Schweser HP 12C User Guide
Contents
1. CHS gt PV Note The CHS key changes the sign of the numeric value 5 gt ENTER gt 4 gt X gt n 14 gt ENTER gt 4 gt gt i 0 gt PMT FV gives the result 1 989 79 Ordinary Annuities In an ordinary annuity a constant cash flow is either paid or received at the end of a particular payment period over the life of an investment or liability Here we begin use of the PMT key Example You would like to buy a 9 semi annual 8 year corporate bond with a par value of 1 000 par value represents the terminal value of the bond Compute the value of this bond today if the appropriate discount rate is 8 Here the 9 is the coupon rate of the bond and represents the annual cash flow associated with the bond Hence the annual PMT 0 09 x 1 000 90 0 09 gt ENTER 1000 X gives the result 90 2003 Schweser Study Program How TO USE YOUR HP 12 C CALCULATOR 5 The value of the bond today is 8 gt ENTER gt 2 gt X gt n 90 ENTER gt 2 gt gt PMT 8 ENTER gt 2 gt gt i 1 000 FV PV gives the result 1 058 26 Example You will receive 100 per month for the next three years and you have nothing today The appropriate annual interest rate is 12 Compute your accumulated funds at the end of three years 3 ENTER gt 12 gt X gt n 0 gt PV 1002. gt PMT 12 gt ENTER gt 12 gt gt i FV gives the result 4 307 69 Annuity Due In an annuity due you receive each constant annuity cash flow at the beginning of each period You must set your calculator to BEGIN mode by pressing lt g gt 7 BEGIN will appear in the calculator s LCD screen Example You will receive 100 per month for the next three years and you have nothing today The appropriate annual interest rate is 12 Compute your accumulated funds at the end of three years 3 gt ENTER gt 12 gt X gt n 0 gt PV 100 gt PMT 12 gt ENTER gt 12 gt gt i FV gives the result 4 350 76 Notice that the future value is larger in this case because you receive each cash flow at the beginning of the period so each cash flow is exposed to one additional compounding period 2003 Schweser Study Program 6 How TO USE YOUR HP 12 C CALCULATOR 5 Continuous Compounding and Discounting If the number of compounding periods is said to be continuous what this means is that the time between compounding periods is infinitesimally small To discount and compound you need the magic number e 2 718281 The formula for continuous compounding of a single cash flow is FV PV e The formula for continuous discounting is PV FV x e where r the annualized interest rate t the number of years Example You have 100 today and have been
3. 800 3 600 4 200 The IRR for Project X is Remember The PV is the WHITE name of the key We 2 000 CHS lt g gt PV use this convention because the 1 000 lt g gt PMT 800 lt g gt PMT 600 lt g gt PMT 200 lt g gt PMT lt f gt IRR gives the result 14 48884 white keys are easier to read and identify A note on Net Present Value NPV For NPV calculations on the examination we recommend computing the present value of each individual cash flow and adding them together No need to memorize more calculator functions you ve got enough to memorize for the exam However for the curious the keystrokes to calculate NPV are provided below The NPV of Project X is 2 000 CHS lt g gt PV 1 000 lt g gt PMT 800 lt g gt PMT 600 lt g gt PMT 200 lt g gt PMT 10 gt i lt f gt PV gives the result 157 63951 2003 Schweser Study Program 8 How TO USE YOUR HP 12 C CALCULATOR 6 Exponents Many of the calculations in the CFA program require taking a number to the N 99 xX power On the HP12C we will use the white y key to perform this function Example An investment has a stated return of 8 percent What is the semi annual effective rate Answer Semi annual effective rate 1 0 08 2 1 1 04 1 1 04 gt ENTER gt 2 gt y gives the result 1 0816 Then subtra
4. How TO USE YOUR HP 12 C CALCULATOR This document is designed to provide you with 1 the basics of how your HP 12C financial calculator operates and 2 the typical keystrokes that will be required on the CFA examination In this tutorial the following keystroke and data entry conventions will be used lt e gt and Denote keystrokes e Denotes data input A Setting Up Your HP 12C Important note The keys of the HP 12C calculator have been assigned multiple functions Keys are assigned white orange and blue color codes To enable the white coded function just press the desired key For the orange coded function press the lt f gt key at the bottom of the calculator followed by the desired key For the blue coded function press the lt g gt key at the bottom of the calculator followed by the desired key In this user guide all keys are referred to by their white coded function as they are easier to read and easier to identify The following is a list of the basic preliminary set up features of your HP 12C You should understand these keystrokes before you begin work on statistical or Time Value of Money TVM functions Please note that your calculator s sign convention requires that one of the TVM inputs PV FV or PMT be a negative number Intuitively this negative value represents the cash outflow that will occur ina TVM problem 1 To set the number of decimal places that show in your calculator display screen
5. ct 1 for the semi annual rate of 8 16 percent Example Calculate the geometric average for the following stock returns 22 percent 5 percent and 5 percent Answer The geometric average 1 22 x 0 95 x 1 05 1 1 21695 1 1 21695 gt ENTER gt 1 gt ENTER gt 3 gt gt y 1 0676 then subtracting 1 gives 6 76 percent 7 The natural log function Primarily for CFA Levels 2 and 3 The natural log function is intimately related to e In Level 1 you will use this function to calculate a continuously compounded return given a specific holding period return The natural log function LN is also used when working Black Scholes and Merton Model problems Example The value of the stock is 45 S today and the exercise price of a call option that trades on that stock is 50 X Calculate the natural log of S X Step 1 Compute S X 45 ENTER gt 50 gt gives the result 0 90 Remember T is the WHITE Step 2 Compute LN S X key We use this convention because the white keys are lt g gt T gives the result 0 10536 easier to read and identify As a check of the relationship between LN and e ENTER gt lt g gt gt 1 x gives the result 0 90 More precisely e x and In e x 2003 Schweser Study Program How TO USE YOUR HP 12 C CALCULATOR 9 Your HP 12C Statistical Functions use at your own risk Understanding
6. lt f gt Desired of decimal places For the exam I would make sure that the number of decimal places is set to 5 2 To switch between annuity due BEGIN and ordinary annuity modes To switch to the begin mode enter lt g gt 7 The word BEGIN will be displayed at the bottom of the display screen To switch back to the ordinary annuity mode enter lt g gt 8 The word BEGIN will disappear from the display screen 2 How TO USE YOUR HP 12 C CALCULATOR 3 Clearing the calculator screen To clear the calculator screen press CLX 4 To clear the time value of money memory registers lt f gt gt xy This is the key to the left of the white CLX key in the second row from below This function clears all entries in the time value of money functions n i PV PMT and FV This function is important because each TVM function button represents a memory register If you do not clear your memory you may have erroneous data left over when you perform new TVM computations Pressing the CLX key clears the screen only It does not clear the memory registers for the TVM functions so please be careful 5 Clearing your work from the statistical data entry registers To clear the single value and X Y coordinate pairs from the statistical memory registers press lt f gt SST 6 Additional memory registers HP 12C provides 20 additional memory registers for data storage These are numbered 0 to 9 f
7. offered a 6 month continuously compounded investment return of 10 How much will the investment be worth in six months Step 1 Compute r x t 0 1 ENTER gt 0 5 X gives the result 0 05 Note that you always use the decimal representative of both the interest rate and time when performing these computations Step 2 Compute e 0 05 gt lt g gt 1 x This gives the result 1 05127 Step 3 Find the future value ENTER 100 X gives the result 105 13 Example You will receive 1 000 eighteen months from today and would like to compute the present value of this amount at 8 with continuous compounding Step 1 Compute r x t 0 08 CHS gt ENTER 1 5 X gives the result 0 12 Step 2 Compute e gt lt g gt gt 1 x This will give the result 0 88692 2003 Schweser Study Program How TO USE YOUR HP 12 C CALCULATOR 7 Step 3 Find the present value ENTER 1000 X will give the result 886 92 Internal Rate of Return IRR and Net Present Value NPV Just in case there is a question on the examination that asks for an IRR calculation the keystrokes are as indicated in the following example Example Project X has the following expected after tax net cash flows The firm s cost of capital is 10 Note Clear all previous work Expected Net After Tax Cash Flows Project X Year Cash Flow 0 initial outlay 2 000 1 1 000 2
8. or the first ten and 0 0 to 0 9 for the last ten registers yes that is a period before 0 and 9 To enter data into a memory register press Desired value gt STO gt Any memory register number 0 to 0 9 Example Store the number 125 in the memory register 0 8 125 gt STO gt 8 will do the job To recall a stored value press RCL Desired memory register number In the above example to recall the stored value 125 press RCL 8 This will display 125 on the screen 2003 Schweser Study Program How TO USE YOUR HP 12 C CALCULATOR To clear all memory registers press lt f gt CLX This will clear all memory registers as well as the TVM registers How to Handle Multiple Payment Periods Per Year When a present value or future value problem calls for a number of payments per year that is different from 1 use the following rules 1 For semi annual computations PMT annual PMT 2 i annual 1 2 n number of years 2 For quarterly computations PMT annual PMT 4 i annual i 4 n number of years 4 For monthly computations PMT annual PMT 12 i annual 1 12 n number of years 12 Time Value of Money TVM Computations 1 Basic Present Value Computations If a single cash flow is to occur at some future time period we must consider the opportunity cost of funds to find the present value of that cash flow Hence our goal here is to disc
9. ount future cash flows to the present using the appropriate discount rate Example suppose you will receive 100 one year from today and that the appropriate discount rate is 8 The value of that cash flow today is 1 gt n 100 gt FV 0 gt PMT 8 gt i PV gives the result 92 59 2003 Schweser Study Program 3 4 How TO USE YOUR HP 12 C CALCULATOR Example Suppose you will receive 1 000 ten years from today and that the appropriate annualized discount rate is 10 Compute the present value of this cash flow assuming semi annual compounding Note HP 12C uses Reverse Polish Notation RPN methodology of data entry when it comes to performing mathematical calculations such as and x 10 gt ENTER gt 2 gt X gt n 10 gt ENTER gt 2 gt gt i 0 gt PMT 1 000 gt FV PV gives the result 376 89 The result is a negative number due to your calculator s sign convention Intuitively to receive 1000 ten years from now at 10 semi annually this would cost you 376 89 Basic Future Value Here we want to compute how much a given amount today will be worth a certain number of periods from today given an expected interest rate or compounding rate Example Suppose that you have 1 000 today and can invest this amount at 14 over the next 5 years with quarterly compounding Compute the value of the investment after 5 years 1000
10. ple variance for this data set Step 1 Enter the data 30 the number 1 will appear in the display 42 the number 2 will appear in the display 32 the number 3 will appear in the display 35 the number 4 will appear in the display 28 the number 5 will appear in the display Step 2 Calculate the statistics Press lt g gt 0 for the mean X 33 4 lt g gt gt for the sample standard deviation Sx 5 459 Computation of population standard deviation with HP 12C is quite involved and we do not recommend that you use it for this purpose 2003 Schweser Study Program 10 How TO USE YOUR HP 12 C CALCULATOR Remember that the population variance differs from the sample variance in that the sum of the squared deviations from the mean is divided by n and n 1 respectively In addition the standard deviation is the square root of the variance Example You have calculated the following returns for an individual stock and the stock market over the past four months For this example we will use the data pair method of entering the data into the HP12C Month Ri Y Rm X 1 12 15 2 8 4 3 9 12 4 10 14 Calculate the stock s mean return the market s mean return and the correlation between the stock s returns and market returns Note Clear all previous work lt f gt CLX Step 1 Enter the data Remember
11. returns relative to the market is 83 1 and the R of the regression is 0 831 0 691 or 69 1 i e 69 1 percent of the variation in stock i s returns is explained by the variability in market returns 2003 Schweser Study Program
12. the previous sections of this document is critical to your success on the exam What follows are some cool short cuts you can take to calculate the mean and variance of a small data set Please beware that in many cases doing these computations by brute force is sometimes quicker If you feel you ll have a hard time memorizing these keystrokes for the exam don t sweat it focus on the actual formulas and basic calculations In other words don t get fancy it could backfire To enter single values as well as data pairs X Y you will use the key on the bottom right and to the left of the key Note that while entering paired values the Y value is entered first followed by the X value and the calculator automatically increases its internal memory register by 1 to identify the location and sequence of the data values entered To clear a value that has just been entered most recent press lt g gt ENTER gt lt g gt To clear the incorrect data point or data pair key in the incorrect data point or data pair and press lt g gt gt You should then re enter the correct data again Remember you cannot directly replace incorrect data You can only clear it and then re enter it again Example You have been given the following observations that measure the speed of randomly selected vehicles as they pass a particular checkpoint 30 42 32 35 28 Compute the mean X population variance and sam
13. to enter the y value first 12 gt ENTER gt 15 gt screen displays 1 8 gt ENTER gt 4 gt screen displays 2 9 ENTER gt 12 gt screen displays 3 10 gt ENTER gt 14 gt screen displays 4 Step 2 Calculate the statistics Mean of X X lt g gt gt 0 gives the result 11 25 Mean of Y Y lt g gt gt 0 gt xy gives the result 9 75 Sample standard deviation x Sx lt g gt gt gives the result 4 992 Population standard deviation not recommended on this calculator Sample standard deviation y Sy lt g gt gt gt x lt y gives the result 1 708 Population standard deviation not recommended on this calculator 2003 Schweser Study Program How TO USE YOUR HP 12 C CALCULATOR 11 Intercept term a Slope Coefficient b and Correlation X Y r To obtain these statistics you must enter the keystrokes in the following order For example you cannot calculate the slope coefficient without first calculating the intercept term e Intercept term a 0 gt lt g gt gt 2 gives the result 6 55 e Slope coefficient b 1 gt lt g gt gt 2 gt key gt RY gt xy gt gives the result 0 284 Whew Now you know why we do not recommend the HP 12C e Correlation X Y r xy gives the result0 831 Given this data we can say that our estimate of the beta of the stock is 0 28 the correlation of stock i s
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