Texas Instrument BAII PLUS Tutorial

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 ON/OFF . To turn off the calculator, press ON/OFF . 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 2nd key is a toggle key that switches back and forth between the “regular” and the “2nd” functions. 2nd is like the typewriter shift key. After you press 2nd , 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: 2nd MEM 2nd CLR WORK clears all 10 memory locations and the display. 2nd QUIT 2nd CLR TVM clears the TVM worksheet. 2nd CLR TVM CE/C 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. 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. 2nd 2nd FORMAT FORMAT 2 4 ENTER ENTER 2nd 2nd QUIT QUIT . 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 P/Y the current setting, press 2nd . 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 2nd P/Y ENTER 1 2nd QUIT . Now the calculator is set to assume 1 period/year. To confirm this setting, press 2nd P/Y 2nd QUIT . 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. N I/Y PV PMT FV 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 2nd ,which sets the CLR TVM 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 2nd CLR TVM Next, enter the data. 3 N 26 I/Y 100 PV 0 V PMT (Optional if registers are cleared.) To determine the FV simply press CPT FV 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 0 500 N I/Y PMT (Optional is registers are cleared.) FV CPT Pressing the 10 percent rate. PV key reveals that $310.46 will grow to $500 in 5 years at a 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 0 1000 N +/- (The +/- key changes the sign.) PV PMT FV Simply press the be 12.18%. CPT I/Y key and the BAII PLUS calculates the rate of return to 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? +/- PV CPT I/Y 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 calculator ON/OFF ON/OFF to turn off the calculator. Then turn on the . The display shows 0.00. Is the memory erased? Not completely. What was on the screen is gone, but press RCL N 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 N I/Y PV 0 100 +/- PMT Now press the CPT FV 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 get $421.24. CPT PV to 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 BGN 2nd SET CE/C analyze annuities due press 2nd . “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 BGN 2nd SET CE/C pressing 2nd . 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: 2nd ↓ ↓ ICONV 10 ↑ 12 ENTER ENTER CPT 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 CLR WORK analyses, 2nd . CF then clear any previous cash flow Next, enter the cash flows: 0 ENTER ↓ Sets CF0 equal to 0 and moves to CF1. ENTER ↓ Sets CF1 equal to 50 and moves to frequency of occurrence of CF1. ENTER ↓ Tells calculator that the $50 CF occurs only once. 100 ENTER ↓ 1 ENTER ↓ 150 ENTER ↓ 1 ENTER ↓ 200 ENTER ↓ 1 ENTER ↓ 50 1 The CFs from the time line are entered. Now enter the interest rate. NPV 10 ENTER ↓ At this point the BAII PLUS knows the cash flows, the number of periods, and the interest rate. To find the PV, press CPT 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. CF First enter the cash flow worksheet by pressing analyses, 0 2nd then clear any previous cash flow . Next, enter the cash flows: CLR WORK ENTER ↓ Sets CF0 equal to 0 and moves to CF1. ENTER ↓ Sets CF1 equal to 100 and moves to frequency of occurrence of CF1. ENTER ↓ ENTER ↓ 2 ENTER ↓ 300 ENTER ↓ 4 ENTER ↓ 100 3 200 Tells calculator that the $100 CF occurs three consecutive times. Now the BAII PLUS knows the cash flows. Thus, enter the interest rate: NPV 10 ENTER ↓ . At this point the BAII PLUS knows the cash flows, the number of periods, and the interest rate. To find the PV, press CPT to get PV = NPV = $1,099.94. To check your entries: CF 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 analyses, 1000 300 400 200 600 2nd +/- CLR WORK CF then clear any previous cash flow . Next, enter the cash flows: ↓ ENTER ENTER ↓ ↓ ENTER ↓ ↓ ENTER ↓ ↓ ENTER ↓ ↓ Sets CF0 equal to -1,000 and moves to CF1. 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. Now the BAII PLUS knows the cash flows. Thus, simply press IRR of 16.71 percent is displayed. IRR CPT and the __________________ If 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). 1 2 If 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 I/YR 8 ↓ ENTER CPT 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? 2nd First select the data-entry portion of the statistics worksheet by pressing CLR WORK then clear any previous data entries, 2nd . Next, enter the data: 150 95 260 ENTER ↓ ↓ ENTER ↓ ↓ ENTER ↓ ↓ DATA This enters 150 as the data entry and tells the calculator there is no Y-variable associated with the X variable. This enters 95 as the second data entry and tells the calculator there is no Y-variable associated with the X-variable. 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 2nd STAT CLR WORK then clear any previous data entries, 2nd . “LIN” should now be displayed on the screen. Keep pressing 2nd then SET 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 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 1 2 3 4 5 Market (Km) 23.8% -7.2 6.6 20.5 30.6 Stock (Kj) 38.6% -24.7 12.3 8.2 40.1 First select the data-entry portion of the statistics worksheet by pressing CLR WORK Then clear any previous statistical entries, 2nd . Next, enter the data as follows: 23.8 ENTER ↓ 38.6 ENTER ↓ 7.2 24.7 This enters 38.6 as the first Y variable. +/- ENTER ↓ +/- ENTER ↓ This enters -7.2 as the second X variable. This enters -24.7 as the second Y variable. ↓ 12.3 ENTER ↓ This enters 12.3 as the third Y variable. 20.5 ENTER ↓ This enters 20.5 as the fourth X variable. 8.2 ENTER ↓ This enters 8.2 as the fourth Y variable. 30.6 bENTER ↓ This enters 30.6 as the fifth X variable. 40.1 ↓ This enters 40.1 as the fifth Y variable. ENTER DATA This enters 23.8 as the first X variable. ENTER 6.6 2nd This enters 6.6 as the third X variable. Now select the statistical calculation portion of the statistics worksheet by pressing then clear any previous statistical entries, 2nd . 2nd STAT CLR WORK “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 2nd DATA 2nd CLR WORK . Amortization The BAII PLUS can also be used to calculate amortization schedules. First, clear the TVM registers by pressing 2nd QUIT 2nd CLR TVM 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. ( 2nd P/Y 2nd QUIT ) Now perform the following steps: 3 N 10 I/Y 1000 PV CPT PMT A payment of -402.11 is displayed. Now we will use the amortization worksheet to generate an amortization schedule for the loan: 2nd ↓ AMORT 1 ENTER 2nd CLR WORK Enters the Amort worksheet and clears any old contents. 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. ↓ CPT 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. 1 2 3 Beg. Bal. 1,000.00 697.89 365.57 Payment 402.11 402.11 402.11 Interest 100.00 69.79 36.56 Princ. Repmt. 302.11 332.32 365.55 Ending Bal. 697.89 365.57 .02