某咨询公司战略分析方法(英文版)

1、Author: Collins QianReviewer: Brian Bilello bcBain MathMarch 1998Copyright 1998 Bain & Company, Inc. 1BOSCopyright 1998 Bain & Company, Inc. Bain MathAgenda Basic mathFinancial mathStatistical math2BOSCopyright 1998 Bain & Company, Inc. Bain MathAgenda Basic math ratioproportionpercentin

2、flationforeign exchangegraphingFinancial mathStatistical math3BOSCopyright 1998 Bain & Company, Inc. Bain 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 reven

3、ue = Given: = =Answer:Price Unit$9MM 1.5MMThe math for ratios is simple. Identifying a relevant unit can be challengingtotal units = price/unit = $9.0 MM1.5 MM$?$6.04BOSCopyright 1998 Bain & Company, Inc. Bain MathProportion Definition:If the ratio of A to B is equal to the ratio of C to D, then

4、 A and B are proportional to C and D.Application: = It follows that A x D = B x CABCDRevenue =SG&A =Given:$135MM$ 83MM$270MM$?19961999Answer:$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 19

5、96, 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)?= $166MM5BOSCopyright 1998 Bain & Company, Inc. Bain MathPercent Definition:A percentage (abbreviated “percent”) is a convenient way to express a ratio. Litera

6、lly, 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. In her second year, she logged 25,000 miles. What is the percentage increase in miles?Given:A percentage can be used to

7、 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 valueoriginal valueThe ratio of 5 to 20 is or 0.255206BOSCopyright 1998 Bain & Company, Inc. Bain MathInflation - Definiti

8、onsIf 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 of a dollar figure over time (e.g., revenue growth, unit cost growth), it is necessary to s

9、ubtract 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 Terminology:1. Real (constant) dollars:2. Nominal(current) dollars:3. Price deflatorPrice deflator

10、 (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 “base” years dollar terms (i.e., inflation has been taken out). Any year can be chosen as the

11、 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).Inflation is defined as the year-over-year decrease in the value of a unit of currency.7BOSCopyri

12、ght 1998 Bain & Company, Inc. Bain 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 all Bain employees to use.Year1996=100*% ChangeYear1996=10

13、0*% Change197027.79 5.32 1996100.00 1.95 197129.23 5.18 1997101.97 1.97 197230.46 4.23 1998104.48 2.46 197332.18 5.64 1999107.10 2.51 197435.07 8.99 2000109.80 2.52 197538.36 9.37 2001112.51 2.47 197640.61 5.86 2002115.41 2.58 197743.23 6.45 2003118.58 2.75 197846.37 7.26 2004122.02 2.90 197950.35 8

14、.58 2005125.65 2.97 198055.00 9.25 2006129.31 2.92 198160.18 9.41 2007132.96 2.82 198263.97 6.30 2008136.57 2.71 198366.68 4.24 2009140.26 2.70 198469.21 3.79 2010144.06 2.71 198571.59 3.43 2011147.89 2.65 198673.46 2.62 2012151.90 2.72 198775.71 3.06 2013156.05 2.73 198878.48 3.65 2014160.29 2.72 1

15、98981.79 4.22 2015164.73 2.76 199085.34 4.34 2016169.25 2.75 199188.72 3.97 2017173.83 2.71 199291.16 2.75 2018178.53 2.70 199393.54 2.62 2019183.33 2.69 199495.67 2.28 2020188.31 2.71 199598.08 2.51 A deflator table lists price deflators for a number of years.8BOSCopyright 1998 Bain & Company,

16、Inc. Bain 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 figures).Since most companies use nominal figures in their annual reports, if you are showing the

17、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 real figuresNote :When to use real vs. Nominal figures :Whether you should use real (constant)

18、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 using real figures, you should also note what you have chosen as the base year.9BOSCopyright 1998 B

19、ain & Company, Inc. Bain 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 1970. When you use nominal dollars, it is impossible to tell how muc

20、h of the price increase was due to inflation.$2,00072Nominal dollars4.5%Price of a GE Washer19707173 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92$0$500$1,000$1,500CAGR10BOSCopyright 1998 Bain & Company, Inc. Bain MathInflation - Example (2) Price of a GE Washer CAGR(1970-1992)(1.0%)4

21、.5%197071 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92$0$500$1,000$1,500$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.11BOSCopyright 1998 Bain &am

22、p; Company, Inc. Bain MathInflation - 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?12BOSCopyright 1998 Bain & Company, Inc. Bain MathInflatio

23、n - Exercise (2) Answer:Step 1: Choose a base year. For this example, 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 (c

24、urrent year) Dollar figure (current year)Price deflator (base year)Dollar 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.

25、54 85.3431.2 X = , X = 32.895.67 85.3436.8 X = , X = 39.698.08 85.3445.5 X = , X = 43.5100.00 85.3451.0 XRevenue ($ Million)199020.5199124.3199225.7199328.5199432.8199539.6199643.5 (1996) = 100.0013BOSCopyright 1998 Bain & Company, Inc. Bain MathForeign Exchange - Definitions Investments employe

26、d in making payments between countries (e.g., paper currency, notes, checks, bills of exchange, and 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

27、 of holding money in that currency relative to in other currencies. In efficient international markets, exchange rates will adjust to compensate for differences in interest and inflation rates between currenciesForeign Exchange:Exchange Rate:14BOSCopyright 1998 Bain & Company, Inc. Bain MathFore

28、ign Exchange Rates1) US$ equivalent = US dollars per 1 selected foreign currency unit2) Currency per US$ = selected foreign currency units per 1 US dollar The Wall Street Journal Tuesday, November 25, 1997Currency TradingMonday, November 24, 1997Exchange RatesCountryArgentina (Peso)Britain(Pound)US$

29、 Equiv.11.00011.6910Currency per US$20.99990.5914CountryFrance(Franc)Germany (Mark)US$ Equiv.0.17190.5752Currency per US$5.81851.7384CountrySingapore (dollar)US$ Equiv.0.6289Currency per US$1.5900Financial publications, such as the Wall Street Journal, provide exchange rates. 15BOSCopyright 1998 Bai

30、n & Company, Inc. Bain MathForeign Exchange - Exercises Question 1:Answer:Question 2:Answer:Question 3:Answer: 650.28 US dollars = ? British poundsfrom table: 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 = ? S

31、ingapore 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$0.5752 1 Mark 1.59 Singapore dollar US$ 116BOSCopyright 1998 Bain & Company, Inc. Bain MathGraphing - Linear X0Y(X1, Y1)(X2, Y2)bXYThe formula fo

32、r 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 x17BOSCopyright 1998 Bain & Company, Inc. Bain MathGraphing - Linear Exercise #1 Formula for line: y = mx + bIn this exercise, y = 15x + 400, where, 02004006008001,0001,20

33、01,4001,6001,800$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 (when people = 0)A caterer charges $400.00 for setting up a party, plus $15.00 fo

34、r 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-versa18BOSCopyright 1998 Bain & Company, Inc. Bain MathGraphing - Linear Exercise #2 (1) A lamp manufacturer has collected a set of produ

35、ction 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?19BOSCopyright 1998 Bain & Company, Inc. Bain MathGraphing - Linear Exercise #2 (2) 08,00

36、016,000Production 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 = 2,000 - 10 (100)

37、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 $16,00020BOSCopyright 1998 Bain & Company, Inc. Bain MathGraphing - Logarithmic

38、(1) Log:A “log” 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=10

39、2 can be written as log10 100=2 or log 100=221BOSCopyright 1998 Bain & Company, Inc. Bain 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,

40、000100101Log paper typically uses base 10Log-log paper is logarithmic on both axes; semi-log paper is logarithmic on one axis and linear on the otherLog ScaleLinear Scale22BOSCopyright 1998 Bain & Company, Inc. Bain MathGraphing - Logarithmic (3) The most useful feature of a log graph is that eq

41、ual multiplicative changes in data are represented by equal distances on the axesthe 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 o

42、f change between data points in a seriesLog scales are often used for:Experience 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 changi

43、ng at the same rate from one point to the nextCurving upwardThe rate of change is increasingCurving downwardThe rate of change is decreasingIn many situations, it is convenient to use logarithms.23BOSCopyright 1998 Bain & Company, Inc. Bain MathAgenda Basic mathFinancial mathsimple interestcompo

44、und interestpresent valuerisk and returnnet present valueinternal rate of returnbond and stock valuationStatistical math24BOSCopyright 1998 Bain & Company, Inc. Bain MathSimple Interest Definition:Simple interest is computed on a principal amount for a specified time periodThe formula for simple

45、 interest is:i = prtwhere,p = the principalr = the annual interest ratet = the number of yearsApplication:Simple interest is used to calculate 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 inter

46、est will she receive at the end of two months?Answer:i = prti = $5,000 x 0.06 x i = $50 2 1225BOSCopyright 1998 Bain & Company, Inc. Bain MathCompound Interest “Money makes money. And the money that money makes, makes more money.”- Benjamin FranklinDefinition:Compound interest is computed on a p

47、rincipal 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 this interest to the original principal. The interest for the following period is computed by using the new principal (i.e., the or

48、iginal 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 raten = the number of times compounding is done in a yeart = the number of yearsr nNotes:As the number of times compounding is done

49、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 annual interest rate (or yield) is the simple interest rate that would generate the same amount of interest as would the compound

50、rate26BOSCopyright 1998 Bain & Company, Inc. Bain 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$1,250Dollarsi1i2i3i4A1A2A3A41st Quarter2nd Quarter3rd Quarter4th QuarterGiven:What amount will you receive at the end of

51、 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, and then added to the principal. This becomes the new principal on which the next periods interes

52、t 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 = $1,030+30.90A3 = $1,060.90+31.83A4 = $1,092.73+32.78= $1,030= $1,060.90= $1,092.73= $1,125.5127BOSCo

53、pyright 1998 Bain & Company, Inc. Bain 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 dollar received tomorrow, because money can be invested with some retur

54、n.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 prese

55、nt 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)n28BOSCopyright 1998 Bain & Company, Inc. Bain MathPresent Value - Definitions (2) The present value of a perpetuity (i.e., a

56、n 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 perpetuity:Annuity:C rC r-gPV =C r-1 (1+ r)

57、nC r29BOSCopyright 1998 Bain & Company, Inc. Bain 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 prefer to

58、 receive? 30BOSCopyright 1998 Bain & Company, Inc. Bain 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

59、 $1.50, PV = = $9.384)A perpetuity 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)5An

60、swer:31BOSCopyright 1998 Bain & Company, Inc. Bain MathRisk 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 without sacrificing returnRisk averse investors demand a higher return on higher risk inv