【正文】 Copyright169。 Company, Inc. 16 CU7112997ECA Bain Math Foreign Exchange Exercises Question 1: Answer: Question 2: Answer: Question 3: Answer: US dollars = ? British pounds from table: 163。 1998 Bain amp。 1998 Bain amp。 1998 Bain amp。 semilog paper is logarithmic on one axis and linear on the other Log Scale Linear Scale BOS Copyright169。 Company, Inc. 24 CU7112997ECA Bain Math Agenda ?Basic math ?Financial math –simple interest –pound interest –present value –risk and return – present value –internal rate of return –bond and stock valuation ?Statistical math BOS Copyright169。 Company, Inc. 26 CU7112997ECA Bain Math Compound Interest “ Money makes money. And the money that money makes, makes more money.” Benjamin Franklin Definition: Compound interest is puted on a principal amount and any accumulated interest. A bank that pays pound interest on a savings account putes interest periodically (., daily or quarterly) and adds this interest to the original principal. The interest for the following period is puted by using the new principal (., the original principal plus interest). The formula for the amount, A, you will receive at the end of period n is: A = p (1 + )nt where, p = the principal r = the annual interest rate n = the number of times pounding is done in a year t = the number of years r n Notes: As the number of times pounding is done per year approaches infinity (as in continuous pounding), the amount, A, you will receive at the end of period n is calculated using the formula: A = pert The effective annual interest rate (or yield) is the simple interest rate that would generate the same amount of interest as would the pound rate BOS Copyright169。 Company, Inc. 28 CU7112997ECA Bain Math Present 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 value allows you to determine how much money that will be received in the future is worth today The formula for present value is: PV = Where, C = the amount of money received in the future r = the annual rate of return n = the number of years is called the discount factor The present 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)n C (1+r)n C1 1+r C2 (1+r)2 Cn (1+r)n BOS Copyright169。 Company, Inc. 30 CU7112997ECA Bain Math Present Value Exercise (1) 1) $ today 2) $ five years from today 3) A perpetuity of $ 4) A perpetuity of $, growing at 5% 5) A six year annuity of $ Assume you can invest at 16% per year Which of the following would you prefer to receive? BOS Copyright169。 Company, Inc. 32 CU7112997ECA Bain Math Risk and Return ?Not all investments have the same risk –investing in the . stock market is more risky than investing in a . government treasury bill, but less risky than investing in the stock market of a developing country ?Most investors are risk averse they avoid risk when they can do so without sacrificing return ?Risk averse investors demand a higher return on higher risk investments A safe dollar is worth more than a risky one. BOS Copyright169。 1998 Bain amp。 Company, Inc. 35 CU7112997ECA Bain Math NPV and IRR Exercise *You can use this abbreviated format since the other data has not changed from part a Given: 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 present value at discount rates of (a) 5%, (b) 10%, and (c) 15%. Also, (d) calculate the project’s IRR. Answer: Using a 5% discount rate, NPV = $2MM + + + = $79,041 $700,000 () $700,000 ()2 $900,000 ()3 For HP12c: Another easy way to calculate an IRR is to use the IRR function in Excel: = IRR (C1, C2, C3, ……C n) where C1 is the cash flow in Year 1, C2 is the cash flow in Year 2, etc. In this example, “ = IRR (2,000,000, 700,000, 700,000, 900,000)” = % f CLX f i CHS CF0 2,000,000 g 700,000 CFj g 700,000 CFj g 900,000 CFj g 5 NPV =79,041 For HP12C: Using 10% discount rate, NPV = $2MM + + + = $108,941 $700,000 () $700,000 ()2 $900,000 ()3 For HP12C: f i 10 NPV = $108941 Using 15% discount rate, NPV = $2MM + + + = $270,239 $700,000 () $700,000 ()2 $900,000 ()3 For HP12C: f i 15 NPV = $270,239 f IRR = % * * * a) b) c) d) BOS Copyright169。 Company, Inc. 37 CU7112997ECA Bain Math Agenda ?Basic math ?Financial math ?Statistical math –averages –weighted averages –linear regression BOS Copyright169。 Company, Inc. 39 CU7112997ECA Bain Math Using Averages (Arithmetic) Mean: ?The mean is an artificial statistic in that it need not coincide with any point in your data set –in the previous example, the mean of is not in the original data set ?Extreme points have more effect than those closer to the middle ?The median is affected by the number of, but not the value of, extreme points in the data set ?The median is least useful in small data sets (., the median of and 10 is 3, which tells us little) ?The mode can be meaningless in a data set with several values that occur repeatedly ?Most useful for data sets that have outliers ?Most useful when you need a simple average that weights all of the data points equally ?Most useful for da