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1、Author: Collins Qian,Reviewer: Brian Bilello,bc,Bain Math,March 1998,Copyright 1998 Bain & Company, Inc.,2,CU7112997ECA,Bain Math,Agenda,Basic math,Financial math,Statistical math,3,CU7112997ECA,Bain Math,Agenda,Basic math ratio proportion percent inflation foreign exchange graphing,Financial math,S
2、tatistical math,4,CU7112997ECA,Bain Math,Ratio,Definition:,Application:,Note:,The ratio of A to B is written or A:B,AB,A ratio can be used to calculate price per unit ( ), given the total revenue and total units,Price Unit,total revenue =,Given:,= =,Answer:,Price Unit,$9MM 1.5MM,The math for ratios
3、is simple. Identifying a relevant unit can be challenging,total units =,price/unit =,$9.0 MM,1.5 MM,$?,$6.0,5,CU7112997ECA,Bain Math,Proportion,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 C,A
4、B,CD,Revenue = SG&A =,Given:,$135MM $ 83MM,$270MM $?,1996,1999,Answer:,$135MM $270MM,$ 83MM $?,135MM x ? = 83MM x 270MM,83MMx270MM 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
5、 1999 are proportional to SG&A and revenue in 1996),?=,= $166MM,6,CU7112997ECA,Bain Math,Percent,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 yea
6、r 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 express the change in a number from one time period to the next,% change = = - 1,new value - original
7、value original value,new value original value,The ratio of 5 to 20 is or 0.25,7,CU7112997ECA,Bain Math,Inflation - Definitions,If 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 valuable W
8、hen calculating the “real” growth of 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
9、inflation over time.,Related Terminology:,1. Real (constant) dollars:,2. Nominal (current) dollars:,3. Price deflator,Price 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
10、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 year, but all dollar figures must be stated in the same base year,Dollar figures for a number of years that are stated in each individual years dollar terms
11、(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.,8,CU7112997ECA,Bain Math,Inflation - U.S. Price Deflators,*1996 is the base year Note: These are the U.S. Price Deflators which WEFA Group has forecasted through the year
12、 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.,9,CU7112997ECA,Bain Math,Inflation - Real vs. Nominal Figures,To understand how a company has performed over time (e.g., in terms of revenue, costs, or profi
13、t), 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, it is preferable to use nominal figures. For an experience curve, where you want to understand how price or cost has c
14、hanged over time due to accumulated experience, you must use real figures,Note :,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 spreadshee
15、ts 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.,10,CU7112997ECA,Bain Math,Inflation - Example (1),(1970 -1992),Adjusting for inflation is critical for any analysis looking at prices over time. In nominal dol
16、lars, 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.,CAGR,11,CU7112997ECA,Bain Math,Inflation - Example (2),Price of a GE Washer,CAGR,(1970-1992),If you use real dollars, you can see what has happened to inflation-adjusted prices. They have fallen an average of 1.0% per year.,
