Introduction to Financial Management FIN 102 – Week 3 Dr. Andrew L. H. Parkes “A practical and...

Introduction to Financial Introduction to Financial ManagementManagementFIN 102 – Week 3FIN 102 – Week 3

Dr. Andrew L. H. ParkesDr. Andrew L. H. Parkes““A practical and hands on course on the valuation A practical and hands on course on the valuation

and financial management of corporations”and financial management of corporations”

Intro. to Financial Managment - WeIntro. to Financial Managment - Week 2ek 2

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The Time Value of MoneyThe Time Value of Money

The Interest RateThe Interest Rate Simple InterestSimple Interest Compound InterestCompound Interest Lump Sum Lump Sum

CalculationsCalculationsBen Bernanke, Fed

Chair

Four Basic Topics:


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The Fed MOVES! WOW!The Fed MOVES! WOW!

The BIG news today that will move the markets!! – Sept. 19, 2007

Crazy American analyst Jim Cramer – “These guys get it!”


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We Will use Excel …We Will use Excel … This chapter is about straight This chapter is about straight

forward calculations of Future forward calculations of Future Values of cash and Present Values Values of cash and Present Values of cashof cash

It’s much easier to use Excel if you It’s much easier to use Excel if you know how to work with it…know how to work with it…

You may use a calculator, which is You may use a calculator, which is often just as fast. These are often just as fast. These are explained in the text of Chapter 3 explained in the text of Chapter 3 and the book PPT.and the book PPT.

However, nowadays everybody However, nowadays everybody uses spreadsheets as well. So you uses spreadsheets as well. So you better learn to use them if you better learn to use them if you don’t know how.don’t know how.


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What do you prefer…What do you prefer…

$ 1000 now or$ 1000 now or $ 1000 next year?$ 1000 next year?

If you are like anybody If you are like anybody else you know the else you know the answer very well…answer very well…

That’s all of us know That’s all of us know there is Time Value to there is Time Value to money and that is what money and that is what this chapter is about…this chapter is about…

Traders on the floor of the New York Stock Exchange watch the news of a bigger-than-

expected rate cut from the Federal Reserve.

Spencer Platt / Getty Images


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Future ValueFuture ValueYou put money in the bank You put money in the bank at 3.27% interest (today’s at 3.27% interest (today’s rate in China), how much rate in China), how much money do you have after ___ money do you have after ___ years?years?

You You must must compound the compound the interest since every year you interest since every year you will earn simple interest on will earn simple interest on the amount you put into the amount you put into bank initially as well as bank initially as well as earning interest on the earning interest on the interest of prior yearsinterest of prior years!

See my website for the IPO article!


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Time and CompoundingTime and Compounding TIME allows you the opportunity to

postpone consumption and earn INTEREST. To Reiterate:

Simple InterestSimple Interest– Interest paid (earned) on only the

original amount, or principal borrowed (lent).

Compound Interest:Compound Interest:-- Interest paid (earned) on any previous Interest paid (earned) on any previous

interest earned, as well as on the interest earned, as well as on the principal borrowed (lent).principal borrowed (lent).


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The “Simple” FormulaThe “Simple” Formula

Future Value (FV) = PV + PV * (1 + i)Future Value (FV) = PV + PV * (1 + i)OROR

FV = PV*(1+i)FV = PV*(1+i)For multiple periods:For multiple periods:

FV = PV*(1+i)FV = PV*(1+i)nn

So for two periods:So for two periods:FV = PV*(1+i)FV = PV*(1+i)22


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Time linesTime lines

Show the timing of cash flows.Show the timing of cash flows. Tick marks occur at the end of periods, so Time 0 is Tick marks occur at the end of periods, so Time 0 is

today; Time 1 is the end of the first period (year, today; Time 1 is the end of the first period (year, month, etc.) or the beginning of the second period.month, etc.) or the beginning of the second period.

CF0 CF1 CF3CF2

0 1 2 3

i%


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Drawing time lines:Drawing time lines:$100 lump sum due in 2 years;$100 lump sum due in 2 years;3-year $100 ordinary annuity3-year $100 ordinary annuity

100 100100

0 1 2 3i%

3 year $100 ordinary annuity

100

0 1 2

i%

$100 lump sum due in 2 years


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Make a Timeline … It Does Make a Timeline … It Does HelpHelp

Drawing time lines: Drawing time lines: Uneven cash flow stream; Uneven cash flow stream;

CF0 = -$50, CF1 = $100, CF2 = $75, and CF3 = $50CF0 = -$50, CF1 = $100, CF2 = $75, and CF3 = $50

100 50 75

0 1 2 3

i%

-50

Uneven cash flow stream


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What is the future value (FV) of an What is the future value (FV) of an initial $100 after 3 years, if I/YR = initial $100 after 3 years, if I/YR =

10%?10%? NOTICE: The FV can be solved by using NOTICE: The FV can be solved by using

the arithmetic, financial calculator, the arithmetic, financial calculator, and/or spreadsheet methods. and/or spreadsheet methods. (All are (All are equivalent!)equivalent!)

FV = ?

0 1 2 3

10%

100


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Solving for FV:Solving for FV:The arithmetic methodThe arithmetic method

After 1 year:After 1 year:– FVFV11 = PV ( 1 + i ) = $100 (1.10) = PV ( 1 + i ) = $100 (1.10)

= $110.00 = $110.00 After 2 years:After 2 years:

– FVFV22 = PV ( 1 + i ) = PV ( 1 + i )2 2 = $100 (1.10)= $100 (1.10)22

=$121.00 =$121.00 After 3 years:After 3 years:

– FVFV33 = PV ( 1 + i ) = PV ( 1 + i )3 3 = $100 (1.10)= $100 (1.10)33

=$133.10 =$133.10 After n years (general case):After n years (general case):

– FVFVnn = PV ( 1 + i ) = PV ( 1 + i )nn


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Solving for FV:Solving for FV:The calculator methodThe calculator method

Solves the general FV equation.Solves the general FV equation. Requires 4 inputs into calculator, and Requires 4 inputs into calculator, and

will solve for the fifth. (Set to P/YR = 1 will solve for the fifth. (Set to P/YR = 1 and END mode.)and END mode.)

INPUTS

OUTPUT

N I/YR PMTPV FV

3 10 0

133.10

-100


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The The Present Value Present Value is simply the is simply the $100$100 you originally deposited. you originally deposited. That That is the value today!is the value today!

Present ValuePresent Value is the current value of a is the current value of a future amount of money, or a series of future amount of money, or a series of payments, evaluated at a given interest payments, evaluated at a given interest rate.rate.

Simple Interest (PV)Simple Interest (PV)Simple Interest (PV)Simple Interest (PV)

What is the What is the Present Value Present Value ((PVPV) of the ) of the previous problem?previous problem?


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PV = ? 100

So what is the present value (PV) of So what is the present value (PV) of $100 due in 3 years, if I/YR = 10%?$100 due in 3 years, if I/YR = 10%?

Finding the PV of a cash flow or series of cash Finding the PV of a cash flow or series of cash flows when compound interest is applied is flows when compound interest is applied is called called discounting discounting (the reverse of (the reverse of compoundingcompounding).).

The PV shows the value of cash flows in terms The PV shows the value of cash flows in terms of of today’s purchasing powertoday’s purchasing power..

0 1 2 310%


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Solving for PV:Solving for PV:The arithmetic methodThe arithmetic method

Solve the general FV equation for PV:Solve the general FV equation for PV:– PV = FVPV = FVnn / ( 1 + i ) / ( 1 + i )nn

– PV = FVPV = FV33 / ( 1 + i ) / ( 1 + i )33

= $100 / ( 1.10 )= $100 / ( 1.10 )33

= $75.13= $75.13


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Julie Miller wants to know how large her deposit ofJulie Miller wants to know how large her deposit of $10,000$10,000 today will become at a compound annual today will become at a compound annual interest rate ofinterest rate of 10%10% for 5 years. (From the PPT for for 5 years. (From the PPT for the Book.)the Book.)

Story Problem Story Problem ExampleExample

Story Problem Story Problem ExampleExample

0 1 2 3 4 55

$10,000$10,000

FVFV55

10%


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Story Problem Story Problem SolutionSolution

Story Problem Story Problem SolutionSolution

Calculation based on the

general formula:

FVFVnn = P0 (1+i)n

FVFV55 = $10,000 (1+ 0.10)5

= $16,105.10$16,105.10


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Compounding PeriodsCompounding Periods Per year:Per year: for every year you keep your for every year you keep your

money in the bank calculate amount money in the bank calculate amount times (1+i) where i= the interest ratetimes (1+i) where i= the interest rate

Per half year:Per half year: for every year amount for every year amount times (1+ i/2) to the power 2. We will times (1+ i/2) to the power 2. We will use the symbol “use the symbol “m=2m=2” indicating that ” indicating that we compound twice per year (every we compound twice per year (every half year).half year).

Per quarterPer quarter (3 months that is 4 times (3 months that is 4 times per year): for every year amount times per year): for every year amount times (1+i/4) to the power 4 (m=4)(1+i/4) to the power 4 (m=4)

Per monthPer month: amount times (1+i/12) to : amount times (1+i/12) to the power 12 (m=12)the power 12 (m=12)

Per dayPer day: amount times (1+i/365) to the : amount times (1+i/365) to the power 365 (m=365)power 365 (m=365)

Compounding…


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Continuous CompoundingContinuous Compounding

Future Value= Amount* e^ Future Value= Amount* e^ (i*t)(i*t)

Present Value= Amount* e^ Present Value= Amount* e^ -(i*t)-(i*t)

Where e is 2.8182… and t is Where e is 2.8182… and t is time.time.


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Sometimes I will ask …Sometimes I will ask … You to calculate the interest You to calculate the interest

raterate

Or the number of periods Or the number of periods that the money is that the money is outstanding…outstanding…

We will look at the formulas We will look at the formulas nownow AND AND of courseof course Excel Excel has got perfect functions to has got perfect functions to help you.help you.

TAKE NOTES!TAKE NOTES!


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We will use the We will use the ““Rule-of-72Rule-of-72””..

Double Your Money!!!Double Your Money!!!Double Your Money!!!Double Your Money!!!

Quick! Quick! How long does it take to double How long does it take to double $5,000 at a compound rate of 12% per $5,000 at a compound rate of 12% per

year (approx.)?year (approx.)?


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Approx. Approx. Years Years to Double to Double = = 7272 / / i%i%

7272 / / 12%12% = = 6 Years6 Years[Actual Time is 6.12 Years][Actual Time is 6.12 Years]

The “Rule-of-72”The “Rule-of-72”The “Rule-of-72”The “Rule-of-72”

Quick! Quick! How long does it take to double How long does it take to double $5,000 at a compound rate of 12% per $5,000 at a compound rate of 12% per

year (approx.)?year (approx.)?


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Find the nominal rate of Find the nominal rate of interestinterest

Find the nominal interest rate pa Find the nominal interest rate pa compounded per half year (semi compounded per half year (semi annually) at which $2500 grows to annually) at which $2500 grows to $4000 in 5 years$4000 in 5 years


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Your answerYour answer

$2500*(1+i/2)^10=$4000 $2500*(1+i/2)^10=$4000 what is i?what is i?

(1+i/2)^10=$4000/$2500(1+i/2)^10=$4000/$2500 1+i/2=(4000/2500)^0.101+i/2=(4000/2500)^0.10 i= (((4000/2500)^0.10)-i= (((4000/2500)^0.10)-

1)*21)*2

i= 9.6245%i= 9.6245%


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Work on ProblemsWork on Problems

You will find a Word Document on my You will find a Word Document on my website that has a number of website that has a number of problems.problems.

Please work on these for Monday. Please work on these for Monday. We will go over the answers then.We will go over the answers then.

Be ready to turn them in, if asked!Be ready to turn them in, if asked!


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The Federal Reserve SystemThe Federal Reserve System The Board of GovernorsThe Board of Governors The Fed BanksThe Fed Banks The Federal Open The Federal Open

Market Committee Market Committee (FOMC)(FOMC)


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The FedThe Fed: The Board of : The Board of GovernorsGovernors


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The Fed:The Fed: The Fed Banks The Fed BanksThe Twelve Federal Reserve Districts – The Fed Banks


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The Fed:The Fed: The FOMC The FOMC The FOMC: The Seven Governors, New York Fed President and

4 other Fed Presidents – 12 total members Set Monetary Policy for the United States In other words, the FOMC sets the “Federal Funds

Rate” – The interest rate that banks borrow funds from each other

The “Fed Funds” rate determines the “Prime” rate or the interest rate that banks charge their “best” corporate customers

An Increase in the fed funds rate means borrowing is more “expensive.”

A decrease?


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The Fed:The Fed: The FOMC The FOMC 2007 Members of the FOMC2007 Members of the FOMC MembersMembers

Ben S. BernankeBen S. Bernanke, Board of Governors, Chairman, Board of Governors, ChairmanTimothy F. Timothy F. GeithnerGeithner, New York, Vice Chairman, New York, Vice ChairmanCharles L. EvansCharles L. Evans, Chicago, ChicagoThomas M. Thomas M. HoenigHoenig, Kansas City, Kansas CityDonald L. KohnDonald L. Kohn, Board of Governors, Board of GovernorsRandall S. Kroszner, Board of GovernorsRandall S. Kroszner, Board of GovernorsFrederic S. Mishkin, Board of GovernorsFrederic S. Mishkin, Board of GovernorsWilliam Poole, St. LouisWilliam Poole, St. LouisEric S. Rosengren, BostonEric S. Rosengren, BostonKevin M. Warsh, Board of GovernorsKevin M. Warsh, Board of Governors

Alternate MembersAlternate MembersRichard W. Fisher, DallasRichard W. Fisher, DallasSandra Pianalto, ClevelandSandra Pianalto, ClevelandCharles I. Plosser, PhiladelphiaCharles I. Plosser, PhiladelphiaGary H. Stern, MinneapolisGary H. Stern, MinneapolisChristine M. Cumming, First Vice President, New York Christine M. Cumming, First Vice President, New York

Next Meeting: Sept. 18, 2007


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The Fed:The Fed: The Chairman The Chairman

Ben Bernanke

Down .25% or ? Sept. 18, 2007


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The Time Value of Money The Time Value of Money Continued Next Week! (Ch. 3)Continued Next Week! (Ch. 3)

ANNUITIES NEXT!ANNUITIES NEXT!

Introduction to Financial Management FIN 102 – Week 3 Dr. Andrew L. H. Parkes “A practical and...

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