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HP_10BII - Hewlett-Packard 1031 Tutorial for Use with...

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Unformatted text preview: Hewlett-Packard 1031! Tutorial for Use with Fundamentals 11/e a nd Concise 5/e This tutorial was developed for use with Brigham and Houston’s Fundamentals of Financial Management, JJ/e and Concise, 5/e, especially Chapter 2, the Time Value of Money. The calculator’s 143-page manual covers all of its functions in detail, and it is worth the time to go through the manual. However, this does take time, and many of the calculator’s features are not necessary for working the problems in the text. Therefore, we focus on just what’s needed to work the text problems. We recommend that you read the text to get an idea about the concepts, then go through the tutorial to learn how to work the problems efficiently. The examples in the tutorial are identical to the examples in the text, which makes simultaneous coverage especially efficient. Although the tutorial focuses on Chapter 2, it does have a section on Statistical Calculations, which are needed for Chapter 8 of the text. You can defer that part of the tutorial until you get to Chapter 8 of the text. Also, note that the TVM applications covered in text Chapter 2 and this tutorial are required for many text chapters, especially those dealing with bond and stock valuation and capital budgeting. Therefore, it will pay big dividends to learn how to use your calculator early in the course, like right now. BASIC CALCULATOR FUNCTIONS The HPIOBII performs all the basic arithmetic functions: addition, subtraction, multiplication, division, exponents, and so on that can be done with any calculator. But it can also solve TVM problems and do certain statistical and math calculations that simple calculators cannot do. The GOLD and PURPLE shift keys Most of the keys have white numbers or lettering on top, then gold lettering on the sloped front side. There is also purple lettering on the case just above the six middle keys. The white, gold, and purple colors are used because some keys can perform multiple functions. The two shift keys with no lettering but a gold (looks orange) and a purple swatch allow the user to activate the gold and purple function keys. If neither key is pressed, then the keys perform the function indicated by the white lettering. Also, note that pressing the gold shift key GOLD places the word “SHIFI'” in the lower left corner of the LCD display. Press the GOLD key again and SHIFT goes away. Likewise, pressing the PURPLE key places the word “STATS” in the lower left area of the display. The GOLD key is a toggle key that switches back and forth between the regular and the gold functions. Likewise, the PURPLE key toggles between regular and purple (STATS) functions. The GOLD and PURPLE keys are like typewriter shift keys. After you press Hewlett-Packard IOBII Tutorial Page 2 the GOLD key, look only at the gold functions, and after pressing the PURPLE key, look only at the purple functions. In this tutorial, whenever you see the GOLD or PURPLE key, the lettering on the next key corresponds to the gold or purple lettering, not the primary (white) lettering. Turning the calculator ON and OFF To turn on the calculator, press ON . Note that the ON key is in the lower left corner of the keypad—the face of the key has a white "ON," while the word "OFF" appears at the bottom of the key in gold. To turn the calculator off, press GOLD OFF . Thus, by pressing the gold shift key first, we are activating the gold function below the “ON” key, which turns the calculator off. To conserve the battery, the calculator turns itself off about 10 minutes after your last keystroke. Note too that the calculator has a continuous memory, so turning it off does not affect any data stored in the calculator. However, the display does go to zero. Clearing the calculator To clear the calculator’s memory, press GOLD C ALL . Clearing the calculator is important, since leftover data in the calculator’s memory can lead to errors. You should get into the habit of automatically clearing memory before starting a new 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. There are three different ways to clear data: 6 clears numbers on the display one at a time. C clears the entire display, but not the memory. GOLD C ALL clears the display and all memory. This is the safest way to clear data, and the procedure we generally use. Changing the decimal display Depending on what you are doing, you may want no decimal places, two decimal places, 4 decimal places, etc. The number of decimals displayed can be changed easily. To demonstrate, type the value 5555.5555 and press the = key. If your display is currently set for two decimal places (the default setting), the value is truncated and you only see 5,555.56. To change the number of decimal places from 2 to 4, press GOLD DISP 4 . The value 5,555.5555 is displayed instantly. To change back from 4 decimal places to 2, press GOLD DISP 2 . Now the value 5,555.56 is displayed. (Rounding is automatic.) Hewlett-Packard loBII Tutorial ewe—3 We usually set the display to 2 places, which is convenient when working with dollars and percentages. However, we often use 4 decimal places when dealing with interest rates and with rates of return that are entered as decimals. If periods and commas are reversed, press GOLD . / , . (Many European countries use a period-comma convention that is the opposite of ours. In other words, the number 5,555.56 would be written as 5.555,56 in some countries.) Operation pending and screen brightness When performing a function, you will notice that “PEND” will often appear in the lower part of the display. This simply means that an operation is pending, or awaiting the next step. For example, press 4 + .The calculator then waits for the denominator, so “PEND” appears in the display. Now proceed as follows: Enter 6 and = to get 0.67. Press GOLD DISP 4 to see 0.6667. Press GOLD DISP 2 to shift back to 2 decimal places. Lastly, to control the brightness of the LCD display, hold down ON and, depending on whether you want more or less brightness, press either + or — . USING THE FINANCIAL FUNCTIONS Settings: Periods per Year (P/YR) The HPloBII comes out-of-the-box set to assume that any payment stream entered into the calculator is based on monthly payments (12 payments per year). However, most textbook problems are based on one payment per year. So, if you tell the calculator there are 8 payments (by setting N = 8), it would assume that they are made monthly, not annually, so the calculated answer would be wrong—you would be too high on PVs and too low on FVs. To check the current payments per year setting, press GOLD and hold down C ALL . To change the setting to one payment per year, press 1 GOLD P/YR (top row, second from right). Now the calculator is set to assume 1 P/YR. To confirm this setting, press and hold GOLD C ALL . We normally leave the calculator setting at 1 P/YR. If a problem calls for monthly payments, we adjust the number of periods and the interest rate as explained later in this tutorial. However, some problems will require you to work with the 12 P/YR setting. Immediately following such problems, we set our calculators right back to 1 P/YR. Hewlett-Packard IOBII Tutorial Page 4 Settings: BEGIN and END Mode Annuities provide payments over a number of periods. For some annuities those payments are made at the beginning of each period, while for others the payments are made at the end of the periods. The calculator can be set to deal with either payment pattern, or at BEGIN or END mode. Most annuities have end-of-period payments, and if no notation is shown on the display screen the calculator is set at END Mode. To toggle between BEGIN and END modes, press GOLD BEG/END . The word “BEGIN” appears in the display when the calculator is in BEGIN mode, and it disappears from the display when in END mode. We recommend leaving the calculator in END mode, then switching to BEGIN when required, and then switching back to END when you are done. BASIC TIME VALUE OF MONEY (TVM) CALCULATIONS These five TVM keys are located on the top row of the keypad, with white notation: N I/YR PV PMT FV . If you know any four of the five TVM variables, the calculator will solve for the fifth. FV and PV for lump sums We first consider TVM calculations with a single (lump) sum. Example 1: Calculating the F V of a lump sum What’s the FV of $100 after 3 years if the interest rate is 5%? First, clear by pressing GOLD C ALL . This sets all the variables, including PMT, to zero. Next, enter the following data: 3 N 5 I/YR 100 +/— PV The +/- key changes the 100 to -100. 0 PMT You could skip this step, but it’s safer to enter the 0. Now press FV to get the answer, $115.76. Since the PV was entered as a negative number, the FV is automatically displayed as a positive number. Example 2: Calculating the PVof a lump sum What is the PV of $115.76 due in 3 years if the interest rate is 5%? Hewlett-Packard loBII Tutorial gag Clear the calculator and then enter the following data: 3 N 5 I/YR 0 PMT 115.76 FV Pressing PV gives the answer, -$100. If we had $100 today, it would grow to $115.76 after 3 years at a 5% rate. Example 3: Calculating I/ YR Assume you lend someone $100 today and they must pay you $150 after 10 years. No payments will occur between now and Year 10. What rate of return would you earn? 10 N 100 +/— PV Convert the 100 to -100 to indicate an outlay. 0 PMT 150 FV Press the I/YR key and the calculator provides the earned rate of return, 4.14, which means 4.14%. Note that the calculator displays 4.14 rather than 0.0414 or 4.14%. Don’t clear the calculator; we need the data for the next example. Example 4: Overriding a value to find a new interest rate, I/ YR Suppose you want to modify the preceding example, lending only $95 but still receiving $150 after 10 years. What rate of return would you earn on the modified loan? If you left data from the preceding example stored in your calculator, you can override (or replace) the PV of 100. Just enter 95 +/— PV , and when you press I/YR , you get 4.67%, the new interest rate on the loan. You could override other variables similarly and thus do “what if" analyses to see how the output changes with changes in the inputs. Example 5: Calculating N Suppose you currently have $500,000 in an account that is earning 4.5%. You want to find out how long it will take your account balance to reach $1,000,000. 4.5 I/YR 500000 +/— PV 0 PMT 1000000 FV Hewlett-Packard IOBII Tutorial Page 6 Press the N key and the calculator returns 15.75, the number of years before you have $1,000,000 in the account. Note that the calculator requires you to enter the interest rate as 4.5 rather than either 0.045 or 4.5%. Recalling information Now press GOLD OFF to turn off the calculator, and then turn it back on. The display shows 0.00. Is the data in the TVM memory erased? No! What was on the display is gone, but the basic data can be recalled by pressing the recall key, RCL , and then the key for the item you want to recall. For example, to recall the interest rate, press RCL I/YR , and 4.5 will appear on the display. Any of the TVM inputs can be recalled, and the input data will remain stored until you press GOLD C ALL . Annuities Annuities can also be analyzed with the TVM keys. Now we have a payment, so we must enter a non-zero value for the PMT. There are 5 terms in the basic TVM equation, and if we enter data for any 4 variables the calculator will solve for the fifth. Example 6: F V of an ordinary annuity What’s the FV of an ordinary annuity of $100 for 3 years if the interest rate is 5%? 0 5% 1 2 3 I—l—I—I 0 -100 -100 -100 There is no beginning amount, so PV = 0. Thus N, I/YR, PV, and PMT are given, and we must solve for the FV: 3 N 5 I/YR 0 PV 100 +/— PMT Now press the FV key to find the answer, FV = $315.25. Example 7: F V of an annuity due If the interest rate is 5%, what is the FV of an annuity due where we deposit $100 at the beginning of each of the next 3 years? 0 5% 1 2 3 I—l—I—I -100 -100 -100 Hewlett-Packard IOBII Tutorial gag After clearing, set the calculator to BEG mode and then enter values for the input variables: GOLD BEG/END (to switch to BEGIN mode) 3 N 5 I/YR 0 PV 100 +/— PMT When you press the FV key, the answer, $331.01, is displayed, along with the word “BEGIN.” Most text problems have end-of-period payments, so it’s a good idea to get into the habit of reverting to END mode after a problem: GOLD BEG/END . Example 8: PVof an ordinary annuity What’s the PV of the ordinary annuity discussed in Example 6? Enter the following data: 3 N 5 I/YR 100 +/— PMT 0 FV Then, press PV to get $272.32. If you left the data in the calculator, pressed GOLD BEG/END , and then pressed PV , you would get the PV of the annuity as an annuity due, $285.94. Again, revert to END mode after finishing this exercise. Example .9: Finding the payments for an annuity (PMT) The future value of an ordinary 5-year annuity is $10,000, and the interest rate is 6%. What are the annual end-of-year payments? What would each payment be if they were made at the beginning of the year? Since payments are made at the end of each year, make sure the calculator is set to END mode. N, I/YR, PV, and FV are given, so we solve for the PMT: 5 N 6 I/YR 0 PV 10000 FV Now, press the PMT key to get the answer, PMT = -$1,773.96. Hewlett-Packard IOBII Tutorial Page 8 To find PMT if the annuity were an annuity due, then we would leave the data in the TVM register, switch to BEGIN mode by pressing GOLD BEG/END , and then pressing PMT to get -$1,673.55. Example 10: Calculating the number of periods (N) Suppose you plan to deposit $1,200 at the end of each year in an account that pays 6% interest each year. How long will it take for your account to reach $10,000? First clear the calculator and make sure you are in END mode. Then make these data entries: 6 I/YR 0 PV 1200 +/— PMT 10000 FV Now press the N key to find the number of years, 6.96, which you might round to 7. Notice that the PMT is entered as a negative because you are making a deposit, while FV is positive because you can withdraw it. Either PMT or FV must be negative—otherwise, the calculator will produce a nonsensical answer, in this case -11.90 years. Note too that if the payments occur at the beginning of each year, you would follow the same procedure, but here your calculator would be set to BEGIN mode. The answer would then be 6.63 years. Example 11: Calculating the interest rate (I/ YR) Continue with the previous example, but now assume you can only save $1,200 at the end of each year. You still want to accumulate $10,000 by the end of 5 years. What interest rate would you have to earn to reach this goal? Here are the keystrokes: 5 N 0 PV 1200 +/— PMT 10000 FV Make sure the calculator is in END mode, and press the I/YR key. The required rate of return, or interest rate, is 25.78%. If the payments occurred at the beginning of the years, you would use the same keystrokes, but with the calculator set to BEGIN mode, the answer would be 17.54%. Example 12: Uneven cash flows: annuity plus a lump sum Assume that you can buy a security that will make the payments shown on the following time line. What is the PV of this stream if the interest rate is 12%? Hewlett-Packard loBII Tutorial ewe—9 o 12% 1 2 3 4 5 l—l—l—l—l—l 100 100 100 100 100 1,000 1,100 Here we have a 5-year ordinary annuity plus a $1,000 lump sum at the end of Year 5. The calculator finds the PV of the annuity, the PV of the Year 5 lump sum payment, and then sums them, using the basic TVM keys as follows: 5 N 12 I/YR 100 PMT 1000 FV Make sure the calculator is in END mode, and press the PV key to find the PV, -$927.90, which shows up as a negative because PMT and FV were entered as positive numbers. Example 13: Irregular series of cash flows Assume that you can buy a security that will make the payments shown on the following time line. At an interest rate of 12%, what is the PV of the security? 0 12% 1 2 3 4 5 l—l—l—l—l—l 100 300 300 300 500 This problem requires us to use the calculator’s “cash flow register," where we enter a series of inputs and then perform a calculation based on those inputs. After clearing the calculator’s memory, make the following entries, which amounts to entering the time line data into the calculator as a kind of “vertical time line." GOLD C ALL 0 CF, (Cash flow att = 0) 100 CFj (Cash flow att = 1) 300 CFj (Cash flow att = 2) 300 CFj (Cash flow att = 3) 300 CFj (Cash flow att = 4) 500 CFj (Cash flow att = 5) These keystrokes tell the calculator to store the cash flows shown on the time line into the cash flow memory. Each time you enter a cash flow and press the CF, key, a number flashes on the screen to indicate which cash flow is being entered. For instance, after the first entry, “0" flashes on the screen because this is the cash flow at time 0. After the second entry, a “1” appears briefly. Note also that if you press and hold down the Hewlett-Packard IOBII Tutorial PagelO CFj key, the entry number will be displayed until you release the key. Finally, note that a “C-FLOW" box appears on the display and says “CF” within it, indicating that the cash flow register is being used. After the CFs have been entered, enter the interest rate as 12 I/YR . Next, to find the PV of the cash flows, press GOLD NPV to find NPV = PV = $1,016.35.1 A short-cut could be used to enter these cash flows. Since the $300 cash flow occurs three times, we could, after first clearing all data, make the following entries: 0 CF,- 100 CF,- 300 CF,- 3 GOLD Nj Tells the calculator that the $300 cash flow occurs 3 times. 500 CF,- 12 I/YR Now press GOLD NPV to find the present value, PV = NPV = 1,016.35. The short-cut procedure is not particularly useful when there are only a few cash flows, but it would be useful if we had a 40-year stream with 2 sets of 20 equal payments. Example 14: The Internal Rate of Return (IRR) Assume that we invest $1,000 today (t = 0) and expect to receive an uneven set of cash flows in the future. Here is the CF time line: 0 12% 1 2 3 4 5 I—l—I—l—I—l -1000 100 300 300 300 500 What rate of return will we earn on the $1,000 investment? Here are the entries: GOLD CALL 1000 +/— CF]- 100 CF,- 300 CF,- 3 GOLD Nj 500 CF,- 1 NPV stands for Net Present Value. Our stream has no negative cash flows, but if there were some negative flows, the calculator would net them out to produce the NPV. There is a negative flow in the next example. Hewlett-Packard loBII Tutorial ERIE—11 Press GOLD IRR/YR to solve for the interest rate, which is 12.55%. So, if we make this investment, we will earn 12.55% on our money. At 12.55%, the sum of the inflow PVs is equal to the $1,000 investment. Leave the data in the calculator, and we will show you how to calculate the NPV without entering new data except for the interest rate. Assuming I/YR = 12%, enter this interest rate by simply pressing 12 I/YR , and then press GOLD NPV to find the NPV, which is $16.35. The NPV and IRR are used in capital budgeting, and we virtually always calculate both with a given set of cash flow data. The important point is that you need to enter the cash flow only once to obtain the NPV and the IRR. Example 15: Effective Annual Rate (EAR, or EFF % ) If interest is paid more than once per year, then we often need to calculate an effective annual rate for use in TVM calculations. The following equation is used to convert nominal rates to effective rates: M EAR = EFF% = [1 + 1:2”) — 1, Here INOM is the stated rate and M is the number of compounding periods per year. The calculator is programmed to solve this equation, as we illustrate with this example: What is the EAR (or EFF%) on a bank account that pays a stated (or nominal) rate of 5% but with semiannual (twice yearly) compounding? Here are the keystrokes: 5 GOLD NOM% Enters the nominal r...
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