【正文】 87 88 89 90 91 92 $0 $500 $1,000 $1,500 $2,000 $2,500 $3,000 Nominal dollars Real (1992) dollars If you use real dollars, you can see what has happened to inflationadjusted prices. They have fallen an average of % per year. BOS Copyright169。 1998 Bain amp。 Company, Inc. 25 CU7112997ECA Bain Math Simple Interest Definition: Simple interest is puted on a principal amount for a specified time period The formula for simple interest is: i = prt where, p = the principal r = the annual interest rate t = the number of years Application: Simple interest is used to calculate the return on certain types of investments Given: 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 = prt i = $5,000 x x i = $50 2 12 BOS Copyright169。 Company, Inc. 33 CU7112997ECA Bain Math Net 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 investment ?Cash outflows have negative present values。 Company, Inc. 38 CU7112997ECA Bain Math Averages *Sometimes referred to as the arithmetic mean Definition: (Sum of data points) Exercise: Answer: Mean* = (Number of data points) Median = The middle value of a set of ranked data points (., the data point for which there is an equal number of data points with values higher and lower). For an even number of data points, the median is the mean of the two middle values. Mode = The value that occurs most frequently in a set of data points. There need not be a mode in a set of data. Calculate the mean, median, and mode of the following data set: 1,2,3,4,5,6,7,8,8,8,9,10,50 Mean = (Sum of data points) (Number of data points) = (1+2+3+4+5+6+7+8+8+8+9+10+50) 13 Median = = 7 (because there are six data points with higher values than 7 and six data points with lower values) Mode = 8 (the only number that occurs repeatedly) BOS Copyright169。 Company, Inc. 31 CU7112997ECA Bain Math Present Value Exercise (2) *The present value is negative because this is the cash outflow required today receive a cash inflow at a later time 1) $ today, PV = $ 2) $ five years from today, For HP12C: 5 16 3) A perpetuity of $, PV = = $ 4) A perpetuity of $, growing at 5%, PV = = $ 5) A six year annuity of $, PV = =$ $ $ The option with the highest present value is 1, receiving $ today $ 1 (1+ )5 $ FV i PV N =()* 20( ) ( ) PV = = $ $ (1+)5 Answer: BOS Copyright169。 Company, Inc. 23 CU7112997ECA Bain Math Graphing Logarithmic (3) ?The most useful feature of a log graph is that equal multiplicative changes in data are represented by equal distances on the axes –the 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, 10 ?It is convenient to use log scales to examine the rate of change between data points in a series ?Log scales are often used for: –Experience curve (a log/log scale is mandatory natural logs (ln or loge) are typically used –prices and costs over time –Growth Share matrices –ROS/RMS graphs Line Shape of Data Plots Explanation A straight line The data points are changing at the same rate from one point to the next Curving upward The rate of change is increasing Curving downward The rate of change is decreasing In many situations, it is convenient to use logarithms. BOS Copyright169。 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。 Company, Inc. 9 CU7112997ECA Bain Math Inflation Real vs. Nominal Figures ?To understand how a pany has performed over time (., in terms of revenue, costs, or profit), it is necessary to remove inflation, (. use real figures). ?Since most panies use nominal figures in their annual reports, if you are showing the client’s 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 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 client’s 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. BOS Copyright169。 1998 Bain amp。 Company, Inc. 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 The math for ratios is simple. Identifying a relevant unit can be challenging total units = price/unit = $ MM MM $? $ BOS Copyright169。 1998 Bain amp。 US$1 $ 1 Franc $ 1 Mark Singapore dollar US