Texas Instrument BAII PLUS Tutorial

To begin, look at the face of the calculator. Almost every key on the BAII PLUS has two functions: each key’s primary function is noted on the key itself, while each key’s secondary function is noted in white above the key. To use the function on the key, simply press the key. To access the white function above each key, first press the gray key with “2nd” printed on it, which we will call the “2nd shift” key, and then press the desired function key. (Note that the 2nd shift key is near the upper left corner of the calculator keyboard.)

Turning the Calculator On and Off

To turn on the calculator, press .

To turn off the calculator, press .

Note that the “ON/OFF” key is on the upper right corner of the keyboard. Also, we will designate keys throughout this tutorial by the use of small boxes, as above. To conserve the battery, the calculator turns itself off about 10 minutes after your last keystroke.

Also, note that pressing the 2nd shift key places a little “2nd” symbol in the upper left corner of the display. Press the 2nd shift key again and the symbol goes away. Thekey is a toggle key that switches back and forth between the “regular” and the “2nd” functions. is like the typewriter shift key. After you press , look only at the white writing above the keys.

Note that the calculator has a continuous memory, so turning it off does not affect any data stored in the calculator, but it will erase any number showing on the screen.

Clearing the Calculator

Five of the most commonly used methods of clearing data are presented below:

clears all 10 memory locations and the display.

clears the TVM worksheet.

clears worksheets other than the TVM worksheet.

clears the entire display, but not the memory. clears the numbers on the display one at a time if you made a mistake entering data.

Review your owner’s manual for other methods of clearing information.

ON/OFF

ON/OFF

2nd

2nd 2nd

2nd MEM 2nd CLR WORK

2nd QUIT 2nd CLR TVM

2nd CLR TVM

CE/C

→

Clearing the calculator is very important, since unwanted data in memory can result in improper calculations, and hence wrong answers. It is best to get into the habit of automatically clearing memory before starting a calculation. Occasionally, you may want to save data, but, in general, you will be entering all new data, so starting with a clear memory is the safest approach.

Changing the Display

To change decimals from 2 to 4, press 0.0000 is displayed.

To change from 4 to 2, press .0.00 is displayed.

We usually set the display to 2 places, which is especially convenient when working with dollars and percentages. However, we often use 4 places when dealing with the interest rates and rates of return that are entered as decimals.

Periods per Year Setting

One important setting that can cause problems is the periods per year setting. To check the current setting, press . The display shows the setting for periods/year. The calculator comes preset at 12 periods per year, that is, it assumes calculations will be done on a monthly basis. However, finance textbook problems generally use 1 period/year. To change to 1/year:

Press 1 .

Now the calculator is set to assume 1 period/year. To confirm this setting, press

. Unless needed for other work, we generally leave the calculator setting at 1 period per year.

Time Value of Money (TVM)

The TVM keys are located on the third row from the top of the keyboard. In general, TVM problems involve four variables – three are known and the fourth is unknown.

2nd FORMAT 4 ENTER 2nd QUIT

2nd FORMAT 2 ENTER 2nd QUIT

2nd P/Y

2nd P/Y ENTER 2nd QUIT

2nd P/Y 2nd QUIT

N I/Y PV PMT FV

Lump Sums

To begin, we consider TVM calculations with single (lump) sums. In this situation, we do not use the PMT key, so be sure to either press ,which sets the

payment (PMT) equal to 0, or enter 0 as the PMT when entering the input data. If you know any three variables, you can find the value of the fourth.

Example 1:

What is the FV of $100 after 3 years if the interest rate is 26 percent? First, clear with

Next, enter the data.

3

26

100

0 (Optional if registers are cleared.)

To determine the FV simply press and the FV of -$200.04 is displayed.

The BAII PLUS is programmed so that if the PV is + then the Fv is displayed as – and vice-versa, because the BAII PLUS assumes that one is an inflow and the other is an outflow. When entering both PV and FV, one must be entered as negative and the other as positive.

Example 2:

What is the PV of $500 due in 5 years if the interest rate is 10 percent? Clear first and then enter the following data.

5 10

0 (Optional is registers are cleared.)

500

Pressing the key reveals that $310.46 will grow to $500 in 5 years at a 10 percent rate.

2nd CLR TVM

2nd

CLR TVM

N

I/Y

PV

VPMT

CPT FV

N

I/Y

PMT

FV

CPT PV

Example 3:

Assume a bond can be purchased today for $200. It will return $1,000 after 14 years. The bond pays no interest during its life. What rate of return would you earn if you bought the bond?

14

200 (The +/- key changes the sign.)

0

1000

Simply press the key and the BAII PLUS calculates the rate of return to be 12.18%.

Remember the BAII PLUS is programmed so that if the PV is + then the FV is displayed as – and vice versa because the BAII PLUS assumes that one is an inflow and the other is an outflow.

Now suppose you learn that the bond will actually cost $300. What rate of return will you earn?

Override the -200 by entering 300 , then press to get 8.98 percent. If you pay more for the bond, you earn less on it. The important thing, though, is that you can do “what if” analyses with the calculator.

Now do nothing except press to turn off the calculator. Then turn on the

calculator . The display shows 0.00. Is the memory erased? Not completely.

What was on the screen is gone, but press to get N = 14.

N

+/- PV

PMT

FV

CPT I/Y

+/- PV CPT I/Y

ON/OFF

ON/OFF

RCL N

Ordinary Annuities

Example 1:

What is the FV of an annuity of $100 paid at the end of each year for 5 years if the interest rate equals 6 percent? 0 1 2 3 4 5 6%

-100 -100 -100 -100 -100

5

6

0

100

Now press the key, and an FV of $563.71 is displayed.

Example 2:

What is the PV of the same annuity?

Leave data in calculator, but enter 0 as the FV to override, the press to get $421.24.

Annuities Due

Each payment of an annuity due occurs at the beginning of the period instead of at the end as with a regular annuity. In essence, each payment is shifted back one period. To analyze annuities due press . “BGN” appears

on the screen and in the upper right corner of the display. Now the BAII PLUS analyzes the cash flows based on beginning of period payments. Change back to end mode by pressing .

N

I/Y

PV

+/- PMT

CPT FV

CPT PV

2nd BGN 2nd SET CE/C

2nd BGN 2nd SET CE/C

Interest Conversion

The following equation is used to convert a nominal rate to an effective rate.

EAR = [ 1 + KNom/m]m – 1.

Given: KNom = 10% and m = 12 payments/year,

EAR = [ 1 + 0.10/12]m – 1 = (1.0083)12 – 1 = 1.1047 – 1 = 0.1047 = 10.47%.

However, it’s much easier to convert the nominal rate using the calculator.

First, we need to set the calculator to 12 payments per year:

12

10

The effective rate of 10.47 percent is displayed on the screen.

Cash Flow Operations

Example 1:

We can also find the PV, FV, an IRR (internal rate of return) of a series of unequal cash flows. Assume the following cash flows: 0 10% 1 2 3 4 0 50 100 150 200

What is the PV of the CFs?First clear the BAII PLUS and make sure that periods/year is set equal to 1.

Enter the cash flow worksheet by pressing then clear any previous cash flow analyses, .

2nd ICONV ↑ ENTER

↓ ENTER

↓ CPT

CF

2nd CLR WORK

Next, enter the cash flows:

0 Sets CF0 equal to 0 and moves to CF1.

50 Sets CF1 equal to 50 and moves to frequency of occurrence of CF1.

1 Tells calculator that the $50 CF occurs only once.

100

1

150

1

200

1

The CFs from the time line are entered. Now enter the interest rate.

10

At this point the BAII PLUS knows the cash flows, the number of periods, and the interest rate. To find the PV, press to get PV = NPV = $377.40.

Example 2:

We have these cash flows, which contain embedded annuities:0 1 2 3 4 5 6 7 8 9 10%

0 100 100 100 100 100 100 100 100 100

What’s the PV?

Clear, set P/YR = 1 if changed.

First enter the cash flow worksheet by pressing then clear any previous cash flow

ENTER ↓

ENTER ↓

ENTER ↓

ENTER ↓

ENTER ↓

ENTER ↓

ENTER ↓

ENTER ↓

ENTER ↓

NPV ENTER ↓

CPT

CF

analyses, . Next, enter the cash flows:

0 Sets CF0 equal to 0 and moves to CF1.

100 Sets CF1 equal to 100 and moves to frequency of occurrence of CF1.

3 Tells calculator that the $100 CF occurs three consecutive times.

200

2

300

4

Now the BAII PLUS knows the cash flows. Thus, enter the interest rate:

10 .

At this point the BAII PLUS knows the cash flows, the number of periods, and the interest rate. To find the PV, press to get PV = NPV = $1,099.94.

To check your entries:

then use the up and down arrow keys to view each cash flow.

Example 3: The Rate of Return Offered by an Investment (IRR)1

2nd CLR WORK

ENTER ↓

ENTER ↓

ENTER ↓

ENTER ↓

ENTER ↓

ENTER ↓

ENTER ↓

NPV ENTER ↓

CPT

CF

Assume that we invest $1,000 now (t=0) and then expect to receive an uneven set of cash flows. Here is the CF time line: 0 1 2 3 4

-1000 300 400 200 600

What rate of return will we earn?

First enter the cash flow worksheet by pressing then clear any previous cash flow analyses, . Next, enter the cash flows:

1000 Sets CF0 equal to -1,000 and moves to CF1.

300 Sets CF1 equal to -1000 and moves to frequency of occurrence of CF1. The second tells the calculator that the $300 CF occurs only once2.

400

200

600

Now the BAII PLUS knows the cash flows. Thus, simply press and the IRR of 16.71 percent is displayed.

__________________ 1If a negative CF occurs at the end of a project’s life, or if a sequence of cash flows has two or more sign changes, there may be multiple IRR solutions. The calculator displays the IRR closest to zero. However, the displayed solution has no financial meaning. Thus, you should use caution in making investment decisions based on IRR computed for a cash flow stream with more than one sign change. When you are solving very complex cash flow problems, the calculator may not be able to find IRR, even if a solution exists. When this is the case, the calculator displays ERROR 7 (iteration limit exceeded).

2If you do not enter a value for frequency after you enter the cash flow value, the calculator assumes a value of 1; however, the down arrow key must be pressed again before entering the next cash flow.

You can also determine the NPV of the investment. Leave data entered and then enter the opportunity cost interest rate, say 8 percent. To find NPV press

CF

2nd CLR WORK

+/- ENTER ↓

ENTER ↓ ↓

↓

ENTER ↓ ↓

ENTER ↓ ↓

ENTER ↓ ↓

IRR CPT

8

The NPV of $220.50 is displayed. Thus, the PV of the cash inflows exceeds the cost of the investment by $220.50.

Statistical Calculations

The BAII PLUS can also be used for several types of statistical calculations.

Mean and Standard Deviation (σ) Year Sales 1994 $150 1995 95 1996 260

What’s the mean (average) and standard deviation (σ) of sales over the 3 years?

First select the data-entry portion of the statistics worksheet by pressing then clear any previous data entries, . Next, enter the data:

150 This enters 150 as the data entry and tells the calculator there is no Y-variable associated with the X variable.

95 This enters 95 as the second data entry and tells the calculator there is no Y-variable associated with the X-variable.

260 This enters 260 as the third entry and tells the calculator there is no Y-variable associated with the X-variable.

Now select the statistical calculation portion of the statistics worksheet by pressing then clear any previous data entries, .

“LIN” should now be displayed on the screen. Keep pressing then until “1-V” (one variable calculation method) is displayed. Press the down arrow key three times to view (1) sample size, n, (2) mean, x, and (3) standard deviation, Sx. The mean equals $168.33. The standard deviation is $84.01.

Line Regression

I/YR ENTER ↓ CPT

2nd DATA

2nd CLR WORK

ENTER ↓ ↓

ENTER ↓ ↓

ENTER ↓ ↓

2nd STAT 2nd CLR WORK

2nd SET

Beta coefficients can be calculated by using the BAII PLUS’s linear regression capabilities. The X (independent variable) and Y (dependent variable) values must be entered in the proper sequence, where the data X is on the horizontal axis (market) and Y data is on the vertical axis (stock).

Year Market (Km) Stock (Kj) 1 23.8% 38.6% 2 -7.2 -24.7 3 6.6 12.3 4 20.5 8.2 5 30.6 40.1

First select the data-entry portion of the statistics worksheet by pressing Then clear any previous statistical entries, .Next, enter the data as follows:

23.8 This enters 23.8 as the first X variable.

38.6 This enters 38.6 as the first Y variable.

7.2 This enters -7.2 as the second X variable.

24.7 This enters -24.7 as the second Y variable.

6.6 This enters 6.6 as the third X variable.

12.3 This enters 12.3 as the third Y variable.

20.5 This enters 20.5 as the fourth X variable.

8.2 This enters 8.2 as the fourth Y variable.

30.6 b This enters 30.6 as the fifth X variable.

40.1 This enters 40.1 as the fifth Y variable.

Now select the statistical calculation portion of the statistics worksheet by pressing then clear any previous statistical entries, .

“LIN” should now be displayed on the screen. Keep pressing until “a=” appears on

the screen. This is the value of the y-intercept of the regression line. Press one

more time and “b=” appears on the screen. This is the value of the slope of the regression line. If you press one more time, “r =” appears on the screen. This is the value of

2nd DATA

2nd CLR WORK

ENTER ↓

ENTER ↓

ENTER ↓+/-

+/- ENTER ↓

ENTER ↓

ENTER ↓

ENTER ↓

ENTER ↓

ENTER ↓

ENTER ↓

2nd STAT 2nd CLR WORK

↓

↓

↓

the correlation coefficient of the regression line. (The intercept value is -8.92, the slope value is 1.60, and the correlation coefficient is 0.91.) Clear the calculator by pressing .

Amortization

The BAII PLUS can also be used to calculate amortization schedules. First, clear the TVM registers by pressing

Example:

Determine the interest and principal paid each year and the balance at the end of each year on a three-year $1,000 amortizing loan which carries an interest rate of 10 percent. The payments are due annually.

First, check payments/year and be sure it’s 1. ( )

Now perform the following steps:

3

10

1000 A payment of -402.11 is displayed.

Now we will use the amortization worksheet to generate an amortization schedule for the loan:

Enters the Amort worksheet and clears any old contents.

1 Ending period set at 1 because we want to view the amortization information for each and every payment.

Now just use the down arrow key to view the balance after the payment as well as the interest and principal portions of the first payment.

To view the results for the second payment, press to move to “P1,” press and use the down arrow key to view the ending balance after the payment is made as well as the interest and principal portions of the second payment.

2nd DATA 2nd CLR WORK

2nd QUIT 2nd CLR TVM

2nd P/Y 2nd QUIT

N

I/Y

PV

CPT PMT

2nd AMORT 2nd CLR WORK

↓ ENTER

↓ CPT

Repeat the third and last payment.

This is the amortization schedule corresponding to the loan.

Beg. Bal. Payment Interest Princ. Repmt. Ending Bal. 1 1,000.00 402.11 100.00 302.11 697.89 2 697.89 402.11 69.79 332.32 365.57 3 365.57 402.11 36.56 365.55 .02

CFA Wednesday, June 23, 2004

How to use Texas BA II plus Financial Calculator

HOW TO USE YOUR TI BA II PLUS CALCULATOR This document is designed to provide you with (1) the basics of how your TI BA II Plus financial calculator operates, and (2) the typical keystrokes that will be required on the CFA examination. A similar guide as published by Texas Instruments is available for download from www.ti.com/calc/baiiplus. In this tutorial, the following keystroke and data entry conventions will be used. [•] Denotes keystroke {•} Denotes data input A. Setting Up Your TI-BA II Plus The following is a list of the basic preliminary set up features of your TI BA II Plus. You should understand these keystrokes before you begin work on statistical or 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 in a TVM problem. 1. To set the number of decimal places that show on your calculator: [2nd]→[FORMAT]→{Desired # of decimal places}→[ENTER]→[CE/C] For the exam, I would make sure that the number of decimal places is set to 5. 2. To set the number of payments per year (P/Y): [2nd]→[P/Y]→{Desired # of payments per year}→[ENTER]→[CE/C] P/Y should be set to 1 for all computations on the Schweser Notes and on the exam. 3. To switch between annuity-due [BGN] and ordinary annuity modes:

[2nd]→[BGN]→[2ND]→[SET]→[CE/C] 4. To clear the time value of money memory registers: [2nd]→[CLR TVM] This function clears all entries into the time value of money functions (N, I/Y, PMT, PV, FV). This function is important because each TVM function button represents a HOW TO USE YOUR TI BA II PLUS CALCULATOR ©2003 Schweser Study Program 2 memory register. If you do not clear your memory, you many have erroneous data left over when you perform new TVM computations. 5. The reset button [2nd] [RESET]. The reset button serves to reset all calculator presets [P/Y], [FORMAT] to their factory default values. If you feel that you’ve accidentally altered your calculator’s presets in a way that could be detrimental, simply press [2nd]→[RESET]→[ENTER] to reinstate the factory defaults. Be sure to reset P/Y to 1 and the number of decimals to the preferred levels. 6. Clearing your work from the statistical data entry registers: To clear the (X, Y) coordinate pairs from the [2nd]→[DATA] memory registers, press: [2nd]→[DATA]→[2nd]→[CLR WORK]→[CE/C] 7. Additional memory registers: You may wish to store the results of certain computations and recall them later. To do this, press [2nd]→[MEM]. To enter data into register M (0), {desired number}→[ENTER]→[CE/C] To enter another number into M (1), [↓]→{desired number}→[ENTER]→[CE/C] B. 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. These rules only work if P/Y is set to 1. 1. For semi-annual computations: PMT = (annual PMT) / 2 I/Y = (annual I/Y) / 2 N = (number of years) × 2 2. For quarterly computations: PMT = (annual PMT) / 4 I/Y = (annual I/Y) / 4 N = (number of years) × 4 HOW TO USE YOUR TI BA II PLUS CALCULATOR ©2003 Schweser Study Program 3 3. For monthly computations: PMT = (annual PMT) / 12 I/Y = (annual I/Y) / 12 N = (number of years) × 12 C. 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 discount future cash flows to the present using the appropriate discount rate. For 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}→[N] {100}→[FV] {0}→[PMT] {8}→[I/Y] [CPT]→[PV] = -92.59 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 {10×2}→[N] {10/2}→[I/Y] {0}→[PMT] {1,000}→[FV] [CPT]→[PV] = -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. 2. 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. HOW TO USE YOUR TI BA II PLUS CALCULATOR ©2003 Schweser Study Program 4 {–1000}→[PV] {5×4}→[N] {14/4}→[I/Y] {0}→[PMT] [CPT]→[FV] = $1,989.79 3. 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) × ($1,000) = $90. The value of the bond today is: {8 × 2}→[N] {$90/2}→[PMT]

{8/2}→[I/Y] {$1,000}→[FV] [CPT]→[PV] = -$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. {3×12}→[N] {0}→[PV] {100}→[PMT] {12/12}→[I/Y] [CPT]→[FV] = -$4,307.69 4. 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 BGN mode by pressing [2nd]→[BGN]→[2nd]→[SET]. BGN will appear in the calculator’s LCD screen. HOW TO USE YOUR TI BA II PLUS CALCULATOR ©2003 Schweser Study Program 5 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: {3×12}→[N] {0}→[PV] {100}→[PMT] {12/12}→[I/Y] [CPT]→[FV] = -$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. 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 × (ert) The formula for continuous discounting is: PV = FV × (e-rt) where: r = the annualized interest rate t = the number of years Example: You have $100 today and have been offered a 6-month continuously compounded investment return of 10%. How much will the investment be worth? Step 1: Compute r × t = 0.1 × 0.5 = 0.05 Note that you always use the decimal representative of both the interest rate and time when performing these computations

Step 2: Compute er×t {0.05}→[2nd]→[ex] = 1.05127 HOW TO USE YOUR TI BA II PLUS CALCULATOR ©2003 Schweser Study Program 6 Step 3: Find the future value $100×1.05127 = $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 × t –0.08×1.5 = –0.12 Step 2: Compute e–rt {–0.12}→[2nd]→[ex] = 0.88692 Step 3: Find the present value $1,000×0.88692 = 886.92 6. 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. To use the IRR and NPV functions in your TI-BA II Plus, you must first familiarize yourself with the up and down arrows (↑↓) at the top of the keyboard. These keys will help you navigate your way through the data entry process. After entering the initial cash flow, you will need to key [↓] once. After each subsequent cash flow, (until the final cash flow) you will need to key [↓] twice, once to enter the cash flow and once to scroll through the display that shows the frequency of the cash flow. After entering the final cash flow, key [↓] once only. Example: Project X has the following expected after-tax net cash flows. The firm’s cost of capital is 10%. Expected Net After-Tax Cash Flows – Project X Year Cash Flow 0 (initial outlay) -$2,000 1 1,000 2 800 3 600 4 200 HOW TO USE YOUR TI BA II PLUS CALCULATOR ©2003 Schweser Study Program 7 The IRR for Project X is: [CF] [2nd] [CLR WORK] 2,000 [+/-] [ENTER] [↓] 1,000 [ENTER] [↓][↓] 800 [ENTER] [↓][↓] 600 [ENTER] [↓][↓] 200 [ENTER] [↓] [IRR] [CPT] gives the result, 14.48884. 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 as follows: The NPV of Project X is: [CF] [2nd] [CLR WORK] 2,000 [+/-] [ENTER] [↓] 1,000 [ENTER] [↓][↓] 800 [ENTER] [↓][↓] 600 [ENTER] [↓][↓] 200 [ENTER] [↓] [NPV] {10} [ENTER] [↓] [CPT] gives the result, $157.63951. 7. The natural log function (Primarily for CFA Levels 2 and 3) The natural log function is intimately related to ex. 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 45/50 = 0.90 Step 2: Compute ln(S/X) {0.90}→[LN] = -0.10536 HOW TO USE YOUR TI BA II PLUS CALCULATOR ©2003 Schweser Study Program 8 As a check of the relationship between [LN] and [ex], press {-1.0536}→[2nd]→[ex]. The result is 0.90. More precisely, eln(x) = x, and, ln(ex) = x D. Your TI-BA II Plus Statistical Functions (use at your own risk). Understanding 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! As with the IRR and NPV calculations, to use the data functions in your TI-BA II Plus, you must first familiarize yourself with the up and down arrows (↑↓) at the top of the keyboard. These keys will help you navigate your way through the data entry process. To enter a data series into your BAII Plus, press [2nd] →[DATA]. Notice that you can enter both X and Y coordinates (you can actually perform a simple linear regression on your calculator!). If you just have one data series (X), you will simply press the down arrow through the prompts for Y data values. Notice that X and Y both begin at X (01) and Y (01) respectively, and that [X (01), Y (01)] represents one X, Y coordinate pair. 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 sample variance for this data set. Step 1: Enter the data: [2nd]→[DATA] X (01) {30}→[ENTER]→[↓]→[↓] X (02) {42}→[ENTER]→[↓]→[↓] X (03) {32}→[ENTER]→[↓]→[↓] X (04) {35}→[ENTER]→[↓]→[↓] X (05) {28}→[ENTER]→ Step 2: Calculate the statistics: [2nd]→ [STAT]→ [↓]→[↓] X = 33.4 [↓] = Sx = sample standard deviation = 5.459 [↓] = σx = population standard deviation = 4.883 HOW TO USE YOUR TI BA II PLUS CALCULATOR ©2003 Schweser Study Program 9 Notice that you’re simply entering through the Y (i) data entry fields – a “1” is placed in the Y data value as you down-arrow through this value. Also, remember that the population variance differs from the sample variance in that the sum of the squared deviations from the mean are 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. Ri (Y) Rm (X) Month 1 12% 15% Month 2 8% 4% Month 3 9% 12% Month 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. Step 1: Enter the data: [2nd]→[DATA] – make sure to [2nd]→[CLR WORK] first!! X (01): {15}→[ENTER]→[↓] Y (01) {12}→[ENTER]→[↓] X (02) {4}→[ENTER]→[↓] Y (02) {8}→[ENTER]→[↓] X (03) {12}→[ENTER]→[↓] Y (03) {9}→[ENTER]→[↓] X (04) {14}→[ENTER]→[↓] Y (04) {10}→[ENTER]→[↓] Step 2: Calculate the statistics: [2nd]→[STAT]→[↓]→ Mean of X [↓] = X = 11.25 Sample standard deviation X [↓] = SX = 4.992 Population standard deviation X [↓] = σx = 4.323 Mean of Y [↓] = Y = 9.75 Sample standard deviation Y [↓] =SY = 1.708 Population standard deviation Y [↓] =σY = 1.479

Intercept term [↓] = a = 6.55 Slope coefficient [↓] = b = 0.284 Correlation X, Y [↓] = r = 0.831 Given this data, we can say that our estimate of the beta of the stock is 0.28, the correlation of stock i’s returns relative to the market is 83.1%, and the R2 of the regression is (0.831) 2 = 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).

posted by Adeel Ashraf @ 10:55 AM

1 Comments:

At 6:15 AM,  Beth said...

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