【正文】 1998 Bain amp。 1998 Bain amp。 1998 Bain amp。 1998 Bain amp。 1998 Bain amp。 Company, Inc. 34 CU7112997ECA Bain Math Internal Rate of Return ?The internal rate of return (IRR) is the discount rate for which the present value is zero (., 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 rate ?Unfortunately, paring IRRs and choosing the highest one sometimes does not lead to the correct answer. Therefore, IRRs should not be used to pare projects. –project A can have a higher IRR but lower NPV than project B。 cash inflows have positive present values ?The 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 (., the return you are giving up to pursue this project) ?An investment is acceptable if the NPV is positive ?In capital budgeting, the discount rate used is called the hurdle rate Definition: BOS Copyright169。 1998 Bain amp。 1998 Bain amp。 1998 Bain amp。 1998 Bain amp。 1998 Bain amp。 1998 Bain amp。 1998 Bain amp。 1998 Bain amp。 1998 Bain amp。 1998 Bain amp。 1998 Bain amp。 Company, Inc. 22 CU7112997ECA Bain Math Graphing Logarithmic (2) For a log scale in base 10, as the linear scale values increase by ten times, the log values increase by 1. 9 8 7 6 5 4 3 2 1 0 1,000,000,000 100,000,000 10,000,000 1,000,000 100,000 10,000 1,000 100 10 1 ?Log paper typically uses base 10 ?Loglog paper is logarithmic on both axes。 Company, Inc. 21 CU7112997ECA Bain Math Graphing Logarithmic (1) Log: 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 number Unless otherwise stated, the base is assumed to be 10 Y = 10x, then log10 Y = X Mathematically, if Where, Y = given number 10 = base X = power (or log) For example: 100=102 can be written as log10 100=2 or log 100=2 BOS Copyright169。 Company, Inc. 20 CU7112997ECA Bain Math Graphing Linear Exercise 2 (2) 0 8,000 16,000 Production Cost/Day 0 500 1,000 1,500 Produced/Day (1,500, 16,000) (1,000, 11,000) ?Formula for line: y = mx + b ?X axis = of lamps produced/day Y axis = production cost/day ?M = slope = = = = 10 ?b = Y intercept = production cost (., the fixed cost) when lamps = 0 y = mx + b b = ymx b = 2,000 10 (100) b = 1,000 The fixed cost is $1,000 ?y = 10x + 1,000 ?For 1,500 lamps: – y = 10 (1,500) + 1,000 – y = 15,000 + 1,000 – y = 16,000 11,0002,000 1,000 100 9,000 900 (100, 2,000) X = 900 Y = 9,000 y x The cost of producing 1,500 lamps is $16,000 BOS Copyright169。 Company, Inc. 19 CU7112997ECA Bain Math Graphing Linear Exercise 2 (1) A lamp manufacturer has collected a set of production data as follows: Number of lamps Produced/Day Production Cost/Day 100 850 900 950 1,000 $2,000 $9,500 $10,000 $10,500 $11,000 What is the daily fixed cost of production, and what is the cost of making 1,500 lamps? BOS Copyright169。 Company, Inc. 18 CU7112997ECA Bain Math Graphing Linear Exercise 1 Formula for line: y = mx + b In this exercise, y = 15x + 400, where, 0 200 400 600 800 1,000 1,200 1,400 1,600 1,800 $2,000 Dollars changing 0 50 100 People (100,1900) (50,1150) The caterer would charge $1900 for a 100 person party. y x X axis = people Y axis = dollars charged m = slope = = 15 b = Y intercept = 400 dollars charged (when people = 0) A caterer charges $ for setting up a party, plus $ 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 viceversa BOS Copyright169。 Company, Inc. 17 CU7112997ECA Bain Math Graphing Linear X 0 Y (X1, Y1) (X2, Y2) b X Y The formula for a line is: y = mx + b Where, m = slope = = y2 y1 x2 x1 b = the y intercept = the y coordinate when the x coordinate is “0” y x BOS Copyright169。 US$1 $ 1 Franc $ 1 Mark Singapore dollar US$ 1 BOS Copyright169。 = US$ $ x = 163。 1998 Bain amp。 1998 Bain amp。 1998 Bain amp。 1998 Bain amp。 1998 Bain amp。 1998 Bain amp。 1998 Bain amp。 1998 Bain amp。 1998 Bain amp。 1998 Bain amp。 1998 Bain amp。A and revenue in 1999 are proportional to SGamp。A costs in 1999, given revenue in 1996, SGamp。 Company, Inc. 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 AB CD Revenue = SGamp。 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。 Company, Inc. 3 CU7112997ECA Bain Math Agenda ?Basic math –ratio –proportion –percent –inflation –foreign exchange –graphing ?Financial math ?Statistical math BOS Copyright169。 Company, Inc. 2 CU7112997ECA Bain Math Agenda ?Basic math ?Financial math ?Statistical math BOS Copyright169。 Company, Inc. BOS Copyright169。Author: Collins Qian Reviewer: Brian Bilello bc