To bein, look at the ace o the calculator. Every key (except the arithmetic unction keys in the ar riht column and the ive keys on the bottom let row) has two or three unctions: each key s primary unction is noted in white on the key itsel, while each key s secondary unction is noted in old above the key or in blue on the lower ace o the key. To use the unction on the key, simply press the key. To access the old unction above each key, irst press the old key, which we will call the old shit key, and then press the desired unction key. (Note that the old shit key is near the lower let corner o the calculator keyboard.) To access the blue unction on the bottom o each key, irst press the blue key, which we will call the blue shit key, and then press the desired unction. (The blue shit key is located just to the riht o the old shit key.) Turnin the Calculator On and O ON To turn on the calculator, press. Note that the ON key is on the lower let corner o the keyboard the ace o the key has a white "ON". Also, we will desinate keys throuhout this tutorial by the use o small boxes, as above. To conserve the battery, the calculator turns itsel o about 10 minutes ater your last keystroke. To turn the calculator o, press ON aain. Also, note that pressin the old shit key places a little in the lower let corner o the display. Pressin CLX the blue shit key places a little at the bottom o the display. Press the key and the symbol oes away. The shit keys are tole keys that switch back and orth between the reular and the old or blue unctions. They are like the typewriter shit key. Ater you press the old (or blue ) key, look only at old (or blue) writin. Note that the calculator has a continuous memory, so turnin it o does not aect any data stored in the calculator. Clearin the Calculator Clearin the calculator is very important, since unwanted data in memory can result in improper calculations, and hence wron answers. It is best to et into the habit o automatically clearin memory beore startin a calculation. Occasionally, you may purposely want to save data, but, in eneral, you will be enterin all new data, so startin with a clear memory is the saest approach.
Pae 2 There are our dierent levels o clearin data: REG clears all memory and the display. CLX clears the entire display, but not the memory. FIN E clears the inancial reister but not the display. clears the statistics reister and the display. Note that the keys above are desinated as CLEAR keys on the ace o the calculator. Chanin the Display Enter 5555.5555. To chane decimals rom 2 to 4, press 4. 5,555.5555 is displayed. To chane rom 4 places to 2, press 2. 5,555.56 is displayed. (Roundin is automatic.) We usually set the display to 2 places, which is especially convenient when workin with dollars and percentaes. However, we oten use 4 places when dealin with interest rates and rates o return that are entered as decimals. Time Value o Money (TVM) The TVM keys are located on the top row o the keyboard. n i PMT FV In eneral, TVM problems involve our variables three are known and the ourth is unknown. Lump Sums To bein, we consider TVM calculations with sinle (lump) sums. In this situation, we do not use the PMT key, so be sure to either clear all, which sets the payment (PMT) equal to 0, or enter 0 as the PMT when enterin the input data. I you know any three variables, you can ind the value o the ourth.
Pae 3 Example 1: FIN What is the FV o $100 ater 3 years i the interest rate is 26 percent? First, clear with. Next, enter the data. 3 n 26 i 100 PMT 0 (Optional i reisters are cleared.) To determine the FV simply press FV and the FV o -$200.04 is displayed. The HP is prorammed so that i the is + then the FV is displayed as - and vice versa, because the HP assumes that one is an inlow and the other is an outlow. When enterin both and FV, one must be entered as neative and the other positive. Example 2: What is the o $500 due in 5 years i the interest rate is 10 percent? Clear irst and then enter the ollowin data: 5 n 10 i PMT 0 (Optional i reisters are cleared.) 500 FV Pressin the key reveals that $310.46 will row to $500 in 5 years at a 10 percent rate.
Pae 4 Example 3: Assume a bond can be purchased today or $200. It will return $1,000 ater 14 years. The bond pays no interest durin its lie. What rate o return would you earn i you bouht the bond? 14 n CHS CHS 200 (The key chanes the sin.) 0 PMT 1000 FV Simply press the i key and the HP calculates the rate o return to be 12.18 percent. Remember that the HP is prorammed so that i the is + then the FV is displayed as - and vice versa, because the HP assumes that one value is an inlow and other is an outlow. Also note that the neative sin is placed on the 200 entry by pressin the key marked CHS or chane sin. Now suppose you learn that the bond will actually cost $300. What rate o return will you earn? CHS i Override the -200 by enterin 300, then press to et 8.98 percent. I you pay more or the bond, you earn less on it. The important thin, thouh, is that you can do what i analyses with the calculator. ON ON Now press to turn o the calculator. Then turn on the calculator. The display still shows 8.98. The memory is not erased. What was on the screen when you turned the calculator o returns when you CLX RCL n turn it back on. Now press. What was on the screen is one, but press to et N = FIN 14. The other memory reisters also retain inormation unless you press.
Pae 5 Ordinary Annuities Example 1: What is the FV o an annuity o $100 paid at the end o each year or 5 years i the interest rate equals 6 percent? 0 6% 1 2 3 4 5 /))))))))3))))))))3))))))))3))))))))3))))))))1-100 -100-100 -100-100 5 n 6 i 0 100 CHS PMT Now press the Example 2: FV key, and an FV o $563.71 is displayed. What is the o the same annuity? Leave data in calculator, but enter 0 as the FV to override, then press to et $421.24. Annuities Due Each payment o an annuity due occurs at the beinnin o the period instead o at the end as with a reular BEG annuity. In essence, each payment is shited back one period. To analyze annuities due press. The word BEGIN appears on the screen. Now the HP analyzes the cash lows based on beinnin o END period payments. Chane back to end mode by pressin. Interest Conversion The ollowin equation is used to convert a nominal rate to an eective rate.
Pae 6
Pae 7 Given: k Nom = 10% and m = 12 payments/year, However, it s much easier to convert the nominal rate usin the calculator: FIN First, clear the inancial reister,. 10 ENTER 12 n i CHS PMT FV 10.47% shows on the screen. Cash Flow Operations We can also ind the, FV, and IRR (rate o return) o a series o unequal cash lows. Example 1: Uneven Cash Flows Assume the ollowin cash lows: What is the o these CFs? 0 10% 1 2 3 4 /))))))))3))))))))3))))))))3))))))))1 0 50 100 150 200 FIN First clear the HP s inancial reister,. CF 0 0 Sets CF 0 equal to 0. CF 50 j Sets CF 1 equal to 50. 100 150 200
Pae 8 The CFs rom the time line are entered. Now enter the interest rate: 10 i At this point the HP knows the cash lows, the number o periods, and the interest rate. To ind the, N press to et = N = $377.40. Example 2: Embedded Annuities We have these cash lows, which contain embedded annuities: 0 10% 1 2 3 4 5 6 7 8 9 /)))))))3))))))3))))))3))))))3))))))3))))))3))))))3))))))3)))) ))1 0 100 100 100 200 200 300 300 300 300 What s the? FIN Clear the HP,. 0 CF 0 100 3 200 2 300 4 N j N j N j Now the HP knows the cash lows. Thus, enter the interest rate: 10 i N Now press to et = N = $1,099.94.
Pae 9
Pae 10 To check your entries: RCL RCL 0 to see CF 0. 1 to see irst CF entry, 100.00 in this example. 1 to see how many times CF 1 is repeated. The display shows that n RCL N j the irst CF occurs three consecutive times. Example 3: The Rate o Return Oered by an Investment (IRR) 1 Assume that we invest $1,000 now (t = 0) and then expect to receive an uneven set o cash lows. Here is the CF time line: What rate o return will we earn? Enter the ollowin: 0 1 2 3 4 /))))))))3))))))))3))))))))3))))))))1-1000 300 400 200 600 FIN 1000 CHS CF 0 300 400 200 600 IRR = 16.71% 1 I a neative CF occurs at the end o a project s lie, then the HP may ive an error messae, indicatin that ENTER RCL R/S there are two IRRs. Enter data, then enter 10 and then to et the irst IRR. Then enter a ENTER RCL R/S lare percentae, such as 100 and then to ind the other IRR. You miht have to experiment with uesses to locate the two IRRs.
Pae 11 You can also determine the N o the investment. Leave data entered and then enter the opportunity cost interest rate, say 8 percent. To ind N press: 8 i N The N o $220.50 is displayed. Thus, the o the cash inlows exceeds the cost o the investment by $220.50. Statistical Calculations The HP can also be used or several types o statistical calculations. Mean and Standard Deviation (F) Year Sales 1994 $150 1995 95 1996 260 What s the mean (averae) and standard deviation (F) o sales over the 3 years? Use the E+ key to enter data: E Clears the statistical reister. E+ 150 A number 1 is displayed. E+ 95 A number 2 is displayed. E+ 260 A number 3 is displayed. Determine the mean and standard deviation by simply pressin _ X The mean equals $168.33. S The standard deviation is $84.01. S is the sample standard deviation.
Pae 12 Linear Reression Beta coeicients can be calculated by usin the HP s linear reression capabilities. The X (independent variable) and Y (dependent variable) values must be entered in the proper sequence, where X data is on the horizontal axis (market) and Y data is on the vertical axis (stock). Enter the data as ollows: Year Market (k M ) Stock (k j ) 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 E Note: The order in which the data is entered is very important. The Y value (k j ) must be entered beore the X value (k M ). ENTER E+ 38.6 23.8 CHS ENTER CHS E+ 24.7 7.2 ENTER E+ 12.3 6.6 ENTER E+ 8.2 20.5 ENTER E+ 40.1 30.6 0 y, ^ r The value -8.92 is y when x = 0, or k j when k M = 0, which is the vertical axis intercept. STO 0 Stores the value o the Y intercept or use in calculatin the slope (beta). 0 x, ^ r 5.57 is the value o x when y = 0. 0 RCL CHS X Y > < The value displayed, 1.60, is the slope coeicient, or the beta coeicient. Amortization
Pae 13 The HP can also be used to calculate amortization schedules. Example: Determine the interest and principal paid each year and the balance at the end o each year on a three-year $1,000 amortizin loan which carries an interest rate o 10 percent. The payments are due annually. Perorm the ollowin steps: 3 n FIN Clears the inancial reister. 10 i 1000 PMT A payment o -402.11 is displayed. This is the amortization schedule correspondin to the loan. Be. Bal. Payment Interest Princ. Repmt. Endin 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 With the data still entered in the TVM menu, do the ollowin: 1 AMORT Tells the calculator that you want to amortize the irst payment only. The display shows -100.000, which is the interest payment durin the irst year. Write it into a table as 100.00. X > < Y The display shows -302.11. This is the repayment o principal in the irst year. Write it in the table. RCL The display shows 697.89. This is the remainin principal balance at the end o the irst year. Write it down. AMORT 1 This tells the calculator that you want to amortize the next payment only. AMORT The number o payments keyed in just beore is taken to be the payments ollowin any that have been already amortized. Thus, keyin in 1 at this step moved you into the second payment period.
Pae 14-69.79 is the interest paid in Year 2.
Pae 15 X > < Y -332.32 is the principal paid in Year 2. RCL 365.57 is the endin balance at end o Year 2. AMORT 1-35.56 is the interest paid in Year 3. X > < Y -365.55 is the principal repayment in Year 3. RCL 0.02 is the balance at end o Year 3. See the manual or an explanation o how to do monthly amortization. Next, with the data still in the calculator, do the ollowin: 1000 This returns the calculator to the oriinal principal balance o $1,000. 3 AMORT Tells the calculator that you want to amortize the irst three payments toether. In this example there are only 3 payments, but that is not always the case. The display shows -206.35. This is the total interest paid over Years 1 to 3. X > < Y -999.98 is the total repayment o principal over Years 1 to 3. RCL 0.02 is the remainin balance.