ࡱ>  bjbj .?O8_6_6_6s6s6s6s6/7,s6a@[8[8[8[8[8Ci_6.![8[8Ah[8_6[8y, [8P?{s6h10a,X0_6"a : 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 keys primary function is noted on the key itself, while each keys 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. The key 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 owners manual for other methods of clearing information. 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. 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  (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. 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  (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. 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 . 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, its 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, . Next, enter the cash flows:  Sets CF0 equal to 0 and moves to CF1.  Sets CF1 equal to 50 and moves to frequency of occurrence of CF1.  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 Whats the PV? Clear, set P/YR = 1 if changed. First enter the cash flow worksheet by pressing then clear any previous cash flow  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 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 projects 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  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 () Year Sales 1994 $150 1995 95 1996 260 What s the mean (average) and standard deviation () 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 Beta coefficients can be calculated by using the BAII PLUSs 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 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 its 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. 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 ON/OFF ON/OFF 2nd 2nd 2nd 2nd MEM 2nd CLR WORK 2nd QUIT 2nd CLR TVM 2nd CLR TVM CE/C ! 2nd FORMAT 4 ENTER 2nd QUIT 2nd FORMAT 2 ENTER 2nd QUIT 2nd P/Y 2nd P/Y ENTER 2nd QUIT 2nd P/Y N 2nd QUIT I/Y PV PMT FV 2nd CLR TVM 2nd CLR TVM N I/Y PVV PMT CPT FV N I/Y PMT FV CPT PV N +/- PV PMT FV CPT I/Y +/- PV CPT I/Y ON/OFF ON/OFF RCL N N I/Y PV +/- PMT CPT FV CPT PV 2nd BGN 2nd SET CE/C 2nd BGN 2nd SET CE/C 2nd ICONV ! ENTER ! ENTER ! CPT CF 2nd CLR WORK ENTER ! ENTER ! ENTER ! ENTER ! ENTER ! 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