Introduction to Financial Management FIN 102 – Week 3 Dr. Andrew L. H. Parkes “A practical and hands on course on the valuation and financial management of corporations”

Intro. to Financial Managment - Week 22 The Time Value of Money  The Interest Rate  Simple Interest  Compound Interest  Lump Sum Calculations Ben Bernanke, Fed Chair Four Basic Topics:

Intro. to Financial Managment - Week 23 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!”

Intro. to Financial Managment - Week 24 We Will use Excel …  This chapter is about straight forward calculations of Future Values of cash and Present Values of cash  It ’ s much easier to use Excel if you know how to work with it …  You may use a calculator, which is often just as fast. These are explained in the text of Chapter 3 and the book PPT.  However, nowadays everybody uses spreadsheets as well. So you better learn to use them if you don ’ t know how.

Intro. to Financial Managment - Week 25 What do you prefer …  $ 1000 now or  $ 1000 next year?  If you are like anybody else you know the answer very well …  That ’ s all of us know there is Time Value to money and that is what 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

Intro. to Financial Managment - Week 26 Future Value  You put money in the bank at 3.27% interest (today’s rate in China), how much money do you have after ___ years?  You must compound the interest since every year you will earn simple interest on the amount you put into bank initially as well as earning interest on the interest of prior years  You must compound the interest since every year you will earn simple interest on the amount you put into bank initially as well as earning interest on the interest of prior years ! See my website for the IPO article!

Intro. to Financial Managment - Week 27 Time and Compounding   TIME allows you the opportunity to postpone consumption and earn INTEREST. To Reiterate:  Simple Interest – –Interest paid (earned) on only the original amount, or principal borrowed (lent).  Compound Interest: - Interest paid (earned) on any previous interest earned, as well as on the principal borrowed (lent).

Intro. to Financial Managment - Week 28 The “Simple” Formula Future Value (FV) = PV + PV * (1 + i) OR FV = PV*(1+i) For multiple periods: FV = PV*(1+i) n So for two periods: FV = PV*(1+i) 2

Intro. to Financial Managment - Week 29 Time 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 today; Time 1 is the end of the first period (year, month, etc.) or the beginning of the second period. Tick marks occur at the end of periods, so Time 0 is today; Time 1 is the end of the first period (year, month, etc.) or the beginning of the second period. CF 0 CF 1 CF 3 CF i%

Intro. to Financial Managment - Week 210 Drawing time lines: $100 lump sum due in 2 years; 3-year $100 ordinary annuity i% 3 year $100 ordinary annuity i% $100 lump sum due in 2 years

Intro. to Financial Managment - Week 211 Make a Timeline … It Does Help  Drawing time lines: Uneven cash flow stream; CF0 = -$50, CF1 = $100, CF2 = $75, and CF3 = $ i% -50 Uneven cash flow stream

Intro. to Financial Managment - Week 212 What is the future value (FV) of an initial $100 after 3 years, if I/YR = 10%? NOTICE: The FV can be solved by using the arithmetic, financial calculator, and/or spreadsheet methods. (All are equivalent!) NOTICE: The FV can be solved by using the arithmetic, financial calculator, and/or spreadsheet methods. (All are equivalent!) FV = ? % 100

Intro. to Financial Managment - Week 213 Solving for FV: The arithmetic method After 1 year: After 1 year: –FV 1 = PV ( 1 + i ) = $100 (1.10) = $ After 2 years: After 2 years: –FV 2 = PV ( 1 + i ) 2 = $100 (1.10) 2 =$ After 3 years: After 3 years: –FV 3 = PV ( 1 + i ) 3 = $100 (1.10) 3 =$ After n years (general case): After n years (general case): –FV n = PV ( 1 + i ) n

Intro. to Financial Managment - Week 214 Solving for FV: The calculator method Solves the general FV equation. Solves the general FV equation. Requires 4 inputs into calculator, and will solve for the fifth. (Set to P/YR = 1 and END mode.) Requires 4 inputs into calculator, and will solve for the fifth. (Set to P/YR = 1 and END mode.) INPUTS OUTPUT NI/YRPMTPVFV

Intro. to Financial Managment - Week 215 The Present Value is simply the $100 you originally deposited. That is the value today! Present Value is the current value of a future amount of money, or a series of payments, evaluated at a given interest rate. Present Value is the current value of a future amount of money, or a series of payments, evaluated at a given interest rate. Simple Interest (PV) What is the Present Value (PV) of the previous problem? What is the Present Value (PV) of the previous problem?

Intro. to Financial Managment - Week 216 PV = ?100 So what is the present value (PV) of $100 due in 3 years, if I/YR = 10%? Finding the PV of a cash flow or series of cash flows when compound interest is applied is called discounting (the reverse of compounding). Finding the PV of a cash flow or series of cash flows when compound interest is applied is called discounting (the reverse of compounding). The PV shows the value of cash flows in terms of today’s purchasing power. The PV shows the value of cash flows in terms of today’s purchasing power %

Intro. to Financial Managment - Week 217 Solving for PV: The arithmetic method Solve the general FV equation for PV: Solve the general FV equation for PV: –PV = FV n / ( 1 + i ) n –PV = FV 3 / ( 1 + i ) 3 = $100 / ( 1.10 ) 3 = $100 / ( 1.10 ) 3 = $75.13 = $75.13

Intro. to Financial Managment - Week 218 Julie Miller wants to know how large her deposit of $10,000 today will become at a compound annual interest rate of 10% for 5 years. (From the PPT for the Book.) Story Problem Example $10,000 FV 5 10%

Intro. to Financial Managment - Week 219 Story Problem Solution u Calculation based on the general formula: FV n FV n = P 0 (1+i) n FV 5 $16, FV 5 = $10,000 ( ) 5 = $16,105.10

Intro. to Financial Managment - Week 220 Compounding Periods Per year: for every year you keep your money in the bank calculate amount times (1+i) where i= the interest rate Per year: for every year you keep your money in the bank calculate amount times (1+i) where i= the interest rate Per half year: for every year amount times (1+ i/2) to the power 2. We will use the symbol “ m=2 ” indicating that we compound twice per year (every half year). Per half year: for every year amount times (1+ i/2) to the power 2. We will use the symbol “ m=2 ” indicating that we compound twice per year (every half year). Per quarter (3 months that is 4 times per year): for every year amount times (1+i/4) to the power 4 (m=4) Per quarter (3 months that is 4 times per year): for every year amount times (1+i/4) to the power 4 (m=4) Per month: amount times (1+i/12) to the power 12 (m=12) Per month: amount times (1+i/12) to the power 12 (m=12) Per day: amount times (1+i/365) to the power 365 (m=365) Per day: amount times (1+i/365) to the power 365 (m=365) Compounding…

Intro. to Financial Managment - Week 221 Continuous Compounding  Future Value= Amount* e^ (i*t)  Present Value= Amount* e^ -(i*t)  Where e is … and t is time.

Intro. to Financial Managment - Week 222 Sometimes I will ask …  You to calculate the interest rate  Or the number of periods that the money is outstanding …  We will look at the formulas now AND of course Excel has got perfect functions to help you.  TAKE NOTES!

Intro. to Financial Managment - Week 223 We will use the “Rule-of-72”. Double Your Money!!! Quick! How long does it take to double $5,000 at a compound rate of 12% per year (approx.)?

Intro. to Financial Managment - Week 224 Approx. Years to Double = 72 / i% 72 / 12% = 6 Years 72 / 12% = 6 Years [Actual Time is 6.12 Years] The “Rule-of-72” Quick! How long does it take to double $5,000 at a compound rate of 12% per year (approx.)?

Intro. to Financial Managment - Week 225 Find the nominal rate of interest Find the nominal interest rate pa compounded per half year (semi annually) at which $2500 grows to $4000 in 5 years Find the nominal interest rate pa compounded per half year (semi annually) at which $2500 grows to $4000 in 5 years

Intro. to Financial Managment - Week 226 Your answer $2500*(1+i/2)^10=$4000 what is i? $2500*(1+i/2)^10=$4000 what is i? (1+i/2)^10=$4000/$2500 (1+i/2)^10=$4000/$ i/2=(4000/2500)^ i/2=(4000/2500)^0.10 i= (((4000/2500)^0.10)-1)*2 i= (((4000/2500)^0.10)-1)*2 i= % i= %

Intro. to Financial Managment - Week 227 Work on Problems You will find a Word Document on my website that has a number of problems. You will find a Word Document on my website that has a number of problems. Please work on these for Monday. We will go over the answers then. Please work on these for Monday. We will go over the answers then. Be ready to turn them in, if asked! Be ready to turn them in, if asked!

Intro. to Financial Managment - Week 228 The Federal Reserve System The Board of Governors The Board of Governors The Fed Banks The Fed Banks The Federal Open Market Committee (FOMC) The Federal Open Market Committee (FOMC)

Intro. to Financial Managment - Week 229 The Fed: The Board of Governors

Intro. to Financial Managment - Week 230 The Fed: The Fed Banks The Twelve Federal Reserve Districts – The Fed Banks

Intro. to Financial Managment - Week 231 The Fed: 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?

Intro. to Financial Managment - Week 232 The Fed: The FOMC  2007 Members of the FOMC  Members Ben S. Bernanke, Board of Governors, Chairman Timothy F. Geithner, New York, Vice Chairman Charles L. Evans, Chicago Thomas M. Hoenig, Kansas City Donald L. Kohn, Board of Governors Randall S. Kroszner, Board of Governors Frederic S. Mishkin, Board of Governors William Poole, St. Louis Eric S. Rosengren, Boston Kevin M. Warsh, Board of Governors Ben S. Bernanke Timothy F. Geithner Charles L. Evans Thomas M. Hoenig Donald L. Kohn Randall S. Kroszner Frederic S. Mishkin William Poole Eric S. Rosengren Kevin M. Warsh Ben S. Bernanke Timothy F. Geithner Charles L. Evans Thomas M. Hoenig Donald L. Kohn Randall S. Kroszner Frederic S. Mishkin William Poole Eric S. Rosengren Kevin M. Warsh  Alternate Members Richard W. Fisher, Dallas Sandra Pianalto, Cleveland Charles I. Plosser, Philadelphia Gary H. Stern, Minneapolis Christine M. Cumming, First Vice President, New York Richard W. Fisher Sandra Pianalto Charles I. Plosser Gary H. Stern Christine M. Cumming Richard W. Fisher Sandra Pianalto Charles I. Plosser Gary H. Stern Christine M. Cumming Next Meeting: Sept. 18, 2007

Intro. to Financial Managment - Week 233 The Fed: The Chairman Ben Bernanke Down.25% or ? Sept. 18, 2007

Intro. to Financial Managment - Week 234 The Time Value of Money Continued Next Week! (Ch. 3) ANNUITIES NEXT!