HP 12C Financial Programmable Calculator Manual do Utilizador

9transaction costs are expected to be 7% of the resale price. The mortgage is the same as that indicated in the preceding example.• What will the Mort

99StatisticsCurve FittingExponential Curve FitUsing the function of the HP-12C, a least squares exponential curve fit may be easily calculated accord

1005. Press to obtain B.6. Press 1 to obtain the effective growth rate (as a decimal).7. To make a y-estimate, key in the x-value and

101 CLEAR 00-01- 34 02- 43 2303- 3404- 49 0005-43, 33 0006- 43 207- 3408- 311 09- 1 10- 43 2 11- 43 220 12- 0 13- 43 2 14- 43 2215- 3116- 3417- 3318

1021. Key in the program and press CLEAR .2. For each input pair of values, key in the y-value and press , key in the corresponding x-value and p

103Logarithmic Curve FitIf your data does not fit a line or an exponential curve, try the following logarithmic curve fit. This is calculated accordin

1041. Press CLEAR .2. Key in the first y-value and press . Key in the first x-value and press . Repeat this step for each data pair.3. After a

105Power Curve FitAnother method of analysis is the power curve or geometric curve. The equation of the power curve is y = AxB, and the values for A a

106levels of the Tower of Pisa (which was leaning even then) and timed its descent by counting his pulse. The following data are measurements Galileo

1071. Press CLEAR .2. If you are summing one set of numbers, key in the first number and press . Continue until you have entered all of the values.3

108this procedure computes the mean, standard deviation, and standard error of the mean.1. Press CLEAR .2. Key in the first value and press .3. K

10KEYSTROKES DISPLAY CLEAR 00-0 01- 002- 11 103- 44 1 704- 45 705- 262 06- 207- 10 708- 44 71 09- 1 110-44 40 11 11- 12 12- 2 13- 42 11 014- 44 0 51

1091. Key in the program.2. Press CLEAR .3. Key in the first value and press . CLEAR 00- 001-44 40 002- 2003- 49 0004-43, 33 00 005- 45 0 106-

1104. Key in the respective frequency and press . The display shows the number of data points entered.5. Repeat steps 3 and 4 for each data point.6.

111If there is a close agreement between the observed and expected frequencies, x2 will be small. If the agreement is poor, x2 will be large.The follo

112The number of degrees of freedom is (n-1). Since n = 6, the degrees of freedom = 5.Consulting statistical tables, you look up x2 to a 0.05 signific

1131. Key in the program.2. Press CLEAR .3. Key in the first Oi value and press .4. Key in the first Ei value and press .5. Repeat steps 3 and 4 f

114Relative error less than 0.042% over the range 0 < x < 5.5Reference:Stephen E. Derenzo, "Approximations for Hand Calculators Using Small

11504- 203 05- 3

1161. Key in program.2. Key in x and press to computed Q(x).5 06- 51 07- 108- 40 009- 45 010- 205 11- 56 12- 62 13- 214- 407 15- 70 16- 03 17- 3 018

1173. Repeat step 2 for each new case.Example: Find Q(x) for x = 1.18 and x = 2.1.CovarianceCovariance is a measure of the interdependence between pai

118Try the previous example using the following HP-12C program:54 62 51 68 40 74 -354.14Sxy 1 1 1 -303.55S'xyKEYSTROKES DISPLAY CLE

11 427- 44 428- 33 29- 43 35 3630-43, 33 36 131- 45 1 32- 42 25 033-44 30 00 34- 0 1735-43, 33 1736- 11 237- 45 2 838- 45 839- 25 240-44 40 241- 3

1191. Key in the program.2. Press CLEAR .3. Key in the y-value and press .4. Key in the x-value and press . Repeat steps 3 and 4 for all data pair

120where m, n are integers and 69 ≥ m ≥ n ≥ 0.Use the following HP-12C program to calculate the number of possible permutations.1. Key in the program.

121CombinationA combination is a selection of one or more of a set of distinct objects without regard to order. The number of possible combinations, e

1221. Key in the program.2. Key in m and press .3. Key in n and press to calculate mCn.4. For a new case, go to step 2.Example: A manager wants to

1231. Key in the program.2. To generate a random number, press .3. Repeat step 2 as many times as desired.Example: Generate a sequence of 5 random nu

124Personal FinanceHomeowners Monthly Payment EstimatorIt is often useful, when comparison shopping for a mortgage or determining the appropriate pric

125The following HP-12C program may be used instead of the above. -672.16 Approximate monthly payment.KEYSTROKES DISPLAY CLEAR 00- 01- 43 8 102- 45

1261. Key in the program.2. Press CLEAR .3. Key in the annual interest rate and press .4. Key in the term of the loan in years and press .5.

127Tax-Free Individual Retirement (IRA) of Keogh Plan.The advent of tax-free retirement accounts (IRA or Keogh) has resulted in considerable benefits

12806- 31 107- 45 108- 485 09- 510- 2511- 161 12- 113- 40 14- 45 1515- 2016- 311 17- 118- 481 19- 10 20- 0 21- 45 1122- 2123- 1024- 31 25- 45 121 26-

121. Press and press CLEAR .2. Key in loan values:• Key in annual interest rate and press • Key in principal to be paid and press • Key in mo

1291. Key in the program.2. Press CLEAR and press .3. Key in the tax rate as a percentage and press 1.4. Key in years to retirement and press

1306. If you invest the same amount ($1500, *after taxes for a not-Keogh or IRA account.) each year with dividends taxed as ordinary income, what will

131• Prices are input in the form XXX.ND where N is the numerator and D is the Denominator of the fractional portion of the price, e.g. 25 5/8 is inpu

132 025-44 40 026- 34 727- 45 728- 20 129-44 40 130- 3331- 20 332-44 40 3 533- 45 5 34- 43 3635- 2436- 31 0137-43, 33 0138- 4039- 34 740- 44 741-

133Instructions:1. Key in the program.2. Initialize the program by pressing CLEAR .3. Key in the number of shares of a stock and press .4. Key in

1349. Next, to evaluate the entire portfolio, press 48.10. Press to see the initial portfolio value.11. Press to see the present portfolio val

13589.78 1.001.3 1.304.55 4.5596.18 6.95 Percent change in Stock's value.500 500.00N. W. Sundial65.14 1.00.6 0.603.50 3.5064.38 -1.34 Percent cha

136Canadian MortgagesIn Canada, interest is compounded semi-annually with payments made monthly. This results in a different monthly mortgage factor t

137Number of Periodic Payments to Fully Amortize a MortgageExample 2: An investor can afford to pay $440 per month on a $56,000 Canadian Mortgage. If

138 CLEAR 6 200 8.75 0.72 Canadian Mortgage factor.612.77 10 75500 -61,877.18Outstanding balance remaining at the end of 10 years.

135. Key in depreciable value and press 4.6. Key in depreciable life and press 5.7. Key in factor (for declining balance only) and press 6.8. Ke

139MiscellaneousLearning Curve for Manufacturing CostsMany production process costs vary with output according to the "learning curve" equat

140 CLEAR 00- 01- 43 232 02- 2 03- 43 2304- 10 205- 44 206- 3307- 34 108- 44 109- 10 10- 43 23 211- 45 212- 10 13- 43 22 214- 44 2 0015-43, 33 00 21

141 427- 44 4 228- 45 2 29- 43 232 30- 2 31- 43 2332- 101 33- 134- 40 035- 44 036- 21 337- 45 3 038- 45 039- 2140- 30 041- 45 042- 10 443- 45 4 344- 4

1421. Key in the program, (Note: If the average cost are not going to be calcu-lated, lines 25 through 48 need not be keyed in).2. To calculate r, the

143Queuing and Waiting TheoryWaiting lines, or queues, cause problems in many marketing situations. Customer goodwill, business efficiency, labor and

144Richard E Trueman, "An Introduction to Quantitative Methods for Decision Making," Holt, Rinehart and Winston, New York, 1977Example 1: Ba

145What is the average number of customers in the waiting line at any time? The average waiting time? What is the average total time for a customer to

14614- 49 0115-43, 33 01 016-45 48 0 717- 45 718- 211 19- 1 020-45 48 0 721- 45 722- 1023- 3024- 10 725- 45 7 26- 43 327- 10 628- 44 6 229- 45 230-

147 342- 44 3 043-45 48 044- 40 445- 44 4 846- 45 847- 10 548- 44 5 349- 45 3 850- 45 851- 10 652- 44 653- 31 854- 45 8 755- 45 7 956- 45 957- 2058-

1481. Key in the program and press CLEAR .2. Key in the number of servers, n and press 0 7.3. Key in the arrival rate of customers, λ, and pres

14Example 2: An office building was purchased for $1,400,000. The value of depreciable improvements is $1,200,000.00 with a 35 year economic life. Str

149 20.65Pb probability all servers are busy. 32.59Lq average # waiting in queue. 44.99 L, average # waiting in system. 54.16 T, average total time in

150AppendixReal EstateWrap-Around Mortgage• n1 = number of years remaining in original mortgage.• PMT1 = yearly payment of original mortgage.• PV1 = r

151LendingLoans with a constant amount paid towards Principal• BALk = remaining balance after time period k.• CPMT = Constant payment to principal.• B

152• FC = (G - AMT - CL)Rule of 78's Rebate• PV = finance charge.• Ik = interest charged at month k.• n = number of months in loan.••• BALk = (n

153Compounding Periods Different From Payment Periods• C = number of compounding periods per year.• P = number of payments periods per year.• i = peri

154Profit and Loss Analysis• Net income = (1 - tax)(net sales price - manufacturing expense - operating expense)• Net sales price = list price(1 - dis

155Simple Moving Average• X = moving average.• m = number of elements in moving average.•••etc.Seasonal Variation Factors Based on a Centered Moving A

156•••Where S1, S2, and S3 are:•••• a, b and c are determined by solving the three equations above simulta-neously.Forecasting With Exponential Smooth

157• Smoothed average St = αXt + (1 - α)St - 1• Change, Ct = St - St - 1• Trend, Tt = αCt + (1 - α)Tt - 1•Current period expected usage, • F

158••••••••Ma 100SC–S--------------=Mu 100SC–C--------------=SC1Ma100----------–-------------------=SC1Mu100----------+=CS1Ma100----------–=CS

15After-Tax Net Cash Proceeds of ResaleThe After-Tax Net Cash Proceeds of Resale (ATNCPR) is the after-tax reversion to equity; generally, the estimat

159Calculations of List and Net Prices with Discounts• L = List price.• N = Net price.• D = Discount(%).•••StatisticsExponential Curve Fit• y = AeBx••

160••• = A + B (ln x)Power Curve Fit• y = AxB (A>0)•ln y = ln A + Bln x••• = AxBStandard Error of the Mean•Mean, Standard Deviation, Standard Error

161•mean •standard deviation •standard error Personal FinanceTax-Free Retirement Account (IRA) or Keogh Plan• n = the number of years to retirement.•

162Portfolio beta coefficient:•Canadian Mortgages• r = annual interest rate expressed as a decimal.•monthly factor MiscellaneousLearning Curve for Man

163Queuing and Waiting Theory• n = number of servers.• λ = arrival rate of customers (Poisson input).• µ = service rate for each server (exponential s

164•where:•• A = number of payments per year• B = number of years that payments increase• C = percentage increase in periodic payments (as a decimal)•

16The user may change to a different depreciation method by keying in the desired function at line 35 in place of .KEYSTROKES DISPLAY CLEAR 00- 01-

1725- 12 226- 45 2 27- 42 23 228- 45 229- 2030- 486 31- 632- 20 133-44 40 1 234- 45 2 35- 42 2536- 34 37- 45 1338- 30 139-44 40 1 640- 45 641- 262 4

181. Key in the program and press CLEAR .2. Key in the loan values:• Key in annual interest rate and press .• Key in mortgage amount and press

1IntroductionThis Solutions Handbook has been designed to supplement the HP-12C Owner's Handbook by providing a variety of applications in the fi

19700000 700,000.00 Mortgage.9.5 0.79 Monthly interest.20 240.00 Number of payments.-6,524.92 Monthly payment.750000 3750,000.00 Depreciable value.

20LendingLoan With a Constant Amount Paid Towards PrincipalThis type of loan is structured such that the principal is repaid in equal installments wit

21Add-On Interest Rate Converted to APRAn add-on interest rate determines what portion of the principal will be added on for repayment of a loan. This

22Example 1: Calculate the APR and monthly payment of a 12% $1000 add-on loan which has a life of 18 months.APR Converted to Add-On Interest Rate.Give

23Add-On Rate Loan with Credit Life.This HP-12C program calculates the monthly payment amount, credit life amount (an optional insurance which cancels

241 22- 123- 4024- 3425- 10 326- 45 327- 20 028- 45 029- 10 30- 42 1431- 1632- 1433- 31 34- 45 14 035- 45 036- 2037- 1638- 13 39- 45 13 240- 45 241- 2

25 51- 43 35 52- 43 35 6153-43, 33 61 554- 45 555- 480 56- 01 57- 158- 40 59- 42 14 560- 44 5 561- 45 562- 31 63- 45 1364- 3465- 30 366- 45 367- 3068

261. Key in the program.2. Press CLEAR .3. Key in the number of monthly payments in the loan and press 0.4. Key in the annual add-on interest rate

27Interest Rebate - Rule of 78'sThis procedure finds the unearned interest rebate, as well as the remaining principal balance due for a prepaid c

28 001- 44 002- 33 203- 44 204- 33 105- 44 1 206- 45 207- 30 208- 44 21 09- 110- 40 011- 45 012- 20 113- 45 114- 3615- 20 116- 45 117- 4018- 10 219- 4

2Real EstateRefinancingIt can be mutually advantageous to both borrower and lender to refinance an existing mortgage which has an interest rate substa

291. Key in the program.2. Key in the number of months in the loan and press .3. Key in the payment number when prepayment occurs and press .4. Key i

30KEYSTROKES DISPLAY CLEAR 00- 01- 43 8 202- 44 203- 341 04- 105- 251 06- 107- 40 008- 44 0 09- 45 11 210- 45 211- 30 12- 43 11 13- 45 12 14- 43 12 1

3128- 1429- 1330- 1631- 151 32- 1 133- 1 134-44 40 1 235- 45 236- 30 37- 43 35 4038-43, 33 40 2539-43, 33 25 340- 45 3 41- 45 1342- 10 443- 44 4 34

321. Key in the program.56- 2057- 16 58- 42 1459- 1460- 3161- 1562- 15 63- 42 1464- 3165- 1666- 131 67- 1 368-44 40 3 169-44 30 1 170- 45 1 71- 43 3

332. Press CLEAR .3. Key in the term of the loan and press .4. Key in the annual interest rate and press .5. Key in the total loan amount and pres

34Variable Rate MortgagesAs its name suggests, a variable rate mortgage is a mortgage loan which provides for adjustment of its interest rate as marke

352. Key in the remaining balance of the loan and press . The remaining balance is the difference between the loan amount and the total principal fro

36Skipped PaymentsSometimes a loan (or lease) may be negotiated in which a specific set of monthly payments are going to be skipped each year. Seasona

378. Key in the loan amount and press 0 to obtain the monthly payment amount when the payment is made at the end of the month.9. Press 0

38SavingsInitial Deposit with Periodic DepositsGiven an initial deposit into a savings account, and a series of periodic deposits coincident with the

3Wrap-Around MortgageA wrap-around mortgage is essentially the same as a refinancing mortgage, except that the new mortgage is granted by a different

39Number of Periods to Deplete a Savings Account or to Reach a Specified Balance.Given the current value of a savings account, the periodic interest r

40The cash flow diagram looks like this:Now suppose that at the beginning of the 6th month you withdrew $80.What is the new balance?You increase your

41Suppose that for 2 months you decide not to make a periodic deposit. What is the balance in the account?This type of procedure may be continued for

42calculate the total amount remaining in the account after a series of transactions on specified dates.KEYSTROKES DISPLAY CLEAR 00-01- 1602- 1303- 3

431. Key in the program2. Press CLEAR and press .3. Key in the date (MM.DDYYYY) of the first transaction and press .4. Key in the annual nomin

4410. For a new case press and go to step 2.Example: Compute the amount remaining in this 5.25% account after thefollowing transactions:1. January

45I savings plans however, money may become available for deposit or investment at a frequency different from the compounding frequencies offered. The

46Example 2: Solving for payment amount.For 8 years you wish to make weekly deposits in a savings account paying 5.5% compounded quarterly. What amoun

47Investment AnalysisLease vs. PurchaseAn investment decision frequently encountered is the decision to lease or purchase capital equipment or buildin

48 15- 45 11 116-44 48 1 17- 45 12 218-44 48 2 519- 45 520- 13 621- 45 622- 11 723- 45 724- 12 025- 45 0 26- 42 24 127-44 40 1 928- 45 929- 13 030

4Sometimes the wrap around mortgage will have a longer payback period than the original mortgage, or a balloon payment may exist.where:n1 = number of

49Instructions:1. Key in the program.-Select the depreciation function and key in at line 26.2. Press and press CLEAR .3. Input the following i

508. For declining balance depreciation, key in the depreciation factor (as a percentage) and press 7.9. Key in the total first lease payment (inclu

51234567891020020020015003003003003003001700170017001700170017001700001000750Keystrokes Display CLEAR 0.0010 12 10000 -10,000.00 Always use negativ

52Break-Even AnalysisBreak-even analysis is basically a technique for analyzing the relationships among fixed costs, variable costs, and income. Until

53The variables are: fixed costs (F), Sales price per unit (P), variable cost per unit (V), number of units sold (U), and gross profit (GP). One can r

54To calculate the sales volume needed to achieve a specified gross profit:1. Key in the desired gross profit and press .2. Key in the fixed cost and

55For repeated calculation the following HP-12C program can be used.12000 12,000.00 Fixed cost.4500 16,500.002500 6.606.75 13.35Sales price per unit t

561. Key in the program and store the know variables as follows:a. Key in the fixed costs, F and press 1.b. Key in the variable costs per unit, V an

57Example 2: A manufacturer of automotive accessories produces rear view mirrors. A new line of mirrors will require fixed costs of $35,00 to produce.

583. Key in the number of units and press .4. Key in the fixed cost and press to obtain the operating leverage.Example 1: For the data given

5Example 2: A customer has an existing mortgage with a balance of $125.010, a remaining term of 200 months, and a $1051.61 monthly payment. He wishes

591. Key in the program.2. Key in and store input variables F, V and P as described in the Break-Even Analysis program.3. Key in the sales volume and

60Any of the five variables: a) list price, b) discount (as a percentage of list price), c) manufacturing cost, d) operating expense (as a percentage)

6123- 161 24- 125- 40 026- 45 027- 20 0028-43, 33 029- 1030- 16 131- 45 132- 40 133- 45 134- 10 035- 45 036- 20 0037-43, 33 00 538- 45 5 639- 45 640

621. Key in the program and press CLEAR , then key in 100 and press 0.2. Key in 1 and press , then key in your appropriate tax rate as a decimal

63b. Press 12 43 .Example: What is the net return on an item that is sold for $11.98, discounted through distribution an average of 35% and ha

64What reduction in manufacturing cost would achieve the same result without necessitating an increase in list price above $11.98? 13 7.79 01 2.30

65SecuritiesAfter-Tax YieldThe following HP-12C program calculate the after tax yield to maturity of a bond held for more than one year. The calculati

661. Key in the program.2. Key in the purchase price and press 1.3. Key in the sales price and press 2.4. Key in the annual coupon rate (as a perc

678. Key in the purchase date (MM.DDYYYY) and press .9. Key in the assumed sell date (MM.DDYYYY) and press to find the after-tax yield (as a percen

68 202- 45 2 03- 43 26 304- 45 305- 10 506- 45 507- 251 08- 109- 3410- 30 411- 45 412- 20 513- 44 514- 31 115- 45 1 216- 45 2 17- 43 26 318- 45 319-

6If you, as a lender, know the yield on the entire transaction, and you wish to obtain the payment amount on the wrap-around mortgage to achieve this

691. Key in the program.2. Press .3. Key in the settlement date (MM.DDYYYY) and press 1.4. Key in the maturity date (MM.DDYYYY) and press 2.5. K

70Example 2: Determine the yield of this security; settlement date June 25, 1980; maturity date September 10, 1980; price $99.45; redemption value $10

71ForecastingSimple Moving AverageMoving averages are often useful in recording of forecasting sales figures, expenses or manufacturing volume. There

72For repeated calculations the following HP 12C program can be used for up to a 12 element moving average: CLEAR 0.00211570 1.00112550 2.00190060 3.0

73 410- 40 511- 45 5 412- 44 4 513- 40 614- 45 6 515- 44 5 616- 40 717- 45 7 618- 44 6 719- 40 820- 45 8 721- 44 7 822- 40 923- 45 924- 44 8 925- 40

74*At step 38, m=number of elements in the moving average, i.e. fir a 5 element moving average line 38 would be 5 and for a 12-element average line 3

755. Continue as above, keying in and storing each data point in its appropriate register until m data points have been stored.6. Press 00 to ca

76Seasonal Variation Factors Based on Centered Moving Averages.Seasonal variation factors are useful concepts in many types of forecasting. There are

771. Key in the program.2. Press CLEAR .3. Key in the quarterly sales figures starting with the first quarter:a. Key in 1st quarter sales and press

78b. Key in 2nd quarter sales and press 2.c. Key in 3rd quarter sales and press 3.d. Key in 4th quarter sales and press 4.e. Key in the 1st quar

7Income Property Cash Flow AnalysisBefore-Tax Cash FlowsThe before-tax cash flows applicable to real estate analysis and problems are:• Potential Gros

79Now average each quarter's seasonal variation for the two years?390 449.75 4th quarter, 1978.111.40530 460.25 1st quarter, 1979.98.86560 476.38

80An HP-12C program to calculate a centered 12-month moving average and seasonal variation factor is as follows: CLEAR 0.00111.4 1.00111.17 2.00 111.2

81 620- 44 621- 40 822- 45 8 723- 44 724- 40 925- 45 9 826- 44 827- 40 028-45 48 0 929- 44 930- 40 131-45 48 1 032-44 48 033- 40 234-45 48 2 135-

821. Key in the program.2. Press CLEAR .3. Key in 12 and press 0.4. Key in the values for the first 13 months, storing them one at a time in registe

83A useful curve for evaluating sales trends, etc., is the Gompertz curve. This is a "growth" curve having a general "S" shape and

8418- 3019- 10 420- 45 421- 2222- 21 623- 44 6 124- 45 1 325- 45 326- 20 227- 45 228- 3629- 2030- 30 131- 45 1 332- 45 333- 40 234- 45 22 35- 236- 203

85 646- 45 6 447- 45 448- 211 49- 150- 3051- 3652- 2053- 10 654- 45 655- 10 256- 45 2 157- 45 158- 3059- 20 60- 43 22 561- 44 562- 3163- 45 664- 3465-

861. Key in the program and press CLEAR .2. Divide the data points to be input into 3 equal consecutive groups. Label them Groups I, II and III for

87present trend continues? What annual sales rate would the curve have predicted for the 5th year of the product's life? (Arrange the data as fol

88Exponential smoothing is often used for short term sales and inventory forecasts. Typical forecast periods are monthly or quarterly. Unlike a moving

8Before-Tax Reversions (Resale Proceeds)The reversion receivable at the end of the income projection period is usually based on forecast or anticipate

89 214- 45 2 115- 45 116- 2017- 40 218- 45 219- 1620- 34 221- 44 222- 40 023- 45 024- 20 125- 45 1 326- 45 327- 2028- 40 329- 44 3 130- 45 131- 20 032

90Selecting the "best" smoothing constant (α):1. Key in the program and press CLEAR .2. Key in the number 1 and press .3. Key in the &qu

911. Key in the number 1 and press .2. Key in the selected and press 0 1.3. From the selection routing or from a previous forecast:o Key in the

92The procedure is repeated for several α's.Smoothing Constant (α) .5 .1 .25 .2Cumulative Error (Σe2) 23.61 25.14 17.01 18.03For t

93Pricing CalculationsMarkup and Margin CalculationsSales work often involves calculating the various relations between markup, margin, selling price

94Example 2: If an item sells for $21.00 and has a markup of 50%, what is its cost? What is the margin?The following HP 12C program may be helpful for

951. Key in program.2. To calculate selling price, given the markup, key in the cost, press , key in the markup and press 00 .3. To calculate c

96list and new and several discounts are known it may be desirable to calculate a missing discount. The following series of keystrokes may be used:1.

971. Key in the program.2. Key in 1 and press 1.3. Key in the first discount rate (as a percentage) and press .4. Repeat step 2 for each of the rem

981 11.0048 0.525 0.951.45 3.28 07 10.51 3rd discount rate (%).0.89Include 3rd discount rate in calculation.3.75 1 1.66 New net price.