貝恩－戰(zhàn)略分析方法之一ppt課件

1、Author: Collins QianReviewer: Brian Bilello bcBain MathMarch 1998Copyright 1998 Bain & Company, Inc. Bain MathAgenda Basic mathFinancial mathStatistical mathBain MathAgenda Basic math ratioproportionpercentinflationforeign exchangegraphingFinancial mathStatistical mathBain MathRatio Definition:Appli

2、cation: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 unit can be challengingtotal units = pri

3、ce/unit = $9.0 MM1.5 MM$?$6.0Bain MathProportion Definition:If the ratio of A to B is equal to the ratio of C to D, then A and B are proportional to C and D.Application: = It follows that A x D = B x CABCDRevenue =SG&A =Given:$MM$ 83MM$270MM$?19961999Answer:$MM $270MM$ 83MM $?MM x ? = 83MM x 270MM83

4、MMx270MM MM=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)?= $166MMBain MathPercent Definition:A percentage (abbreviated “percent) is

5、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. In her second year, she logged 25,000 miles. What is the percentage increase

6、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 valueoriginal valueThe ratio of 5 to 20 is or 0.25520Bain MathInflation - Definition

7、sIf 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 subt

8、ract 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 (cu

9、rrent 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 base

10、 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.Bain Math Infla

11、tion - 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.A deflator table lists price deflators for a number of years.Bain MathInflation -

12、 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 clients revenue over time

13、, 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) figures or nominal (curre

14、nt) 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.Bain MathInflation - Example (1) (1970 -1992)

15、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 much of the price increase was due to inflation.$2,00072Nominal dollars4

16、.5%Price of a GE Washer1970717374757677787980818283848586878889909192$0$500$1,000$1,500CAGRBain MathInflation - Example (2) Price of a GE Washer CAGR(1970-1992)(1.0%)4.5%197071727374757677787980818283848586878889909192$0$500$1,000$1,500$2,000$2,500$3,000Nominal dollarsReal (1992) dollarsIf you use r

17、eal dollars, you can see what has happened to inflation-adjusted prices. They have fallen an average of 1.0% per year.Bain MathInflation - Exercise (1) Consider the following revenue stream in nominal dollars:Revenue ($ million)199020.5199125.3199227.4199331.2199436.8199545.5199651.0How do we calcul

18、ate the revenue stream in real dollars?Bain MathInflation - 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

19、 the formula to calculate real dollars:Price deflator (current 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 8

20、5.3425.3 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 85.3445.5 X = , X = 43.5100.00 85.3451.0 XRevenue ($ Million)199020.5199124.3199225.7199328.5199432.8199539.6199643.5 (1996) = 100.00Bain MathForeign Exchange - Definitions Investme

21、nts employed 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 determin

22、e the value 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:Bain MathForeign Exchange Rates1) US$ equivalen

23、t = 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$ Equiv.11.00011.6910Currency per U

24、S$20.99990.5914CountryFrance(Franc)Germany (Mark)US$ 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. Bain MathForeign Exchange - Exercises Question 1:Answer:Q

25、uestion 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 = ? Singapore dollarsfrom table: $0.5752 = 1 Mark 1.59 Singapore dollar =US$ 1 1,000

26、 German Marks x x = 914.57 Singapore dollars 0.5914 US$1$0.1719 1 Franc$0.5752 1 Mark 1.59 Singapore dollar US$ 1Bain 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 “0y

27、xBain MathGraphing - Linear Exercise #1 Formula for line: 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 = s

28、lope = = 15b = Y intercept = 400 dollars charged (when 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-versaBain M

29、athGraphing - Linear Exercise #2 (1) A 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?Bain Mat

30、hGraphing - Linear Exercise #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 =

31、 0y = mx + bb = y-mxb = 2,000 - 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 $16,000Bain MathGraphing - Logarithmic (1) L

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

33、be written as log10 100=2 or log 100=2Bain 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-log pa

34、per is logarithmic on both axes; semi-log paper is logarithmic on one axis and linear on the otherLog ScaleLinear ScaleBain 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 axesthe distance be

35、tween 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:Experience curve (a log/lo

36、g 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 is increasingCurv

37、ing downwardThe rate of change is decreasingIn many situations, it is convenient to use logarithms.Bain MathAgenda Basic mathFinancial mathsimple interestcompound interestpresent valuerisk and returnnet present valueinternal rate of returnbond and stock valuationStatistical mathBain MathSimple Inter

38、est 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 calculate the return on certain types of investmentsG

39、iven: 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 12Bain MathCompound Interest “Money makes money. And the money that money makes, makes more mone

40、y.- 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 this interest to the original principal. The interest for the f

41、ollowing 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 raten = the number of times compounding is done in a yeart = the

42、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 annual interest rate (or yield) is the simple interest rate tha

43、t would generate the same amount of interest as would the compound rateBain 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

44、 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, and then added to the principal. This becomes the new principal on which th

45、e 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 = $1,030+30.90A3 = $1,060.90+31.83A4 = $1,092.73+32.78= $1,030= $1,060.90= $1,09

46、2.73= $1,125.51Bain 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 return.Present Value:Present

47、 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

48、 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)nBain MathPresent Value - Definitions (2) The present value of a perpetuity (i.e., an infinite cash stream) of is: PV = A perpetuity growing at rate of

49、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)nC rBain MathPresent Value - Exercise (1) 1)$10.00 today2)$20.00 fiv

50、e 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 receive? Bain MathPresent Value - Exercise (2) *The present value is negative because this is the cash outflow r

51、equired 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 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

52、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: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 treas

53、ury 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 investmentsA safe dollar is worth more than a risky one.Bain M

54、athNet Present Value Net present value (NPV) is the method used in evaluating investments whereby the present value of all case outflows required for the investment are added to the present value of all cash inflows generated by the investmentCash outflows have negative present values; cash inflows

55、have positive present valuesThe rate used to calculate the present values is the discount rate. The discount rate is the required rate of return, 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

56、 budgeting, the discount rate used is called the hurdle rateDefinition:Bain MathInternal Rate of Return The internal rate of return (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 invest

57、ment is acceptable when the IRR is greater than the required rate of return, or hurdle rateUnfortunately, comparing IRRs and choosing 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 th

58、an project B; that is, IRRs do NOT indicate the magnitude of an opportunityprojects with cash flows that fluctuate between negative and positive more than once have multiple IRRsIRRs cannot be calculated for all negative cash flowsDefinition:Bain MathNPV and IRR - Exercise *You can use this abbrevia

59、ted format since the other data has not changed from part aGiven:An investment costing $2MM will produce cash flows of $700,000 in Year 1, $700,000 in Year 2, and $900,000 in Year 3. Calculate its net present value at discount rates of (a) 5%, (b) 10%, and (c) 15%. Also, (d) calculate the projects I

60、RR.Answer:Using a 5% discount rate, NPV = -$2MM + + + = $79,041$700,000 (1.05)$700,000 (1.05)2$900,000 (1.05)3For HP12c: Another easy way to calculate an IRR is to use the IRR function in Excel:= IRR (C1, C2, C3, Cn) where C1 is the cash flow in Year 1, C2 is the cash flow in Year 2, etc.In this exa