战略分析工具分析方法bainmath

1、Author: Collins QianReviewer: Brian Bilello bcBain MathMarch 1998Copyright 1998 Bain & Company, Inc. 1CU7112997ECABain MathAgenda Basic mathFinancial mathStatistical math2CU7112997ECABain MathAgenda Basic math ratioproportionpercentinflationforeign exchangegraphingFinancial mathStatistical math3CU71

2、12997ECABain MathRatio Definition:Application:Note:The ratio of A to B is written or A:BABA ratio can be used to calculate price per unit ( ), given the total revenue and total unitsPrice Unittotal revenue = Given: = =Answer:Price Unit$9MM 1.5MMThe math for ratios is simple. Identifying a relevant u

3、nit can be challengingtotal units = price/unit = $9.0 MM1.5 MM$?$6.04CU7112997ECABain MathProportion Definition:If the ratio of A to B is equal to the ratio of C to D, then A and B are proportional to C and D.Application: = It follows that A x D = B x CABCDRevenue =SG&A =Given:$135MM$ 83MM$270MM$?19

4、961999Answer:$135MM $270MM$ 83MM $?135MM x ? = 83MM x 270MM83MMx270MM 135MM=The concept of proportion can be used to project SG&A costs in 1999, given revenue in 1996, SG&A costs in 1996, and revenue in 1999 (assuming SG&A and revenue in 1999 are proportional to SG&A and revenue in 1996)?= $166MM5CU

5、7112997ECABain MathPercent Definition:A percentage (abbreviated “percent”) is a convenient way to express a ratio. Literally, percentage means “per 100.”Application:In percentage terms, 0.25 = 25 per 100 or 25%In her first year at Bain, an AC logged 7,000 frequent flier miles by flying to her client

6、. In her second year, she logged 25,000 miles. What is the percentage increase in miles?Given:A percentage can be used to express the change in a number from one time period to the nextAnswer: - 1 = 3.57 - 1 = 2.57 = 257%25,000 7,000% change = = - 1 new value - original value original valuenew value

7、original valueThe ratio of 5 to 20 is or 0.255206CU7112997ECABain MathInflation - DefinitionsIf an item cost $1.00 in 1997 and cost $1.03 in 1998, inflation was 3% from 1997 to 1998. The item is not intrinsically more valuable in 1998 - the dollar is less valuableWhen calculating the “real” growth o

8、f a dollar figure over time (e.g., revenue growth, unit cost growth), it is necessary to subtract out the effects of inflation. Inflationary growth is not “real” growth because inflation does not create intrinsic value.Definition:A price deflator is a measure of inflation over time. Related Terminol

9、ogy:1. Real (constant) dollars:2. Nominal(current) dollars:3. Price deflatorPrice deflator (current year) Price deflator (base year)Inflation between current year and base year=Dollar figure (current year) Dollar figure (base year)=Dollar figures for a number of years that are stated in a chosen “ba

10、se” years dollar terms (i.e., inflation has been taken out). Any year can be chosen as the base year, but all dollar figures must be stated in the same base yearDollar figures for a number of years that are stated in each individual years dollar terms (i.e., inflation has not been taken out).Inflati

11、on is defined as the year-over-year decrease in the value of a unit of currency.7CU7112997ECABain Math Inflation - U.S. Price Deflators *1996 is the base yearNote: These are the U.S. Price Deflators which WEFA Group has forecasted through the year 2020. The library has purchased this time series for

12、 all Bain employees to use.A deflator table lists price deflators for a number of years.8CU7112997ECABain MathInflation - Real vs. Nominal Figures To understand how a company has performed over time (e.g., in terms of revenue, costs, or profit), it is necessary to remove inflation, (i.e. use real fi

13、gures).Since most companies use nominal figures in their annual reports, if you are showing the clients revenue over time, it is preferable to use nominal figures.For an experience curve, where you want to understand how price or cost has changed over time due to accumulated experience, you must use

14、 real figuresNote :When to use real vs. Nominal figures :Whether you should use real (constant) figures or nominal (current) figures depends on the situation and the clients preference.It is important to specify on slides and spreadsheets whether you are using real or nominal figures. If you are usi

15、ng real figures, you should also note what you have chosen as the base year.9CU7112997ECABain MathInflation - Example (1) (1970 -1992)Adjusting for inflation is critical for any analysis looking at prices over time. In nominal dollars, GEs washer prices have increased by an average of 4.5% since 197

16、0. When you use nominal dollars, it is impossible to tell how much of the price increase was due to inflation.$2,00072Nominal dollars4.5%Price of a GE Washer1970717374757677787980818283848586878889909192$0$500$1,000$1,500CAGR10CU7112997ECABain MathInflation - Example (2) Price of a GE Washer CAGR(19

17、70-1992)(1.0%)4.5%197071727374757677787980818283848586878889909192$0$500$1,000$1,500$2,000$2,500$3,000Nominal dollarsReal (1992) dollarsIf you use real dollars, you can see what has happened to inflation-adjusted prices. They have fallen an average of 1.0% per year.11CU7112997ECABain MathInflation -

18、 Exercise (1) Consider the following revenue stream in nominal dollars:Revenue ($ million)199020.5199125.3199227.4199331.2199436.8199545.5199651.0How do we calculate the revenue stream in real dollars?12CU7112997ECABain MathInflation - Exercise (2) Answer:Step 1: Choose a base year. For this example

19、, we will use 1990Step 2: Find deflators for all years (from the deflator table):(1990) = 85.34(1991) = 88.72(1992) = 91.16(1993) = 93.54(1994) = 95.67(1995) = 98.08Step 3: Use the formula to calculate real dollars:Price deflator (current year) Dollar figure (current year)Price deflator (base year)D

20、ollar figure (base year)Step 4: Calculate the revenue stream in real (1990) dollars terms:1990:1991:1992:1993: = , X = 20.585.34 85.341994:1995:1996:=20.5 X = , X = 24.388.72 85.3425.3 X = , X = 25.791.16 85.3427.4 X = , X = 28.593.54 85.3431.2 X = , X = 32.895.67 85.3436.8 X = , X = 39.698.08 85.34

21、45.5 X = , X = 43.5100.00 85.3451.0 XRevenue ($ Million)199020.5199124.3199225.7199328.5199432.8199539.6199643.5 (1996) = 100.0013CU7112997ECABain MathForeign Exchange - Definitions Investments employed in making payments between countries (e.g., paper currency, notes, checks, bills of exchange, and

22、 electronic notifications of international debits and credits)Price at which one countrys currency can be converted into anothersThe 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 mark

23、ets, exchange rates will adjust to compensate for differences in interest and inflation rates between currenciesForeign Exchange:Exchange Rate:14CU7112997ECABain MathForeign Exchange Rates1) US$ equivalent = US dollars per 1 selected foreign currency unit2) Currency per US$ = selected foreign curren

24、cy units per 1 US dollar The Wall Street Journal Tuesday, November 25, 1997Currency TradingMonday, November 24, 1997Exchange RatesCountryArgentina (Peso)Britain(Pound)US$ Equiv.11.00011.6910Currency per US$20.99990.5914CountryFrance(Franc)Germany (Mark)US$ Equiv.0.17190.5752Currency per US$5.81851.7

25、384CountrySingapore (dollar)US$ Equiv.0.6289Currency per US$1.5900Financial publications, such as the Wall Street Journal, provide exchange rates. 15CU7112997ECABain MathForeign Exchange - Exercises Question 1:Answer:Question 2:Answer:Question 3:Answer: 650.28 US dollars = ? British poundsfrom table

26、: 0.5914 = US$ 1.00 $650.28 x = 384.581490.50 Francs = ? US$from table: $0.1719 = 1 Franc 1490.50 Franc x = $256.221,000 German Marks = ? Singapore dollarsfrom table: $0.5752 = 1 Mark 1.59 Singapore dollar =US$ 1 1,000 German Marks x x = 914.57 Singapore dollars 0.5914 US$1$0.1719 1 Franc$0.5752 1 M

27、ark 1.59 Singapore dollar US$ 116CU7112997ECABain MathGraphing - Linear X0Y(X1, Y1)(X2, Y2)bXYThe 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 x17CU7112997ECABain MathGraphing - Linear Exercise #1 Formula for l

28、ine: y = mx + bIn this exercise, y = 15x + 400, where, 02004006008001,0001,2001,4001,6001,800$2,000Dollars changing050100People(100,1900)(50,1150)The caterer would charge $1900 for a 100 person party. yxX axis = peopleY axis = dollars chargedm = slope = = 15b = Y intercept = 400 dollars charged (whe

29、n people = 0)A caterer charges $400.00 for setting up a party, plus $15.00 for each person. How much would the caterer charge for a 100 person party? Using this formula, you can solve for dollars charged (y), given people (x), and vice-versa18CU7112997ECABain MathGraphing - Linear Exercise #2 (1) A

30、lamp manufacturer has collected a set of production data as follows: Number of lamps Produced/DayProduction 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?19CU7112997ECABain MathGraphing - Linear Exerci

31、se #2 (2) 08,00016,000Production Cost/Day05001,0001,500Produced/Day(1,500, 16,000)(1,000, 11,000)Formula for line: y = mx + bX axis = # of lamps produced/day Y axis = production cost/dayM = slope = = = = 10b = Y intercept = production cost (i.e., the fixed cost) when lamps = 0y = mx + bb = y-mxb = 2

32、,000 - 10 (100)b = 1,000 The fixed cost is $1,000y = 10 x + 1,000For 1,500 lamps:y = 10 (1,500) + 1,000y = 15,000 + 1,000y = 16,00011,000-2,000 1,000 - 1009,000 900(100, 2,000)X = 900Y = 9,000yxThe cost of producing 1,500 lamps is $16,00020CU7112997ECABain MathGraphing - Logarithmic (1) Log:A “log”

33、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 = 10 x, then log10 Y = XMathematically, ifWhere, Y = given number10 = base X = power (or log)For example: 100=102 can be written

34、 as log10 100=2 or log 100=221CU7112997ECABain MathGraphing - Logarithmic (2) For a log scale in base 10, as the linear scale values increase by ten times, the log values increase by 1.98765432101,000,000,000100,000,00010,000,0001,000,000100,00010,0001,000100101Log paper typically uses base 10Log-lo

35、g paper is logarithmic on both axes; semi-log paper is logarithmic on one axis and linear on the otherLog ScaleLinear Scale22CU7112997ECABain MathGraphing - Logarithmic (3) The most useful feature of a log graph is that equal multiplicative changes in data are represented by equal distances on the a

36、xesthe distance between 10 and 100 is equal to the distance between 1,000,000 and 10,000,000 because the multiplicative change in both sets of numbers is the same, 10It is convenient to use log scales to examine the rate of change between data points in a seriesLog scales are often used for:Experien

37、ce curve (a log/log scale is mandatory - natural logs (ln or loge) are typically usedprices and costs over timeGrowth Share matricesROS/RMS graphsLine Shape of Data PlotsExplanationA straight lineThe data points are changing at the same rate from one point to the nextCurving upwardThe rate of change

38、 is increasingCurving downwardThe rate of change is decreasingIn many situations, it is convenient to use logarithms.23CU7112997ECABain MathAgenda Basic mathFinancial mathsimple interestcompound interestpresent valuerisk and returnnet present valueinternal rate of returnbond and stock valuationStati

39、stical math24CU7112997ECABain MathSimple Interest Definition:Simple interest is computed on a principal amount for a specified time periodThe formula for simple interest is:i = prtwhere,p = the principalr = the annual interest ratet = the number of yearsApplication:Simple interest is used to calcula

40、te the return on certain types of investmentsGiven: A person invests $5,000 in a savings account for two months at an annual interest rate of 6%. How much interest will she receive at the end of two months?Answer:i = prti = $5,000 x 0.06 x i = $50 2 1225CU7112997ECABain MathCompound Interest “Money

41、makes money. And the money that money makes, makes more money.”- Benjamin FranklinDefinition:Compound interest is computed on a principal amount and any accumulated interest. A bank that pays compound interest on a savings account computes interest periodically (e.g., daily or quarterly) and adds th

42、is interest to the original principal. The interest for the following period is computed by using the new principal (i.e., the original principal plus interest).The formula for the amount, A, you will receive at the end of period n is:A = p (1 + )ntwhere,p = the principalr = the annual interest rate

43、n = the number of times compounding is done in a yeart = the number of yearsr nNotes:As the number of times compounding is done per year approaches infinity (as in continuous compounding), the amount, A, you will receive at the end of period n is calculated using the formula:A = pertThe effective an

44、nual interest rate (or yield) is the simple interest rate that would generate the same amount of interest as would the compound rate26CU7112997ECABain MathCompound Interest - Application $1,000.00$30.00$1,030.00$30.90$1,060.90$31.83$1,092.73$32.78$1,125.51$0$250$500$750$1,000$1,250Dollarsi1i2i3i4A1A

45、2A3A41st Quarter2nd Quarter3rd Quarter4th QuarterGiven:What amount will you receive at the end of one year if you invest $1,000 at an annual rate of 12% compounded quarterly?Answer:A = p (1+ ) nt = $1,000 (1 + ) 4 = $1,125.51r n0.12 4Detailed Answer:At the end of each quarter, interest is computed,

46、and then added to the principal. This becomes the new principal on which the next periods interest is calculated.Interest earned (i = prt):i1 = $1,000 x0.12x0.25i2 = $1,030 x0.12x0.25i3 = $1,060.90 x0.12x0.2514 = $1,092.73x0.12x0.25= $30.00= $30.90= $31.83= $32.78New principleA1 = $1,000+$30A2 = $1,

47、030+30.90A3 = $1,060.90+31.83A4 = $1,092.73+32.78= $1,030= $1,060.90= $1,092.73= $1,125.5127CU7112997ECABain MathPresent Value - Definitions (1) Time Value of Money:At different points in time, a given dollar amount of money has different values.One dollar received today is worth more than one dolla

48、r 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 re

49、turnn = 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)n28CU7112997ECABain MathPresent Value - Definitions (2) The pre

50、sent value of a perpetuity (i.e., an infinite cash stream) of is: PV = A perpetuity growing at rate of g has present value of: PV = The present value PV of an annuity, an investment which pays a fixed sum, each year for a specific number of years from year 1 to year n is: Perpetuity:Growing perpetui

51、ty:Annuity:C rC r-gPV =C r-1 (1+ r)nC r29CU7112997ECABain MathPresent Value - Exercise (1) 1)$10.00 today2)$20.00 five years from today3)A perpetuity of $1.504)A perpetuity of $1.00, growing at 5%5)A six year annuity of $2.00Assume you can invest at 16% per yearWhich of the following would you prefe

52、r to receive? 30CU7112997ECABain MathPresent Value - Exercise (2) *The present value is negative because this is the cash outflow required today receive a cash inflow at a later time1)$10.00 today, PV = $10.002)$20.00 five years from today, For HP12C: 5 163)A perpetuity of $1.50, PV = = $9.384)A per

53、petuity of $1.00, growing at 5%, PV = = $9.095)A six year annuity of $2.00, PV = - =$7.37 $1.50 0.16$1.00 0.16-0.05The option with the highest present value is #1, receiving $10.00 today$2.00 0.16 1 (1+ 0.16)5 $2.00 0.16FViPVN=(9.52)*20( )( ) PV = = $9.52$20.00 (1+0.16)5Answer:31CU7112997ECABain Mat

54、hRisk and Return Not all investments have the same riskinvesting in the U.S. stock market is more risky than investing in a U.S. government treasury bill, but less risky than investing in the stock market of a developing countryMost investors are risk averse - they avoid risk when they can do so wit

55、hout sacrificing returnRisk averse investors demand a higher return on higher risk investmentsA safe dollar is worth more than a risky one.32CU7112997ECABain MathNet Present Value Net present value (NPV) is the method used in evaluating investments whereby the present value of all case outflows requ

56、ired for the investment are added to the present value of all cash inflows generated by the investmentCash outflows have negative present values; cash inflows have positive present valuesThe rate used to calculate the present values is the discount rate. The discount rate is the required rate of ret

57、urn, or the opportunity cost of capital (i.e., the return you are giving up to pursue this project)An investment is acceptable if the NPV is positiveIn capital budgeting, the discount rate used is called the hurdle rateDefinition:33CU7112997ECABain MathInternal Rate of Return The internal rate of re

58、turn (IRR) is the discount rate for which the net present value is zero (i.e., the cost of the investment equals the future cash flows generated by the investment)The investment is acceptable when the IRR is greater than the required rate of return, or hurdle rateUnfortunately, comparing IRRs and ch

59、oosing the highest one sometimes does not lead to the correct answer. Therefore, IRRs should not be used to compare ject A can have a higher IRR but lower NPV than project B; that is, IRRs do NOT indicate the magnitude of an opportunityprojects with cash flows that fluctuate between nega

60、tive and positive more than once have multiple IRRsIRRs cannot be calculated for all negative cash flowsDefinition:34CU7112997ECABain MathNPV and IRR - Exercise *You can use this abbreviated format since the other data has not changed from part aGiven:An investment costing $2MM will produce cash flo