【正文】 t different points in time, a given dollar amount of money has different values.One dollar received today is worth more than one dollar received tomorrow, because money can be invested with some return.Present Value: Present value allows you to determine how much money that will be received in the future is worth todayThe formula for present value is: PV = Where, C = the amount of money received in the futurer = the annual rate of returnn = the number of years is called the discount factorThe present value PV of a stream of cash is then: PV = C0+ + +Where C0 is the cash expected today, C1 is the cash expected in one year, etc. 1 (1+r)nC (1+r)nC1 1+rC2 (1+r)2Cn (1+r)n28CU7112997ECABOSCopyright169。 1998 Bain Company, Inc. Bain MathCompound Interest “Money makes money. And the money that money makes, makes more money.” Benjamin FranklinDefinition: Compound interest is puted on a principal amount and any accumulated interest. A bank that pays pound interest on a savings account putes interest periodically (., daily or quarterly) and adds this interest to the original principal. The interest for the following period is puted by using the new principal (., the original principal plus interest).The formula for the amount, A, you will receive at the end of period n is:A = p (1 + )nt where, p = the principalr = the annual interest raten = the number of times pounding is done in a yeart = the number of yearsr nNotes: As the number of times pounding is done per year approaches infinity (as in continuous pounding), the amount, A, you will receive at the end of period n is calculated using the formula:A = pertThe effective annual interest rate (or yield) is the simple interest rate that would generate the same amount of interest as would the pound rate26CU7112997ECABOSCopyright169。 1998 Bain Company, Inc. Bain MathAgenda ?Basic math?Financial math–simple interest–pound interest–present value–risk and return– present value–internal rate of return–bond and stock valuation?Statistical math24CU7112997ECABOSCopyright169。 semilog paper is logarithmic on one axis and linear on the otherLog Scale Linear Scale22CU7112997ECABOSCopyright169。 1998 Bain Company, Inc. Bain MathGraphing Logarithmic (1) Log: A “l(fā)og” or logarithm of given number is defined as the power to which a base number must be raised to equal that given numberUnless otherwise stated, the base is assumed to be 10Y = 10x, then log10 Y = XMathematically, ifWhere, Y = given number10 = base X = power (or log)For example: 100=102 can be written as log10 100=2 or log 100=221CU7112997ECABOSCopyright169。 1998 Bain Company, Inc. Bain MathGraphing Linear Exercise 2 (1) A lamp manufacturer has collected a set of production data as follows: Number of lamps Produced/Day Production Cost/Day1008509009501,000$2,000$9,500$10,000$10,500$11,000What is the daily fixed cost of production, and what is the cost of making 1,500 lamps?19CU7112997ECABOSCopyright169。 1998 Bain Company, Inc. Bain MathGraphing Linear X0Y(X1, Y1)(X2, Y2)b XYThe formula for a line is:y = mx + bWhere,m = slope = = y2 y1 x2 x1b = the y intercept = the y coordinate when the x coordinate is “0”y x17CU7112997ECABOSCopyright169。 Francs = ? US$ from table: $ = 1 Franc Franc x = $1,000 German Marks = ? Singapore dollars from table: $ = 1 Mark Singapore dollar =US$ 1 1,000 German Marks x x = Singapore dollars 163。 1998 Bain Company, Inc. Bain MathForeign Exchange Exercises Question 1:Answer:Question 2:Answer:Question 3:Answer: US dollars = ? British poundsfrom table: 163。 1998 Bain Company, Inc. Bain MathForeign Exchange Definitions Investments employed in making payments between countries (., paper currency, notes, checks, bills of exchange, and electronic notifications of international debits and credits)Price at which one country’s currency can be converted into another’sThe interest and inflation rates of a given currency determine the value of holding money in that currency relative to in other currencies. In efficient international markets, exchange rates will adjust to pensate for differences in interest and inflation rates between currencies Foreign Exchange:Exchange Rate:14CU7112997ECABOSCopyright169。 1998 Bain Company, Inc. Bain MathInflation Exercise (1) Consider the following revenue stream in nominal dollars:Revenue ($ million) 1990199119921993199419951996How do we calculate the revenue stream in real dollars?12CU7112997ECABOSCopyright169。 1998 Bain Company, Inc. Bain MathInflation Example (1) (1970 1992)Adjusting for inflation is critical for any analysis looking at prices over time. In nominal dollars, GE’s washer prices have increased by an average of % since 1970. When you use nominal dollars, it is impossible to tell how much of the price increase was due to inflation.$2,00072Nominal dollars %Price of a GE Washer197071 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92$0$500$1,000$1,500CAGR10CU7112997ECABOSCopyright169。 1998 Bain Company, Inc. Bain Math Inflation . Price Deflators *1996 is the base yearNote: These are the . Price Deflators which WEFA Group has forecasted through the year 2023. The library has purchased this time series for all Bain employees to use.A deflator table lists price deflators for a number of years.8CU7112997ECABOSCopyright169。 1998 Bain Company, Inc. Bain MathPercent Definition: A percentage (a