas Gilbert

September 17th 2010

About Myself

Finance assistant professor

Ph.D. in Finance from U.C. Berkeley, 2008

Masters in Finance from U.C. Berkeley, 2005

Masters in Physics from Imperial College (London, U.K.), 2002

Teaches finance and investment classes in various executive programs, as

well as in the full-time MBA and Ph.D. programs at the University of

Washington and at U.C. Berkeley

Winner of the Professor of the Quarter and Professor of the Year Awards in

2009-2010 as well as the PACCAR Award for Teaching Excellence

Research focus is on the im act of ublic information releases GDP

Thomas GilbertFinance Day 1 Page 2

employment, earnings) on financial markets

Contact information:

[email protected]

http://faculty.washington.edu/gilbertt/


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Jump Start Goals

Your goals:

Build skills Learn financial calculations

Time value of money

Bad news:

All the material in this

workshop will be assumed

known at the start of BA 500 -

Finance (assignment due on

second day of class)

n a rea use or ma

Get comfortable with a new schedule

Transition from work schedule to academic schedule

Meet new classmates

Set expectations for the coming year

Answer questions you might have

Discuss class formats


My goals:

Introduce you to finance

Get you prepared and enthusiastic for your core MBA finance class

Get to know more of you!

1. Time Value of Money


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Time Value of Money

Jump right in and learn!!!

Understand how to compare:

Payments made today

Payments made in the future

Understand the following terms:

Present value (PV)

Discount rate (r)

Future value (FV)


Net present value (NPV)

Learn how to draw project cashflows

Inter-Temporal Choices

Which would you rather receive?

$100,000 today

$250,000 in exactly seventeen years

Both payments are riskless

Consider the payments as backed by the U.S. government

They are backed by collateral accounts that contain $100,000 or

$250,000 and only accessible by you

There is a 100% probability that you will be paid

There is a 0% probability that you will not be paid


Why is this riskless stuff important?


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Risk

What is risk?

Risk means that there is uncertainty in the delivery of the future cashflows

Probability distribution of future outcomes

Get paid if, with probability

Dont get paid if, with probability

Riskless cashflows are easier to deal with than risky cashflows since we do

not have to think about risk

They serve as a baseline/benchmark for comparison


Risk is a major topic of the core finance class

Definition #1: Cashflow

A cashflow is a time-dated money amount

It has an amount (such as 2 or 3,000,000,000)

It has a unit (such as USD or CHF)

It has a date (one point in time)

It has a sign (positive = inflow, negative = outflow)

Absolute rule of finance:

ALWAYS DRAW A TIMELINE!!!



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Inter-Temporal Choices (2)

Why is it hard to compare?

$100,000 today


This is not an apples to apples comparison

Rule #1 of time travel:

You can only compare cashflows at the same point in time


Your first timeline:

Definition #2: Present Value

In order to compare, we need to convert the future cashflows into presentvalues:

01

tt t

CFPV

r= =

+

where PVt=0 = present value at time zero

CFt = cashflow at time t

rt = discount rate for payments in tyears (annualized)

1/(1+rt)t = discount factor


Calculating present values (moving cashflows backwards in time) is alsocalled discounting

Can we now answer our first question?


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Present Value

Which would you rather receive?

$100,000 today


If the discount rate for year-seventeen cashflows is 6% per year, then:


Decision?

Compound Interest

The ability to earn interest on interest

Interest payments are reinvested

Subsequently, these payments earn interest

Example 1: $100 invested for 3 years at 8% per year

$100 100*(1+0.08) 100*(1+0.08)2 100*(1+0.08)3

$100 108.00 116.64 125.97

Example 2: $523 invested for 20 years at 7% = ???



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Why is the PV Math Reasonable?

Think about the opposite direction of time travel: forward

You place $100,000 today in a secured savings account which earns an

interest rate of 6% per year for seventeen years

How much do you have at the end?


This is called the Future Value

Definition #3: Future Value

To move cashflows forward in time, we compound:

( )0 1t

t t tFV CF r == +

where FVt = future value at time t

CFt=0 = cashflow at time zero

rt = discount rate for payments in 17 years (annualized)

The Present Value calculation is simply the inverse of this


Did we reach the same conclusion about our problem?


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Summary

Rule #1: You can only compare $ at the same point in time

Rule #2: To move cash flows backwards in time, we discount them: /(1+r)t

Rule #3: To move cash flows forward in time, we compound them: *(1+r)t

The Rule:

( )0

1

t

t

t

CFPV

r=

+


ALWAYS DRAW A TIMELINE!!!!

2. Problem-Solving


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Class Expectations #1: Practice

To get better at piano, a reasonable person can expect to practice piano

a lot!!! Some practice may be boring, like doing scales

Some practice time may be spent learning new pieces

Some practice may be repetitive

Some practice time may be spent trying new things

Finance is very, very similar

You should do practice problems on your own and/or with your study

group


yourself to do problems

Practice makes perfect!!!

Problem #1

What is the present value of $100,000 received in one year (one year in thefuture) if the discount rate (for one-year horizons) is 6%?

Step 1: Think!

< > ,

Step 2: Draw timeline



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Problem #2

What is the present value of $100,000 received in year 10 if the discount

rate (for ten-year horizons) is 6%?

Step 1: Think!

< > ,



Problem #3

What is the present value of $100,000 received in year 17 if the discountrate (for seventeen-year horizons) is 6%?

Step 1: Think!

< > ,




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Class Expectations #2: Calculators

All students are required to have and use a financial calculator

I will use (and thereby require you to use) the HP-12C

The platinum version is recommended since it allows algebraic notation

The regular version only allows reverse polish notation

In the CFA exam, only the HP-12C (regular or platinum) or the TI-BA2+


u w x

In your finance exam, you will only be allowed to use a calculator

If you want to use another calculator, make sure that it has financial

functions built in, such as IRR, bond pricing

Solving for PV and FV on the HP-12C

n Number of periods

i Interest rate in % (constant for all periods)

PV Present value at time 0

PMT Periodic payment (repeats every period, starting at time 1)

FV Future value (one-time payment at time n)



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Problem #3 on HP-12C

An earlier problem, now done on the HP-12C:

What is the present value of $100,000 received in year 17 if thediscount rate (for seventeen-year horizons) is 6%?

s ng my - :

n =

i =

=


PMT =

FV =

Inter-Temporal Rates

Is it reasonable to assume the same discount rate for 1-year cashflows andfor 17-year cashflows?

Do you receive the same interest rate for 1-year loans and for 17-year

loans?

We have a menu of inter-temporal discount rates:

1 year: r1 = 6%

2 years: r2 = 7%

3 years: r3 = 7.5%

4 years: r4 = 8.25%

=


5

This is called the term structure of interest rates (spot rates)


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Present Value of Multiple Cashflows

Cashflows at different points in time are discounted at their own discount

rates: r1 forCF1, r10 forCF10, r17 forCF17

Timeline for multiple cashflows:

The present value of multiple cashflows is simply the sum of their present

values:


( ) ( ) ( ) ( )

31 20 2 3

1 2 31 1 1 1

t

t

t

CF CF CF CF PV

r r r r

= + + + + +

+ + + +

Problem #4

If you are given the following set of cashflows and discount rates, can youcalculate the PV?

C1 = $50 and r1 = 6%

C2 = $60 and r2 = 7%

Step 1: Think!

PV $110

Step 2: Draw the timeline


Step 3: Solve


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3. Net Present Value

Projects

A project is a general term used in finance Invest some money today (cash outflow)

Receive payoffs in the future (cash inflows)

s s a s y ze way o raw pro ec cas ows:

Time (years)0

1 2

Investment

Expected payoff


Projects come in varied forms

Entrepreneur starts a company (real investment)

Investor purchases a stock (monetary investment)

My friend buys a lottery ticket (gamble)


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Problem #5

A merchant pays $100,000 for a load of grain and is certain that it can be

resold at the end of one year for $132,000.

a. What is the return on this investment?

b. If this return is lower than the rate of interest, does the investment have a


Problem #5 (2)

c. If the rate of interest is 10 percent, what is the PV of the future cashflow(s)?

d. What is the NPV?



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Definition #4: Net Present Value

The net present value combines the initial investment (usually made at

time zero) and the PV of the expected future cashflow(s):

31 20 0 2 3

t

t

CF CF CF CF NPV CF = + + + + + +

It basically is a cost-benefit analysis, but taking into account the time value

( )

1 2 3

0

1

1 1 1

1

t

Tt

tt t

r r r r

CFCF

r=

+ + + +

= ++


, . .

In firms, managers have to choose projects, and the following rule applies:

Choose projects with 0NPV >

Problem #6

If you are given the following set of cashflows and discount rates, can youcalculate the NPV?

C0 = -$90

C1 = $50 and r1 = 6%

= =

Step 1: Think!

PV $20

Step 2: Draw the timeline


Step 3: Solve


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Discount Rates

What does the rt represent?

The discount rate used for computing NPV should represent the best

alternative use of your capital

This is sometimes referred to as the hurdle rate oropportunity cost of

capital

In practice, the discount rate often comes from the return on an asset (bond,

traded stock, etc.) with comparable risk

This is called the risk-adjusted discount rate


In the world of riskless payoffs, we can get the rate from U.S. Government

bonds and bills (since they are considered riskless)

Problem #7

A parcel of land costs $500,000. For an additional $800,000 you can builda motel on the property. The land and motel should be worth $1,500,000

next year. Suppose that common stocks with the same risk as this

investment offer a 10 percent expected return. Would you construct the



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Practice Quiz #1 and Break

Please spend a few minutes and complete the practice quiz on the next page

Timeline

NPV

Decision

The answers will be handed in at the end of class

Then take a 10-minute break to stretch your legs


4. Perpetuities & Annuities


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Class Expectations #3: Lectures

Your professors use a variety of lecturing styles

Some write on the board

Some use Powerpoint

Some lead case discussions

Some use Tablet PCs

Professors choose the method that most enhances learning

Different styles for different subjects

Different styles for different parts of the same subject

Some professors make class notes available before class; some make them

available after class


v y u w

some professors give you homework problems after class

Cases are always to be prepared ahead of class and you have to be ready for

in-class discussion

Definition #5: Perpetuities

If a project makes a level, periodic payment forever, it is called aperpetuity

Lets suppose your friend promises to pay you $1 every year, starting in

one year, orever

His future family will continue to pay you and your future family

The discount rate is assumed constant at 8.5%

How much is this promise worth?

$1 $1 $1 $1 $1 $1


PV0 = ?

Time (years)

1 2 3 4 5 infinity


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Perpetuity Formula

Valuing the perpetuity could be hard:

( ) ( ) ( ) ( ) ( )0 2 3

1 1 1 1 1

1 1 1 1 1

1

tPV

r r r r r

= + + + + + ++ + + + +

Luckily, mathematicians figured this out a long time ago (students who like

math can work on this)

( )1 1

???

tt r=

=+

=


v u perpe u y y w x

period and has a periodic discount rate r is:

CPV

r=

Problem #8

Lets suppose your friend promises to pay you $1 every year, starting inone year, forever

His future family will continue to pay you and your future family

The discount rate is assumed constant at 8.5%

How much is this promise worth?



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Real-World Example

There is common saying in the investment world:

Businesses are worth ten times cashflow

Given what we have just learned about perpetuities, can someone explain

t s


Definition #6: Growing Perpetuities

Suppose now that the cashflow next year is C and then grows every yearafter that at g percent per year

Timeline:

The value of a growing perpetuity that pays cashflow C next period,


,

periodic discount rate r is:

CPV

r g=


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Problem #9

Suppose your friend now promises to pay you $100 next year and this

cashflow will grow by 3% every year forever. The discount rate is 12% How much is this promise worth?


Real-World Example (2)

There is common saying in the investment world:Businesses are worth ten times cashflow

Given what we have just learned about growing perpetuities, can someone

exp a n t s



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Jump Start Website

For information related to the summer workshop website

http://faculty.washington.edu/gilbertt

Go to MBA Teaching, 2009 Foster MBA Finance Jump Start

Syllabus, class notes, quizzes, answers, and Excel spreadsheets are all

posted there

I also posted some files on how to use the HP-12C


w w y

Definition #7: Annuities

A project might not pay you forever

Instead, consider a project that promises to pay you a level amount C

every year (starting next year), for the next T years

This is called an annuity

PV = ?

$C $C $C $C $C $C

Time (years)1 2 3 4 5 T


Can you think of examples of annuities in the real world?


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Annuity Formula

How do we value an annuity?

Again, students who like math can work on this by starting with the

intuition that an annuity is the difference between two perpetuities, one that

starts at t me an one t at starts at t me +

The value of an annuity with constant cashflow C starting at time 1 and

ending at time T, with discount rate r is:

11

TC

PV

=


Problem #10

You just won the $20,000,000 lottery!!! However, you are actually gettingpaid $1,000,000 per year for the next 20 years.

If the discount rate is a constant 8% and the first payment is in one year,

how much have you actually won (in PV-terms)?



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Annuities on the HP-12C

Annuities are very easy on the HP-12C:

n = number of periodic payments

i = discount rate

PV = ???

PMT = periodic payment

FV = 0 (the last periodic payment is included in PMT)

Problem #10 on the HP-12C:


NPV of Problem #10

Paper reports: Todays jackpot = $20 million!!!

Paid in installments exactly as previously described (tax-free)

Odds of winning the lottery are 13 million to 1

Ticket costs $1

First introduction to risk!

Is this a positive NPV project?



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Definition #8: Growing Annuities

Suppose now that the cashflow next year is C and then grows every year

after that at g percent per year, for T years

Timeline:

The value of a growing annuity that pays C starting next period, with a

periodic growth rate g after that, for the next T periods, and a periodic

discount rate r is


There unfortunately is no calculator shortcut for this

11

1

C gPV

r g r

+=

+

Formula Overview Slide

Perpetuities Annuities

Level

Payments

T

11

1

CPV

r r

= +

CPV

r=


Growing

Payments 1 1PV r g r= + PV r g=


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Very Important Thing to Remember

WARNING!!!

If you want to use any of the perpetuity/annuity formulae, you must

understand something critical

The formulae give you present values at time t given that the

first periodic cashflow is at time t+1

Problem #11: What is the PV of a $10 perpetuity starting in year 11 if the

discount rate is 5%?


Very Important Thing to Remember (2)

End of Problem #11:



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Problem #12

This morning, you received a promissory note guaranteeing annual

payments of $15,000 for 30 years, starting today. If your opportunity costof capital is 7%, what is the PV of this note?


Quiz #2 and Summary

Please spend a few minutes and complete the practice quiz on the next page

Annuity

Growing perpetuity

The answers will be handed in at the end of class

Today, we learned about the time value of money

Comparing payments made today and payments made in the future

Present values

Drawing cashflow timelines


Net present values

Special streams of cashflows: perpetuities and annuities


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Next Class

This afternoon/tonight, you should review todays class

Do the practice problems listed on the syllabus

And prepare for the next class

Do the reading

I expect students to spend one to two hours per night studying finance

Next time

Learn to calculate mortgage payments

Learn to price bonds


Learn to calculate yield-to-maturity

Learn about compounding

Documents

Foster MBA 2010 Finance Jump Start - Gilbert - Day 1 with notes and answers