HP (Hewlett-Packard) HP-12C manuel d'utilisation

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1 Introduction This Solutions Handboo k has been designed to su pplement the HP-12C Owner's Handbook by providing a variet y of ap plications in the financial area. Programs and/or step- by-step keystroke procedures with corresponding exam ples in each sp ecific topic are explained . We hope that this book will serve as a refere nce guide to m[...]

2 Real Est ate Refinancing It can be mutually advant ageous to b oth borrower and lender to refinance an existing mortgage which has an in terest rate substantially below the current market rate, with a loan at a below-ma rket rate. The borrower has the immediate u se of ta x-free cash , while the lend er has subst antially increased debt service o[...]

3 Wr ap-Around Mortgage A wrap-around mortgage is essentially the same as a refinancing mortgage, except that the new mortgage is grant ed by a dif ferent lender , who assumes the payment s on the existing mortgage, which remains in full force. The new (second) mortgage is thus “wrapped around” the existing mortgage. The "wrap-around"[...]

4 Sometimes the wrap around mortgage will have a longer p ayback period than the origina l mortgage, or a balloon p ayment may exist. where: n 1 = number of years remaining i n original mortgage PMT 1 = yearly payment of original mortgage PV 1 = remaining balance of original mo rtgage n 2 = number of years in wrap-around mortgage PMT 2 = yearly pay[...]

5 Example 2: A customer has an existing mortgag e with a balance of $125.010, a remaining term of 2 00 months, and a $ 1051.61 monthly payment. He wishes to obtain a $200 ,000, 9 1/2% wrap-aroun d with 240 monthly payme nts of $1681.71 and a balloon paymen t at the end of the 240th month of $129,9 63.35. If you, as a lender , accept the pr oposal, [...]

6 If you, as a lender , know the yield on the entire transaction, and you wish to obta in the p ayment amount on the wrap-a round mortgag e to achieve this yield, use the following procedure. Once the monthly pa yment is known, the borrower's peri odic inte rest rate may also be determined. 1. Press the and press CLEAR . 2. Key in the remainin[...]

7 Income Property Cash Flow Analysis Before-T ax Cash Flows The before-tax cash flows app licable to real est ate analysis and problems are: • Potential Gross Income • Effectiv e Gross Income • Net Operating Income (also called Net Income Befo re Recapture.) • Cash Throw-off to Equity (also called Gross S pendable Cash) The derivation of th[...]

8 Before-T ax Reversions (Resale Proce eds) The reversion receivable at the end of the income projection period is usually based on fore cast or anticip ated resale of the property at tha t time. The before tax reve rsion amount applicable to real est ate analysis and problems ar e: • Sale Price. • Cash Proceeds of Resale. • Outstanding Mortg[...]

9 transaction cost s are expecte d to be 7% of the re sale price. The mor tgage is the same as that in dicated in the preceding example. • What will the Mortgage Bala nce be in 10 years? • What are the Cash Proce eds of Resale and Net Cash Pro ceeds of Resale? Af ter-T ax Cash Flows The After-T a x Cash Flow ( AT C F ) is found for the each yea[...]

10 KEYSTROKES DISPLA Y CLEAR 00- 0 01- 0 02- 11 1 03- 44 1 7 04- 45 7 05- 26 2 06- 2 07- 10 7 08- 44 7 1 09- 1 1 10-44 40 1 1 11- 1 2 12- 2 13- 42 11 0 14- 44 0 5 15- 45 5 16- 11 17- 45 12 6 18- 45 6 19- 12 20- 33 6 21- 44 6 22- 33 23- 45 13 4 24- 45 4 25- 13 26- 33[...]

11 4 27- 44 4 28- 33 29- 43 35 36 30-43, 33 36 1 31- 45 1 32- 42 25 0 33-44 30 0 0 34- 0 17 35-43, 33 17 36- 11 2 37- 45 2 8 38- 45 8 39- 25 2 40-44 40 2 41- 33 0 42-45 48 0 43- 25 44- 30 3 45- 45 3 9 46- 45 9 47- 25 3 48-44 40 3 49- 33 50- 30 1 51- 1 7 52- 45 7 0 53-44 20 0 54- 30[...]

12 1. Press and press CLEAR . 2. Key in loan values: • Key in annua l interest rate and press • Key in principal to be paid and press • Key in monthly payment and press (If any of the values ar e not known, they shou ld be solved for .) 3. Key in Potential Gross Income ( PGI ) and press 2. 4. Key in Operational cost and press 3. 55- 20 56- 45[...]

13 5. Key in depreciable value and press 4. 6. Key in depreciable life and press 5. 7. Key in f actor (for de clining bala nce only) an d press 6. 8. Key in the Marginal T ax Rate (as a percentage) and press 7. 9. Key in the growth rate in Potential Gross Income ( 0 for no growth) and press 8. 10. Key in the growth rate in operationa l cost (0 if n[...]

14 Example 2: An office building was purchased for $1,4 00,000. The value of depreciable improvement s is $1,20 0,000.00 with a 35 year economic life. S traight line depreciation will be used. The property is financed with a $1,050,000 loan. The terms of the loan are 9.5 % interest and $9,173.81 monthly p ayments for 25 years. The of fice build ing[...]

15 Af ter-T ax Net Cash Proceeds of Resale The After-T ax Net Cash Proceeds of Resale ( A TNCPR ) is the after-tax reversion to eq uity; generally , the estimated res ale price of the proper ty less commissions, outst anding debt and any t ax claim. The After-T ax Net Cash Procee ds can be found using the HP-12C program which follows. In calculati [...]

16 The user may change to a d ifferen t depreciation m ethod by keying in th e desired function at lin e 35 in place of . KEYSTROKES DISPLA Y CLEAR 00- 01- 43 8 2 02- 44 2 03- 33 04- 25 05- 30 06- 44 0 07- 30 08- 48 4 09- 4 10- 20 1 11- 44 1 12- 45 14 13- 42 14 14- 14 2 15- 45 2 16- 43 11 17- 15 0 18-44 40 0 CLEAR 19- 42 34 3 20- 45 3 21- 13 4 22- [...]

17 25- 12 2 26- 45 2 27- 42 23 2 28- 45 2 29- 20 30- 48 6 31- 6 32- 20 1 33-44 40 1 2 34- 45 2 35- 42 25 36- 34 37- 45 13 38- 30 1 39-44 40 1 6 40- 45 6 41- 26 2 42- 2 43- 10 1 44- 45 1 45- 20 0 46- 45 0 47- 40 00 48-43 33 00 REGISTERS n: Used i: Used PV : Used PMT : Used FV : Used R 0 : Used R 1 : Used R 2 : Desired yr .[...]

18 1. Key in the program and press CLEAR . 2. Key in the loan values: • Key in annua l interest rate and press . • Key in mortgage amount and press . • Key in monthly payment and press . (If any of the values are unknown, they should be solved for .) 3. Key in depreciable value and press 3. 4. Key in depreciable life in years and press 4. 5. [...]

19 700000 700,000.00 Mortgage. 9.5 0.79 Monthly intere st. 20 240.00 Number of payments. -6,524.92 Monthly payment. 750000 3 750,000.00 Depreciable value. 25 4 25.00 Depreciable life. 125 5 125.00 Factor . 48 6 48.00 Marginal T ax Ra te. 900000 900,000.00 Purchase price. 1750000 1,750,000.00 Sale price. 8 8.00 Commission rate . 10 91 1,372 .04 A TN[...]

20 Lending Loan With a Const ant Amount Paid T owards Princip al This type of loan is stru ctured such that the prin cipal is repaid in equal installment s with the intere st paid in addition. Th erefor each periodic payment ha s a constant amount app lied toward the principle and a varying amount of interest. Loan Reduction Sche dule If the const [...]

21 Add-On Interest Rate Converted to APR An add-on interest rate determines what portion of the principal will be added on for rep ayment of a loan. T his sum is then divided by the number of months in a loan to determine the monthly p ayment. For example, a 10% add-on rate for 36 months on $3000 means ad d one-tenth of $3000 for 3 years (300 x 3) [...]

22 Example 1: Calculate the APR and monthly p ayment of a 12% $1000 add-on loan which has a life of 18 months. APR Converted to Add-On Interest Rate. Given the number of months and annual percent age rate, this procedure calculates the corresponding add-on interest rate. 1. Press and press CLEAR . 2. Enter the following information: a. Key in n umb[...]

23 Add-On Rate Loan with Credit Life. This HP-12C program calculates th e monthly payment amount, credit life amount (an optional insu rance which cancels any rem aining indebtedness at the death of the borr ower), total finance ch arge, and annual p ercenta ge rate (APR) for an add-o n interest rate (A IR) loan. The monthly p ayment is rounded (in[...]

24 1 22- 1 23- 40 24- 34 25- 10 3 26- 45 3 27- 20 0 28- 45 0 29- 10 30- 42 14 31- 16 32- 14 33- 31 34- 45 14 0 35- 45 0 36- 20 37- 16 38- 13 39- 45 13 2 40- 45 2 41- 25 0 42- 45 0 43- 20 1 44- 1 2 45- 2 46- 10 5 47- 44 5 48- 26 2 49- 2 50- 20[...]

25 51- 43 35 52- 43 35 61 53-43, 33 61 5 54- 45 5 55- 48 0 56- 0 1 57- 1 58- 40 59- 42 14 5 60- 44 5 5 61- 45 5 62- 31 63- 45 13 64- 34 65- 30 3 66- 45 3 67- 30 68- 16 69- 31 5 70- 45 5 3 71- 45 3 72- 40 73- 13 0 74- 45 0 75- 11 76- 12 77-45, 43 12 00 78-43, 33 00[...]

26 1. 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 ad d-on interest rate as a p ercentage and press 1. 5. Key in the credit life as a percentage and press 2. 6. Key in the loan amount and press 3. 7. Press to find the mont hly paymen t amount. 8. Press to obtain the amou[...]

27 Interest Rebate - Rule of 78's This procedure finds the unear ned interest rebate, as well as the remaining princip al balance due for a prep aid consumer loan using the Rule of 78's. The known values are the current inst allment number , the total number of inst allments for whic h the loan was written, and the tot al finance charge ([...]

28 0 01- 44 0 02- 33 2 03- 44 2 04- 33 1 05- 44 1 2 06- 45 2 07- 30 2 08- 44 2 1 09- 1 10- 40 0 11- 45 0 12- 20 1 13- 45 1 14- 36 15- 20 1 16- 45 1 17- 40 18- 10 2 19- 45 2 20- 20 21- 31 2 22- 45 2 23- 20 24- 34 25- 30 00 26-43, 33 00 REGISTERS n: Unused i: Unused[...]

29 1. 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 in the total finance charge and press to obtain the unearned interest (rebate). 5. Key in the periodic payment amount and press to find the amount of principal outstanding. 6. For a new case return [...]

30 KEYSTROKES DISPLA Y CLEAR 00- 01- 43 8 2 02- 44 2 03- 34 1 04- 1 05- 25 1 06- 1 07- 40 0 08- 44 0 09- 45 11 2 10- 45 2 11- 30 12- 43 11 13- 45 12 14- 43 12 15- 45 13 3 16- 44 3 1 17- 1 18- 16 19- 14 20- 13 21- 16 22- 15 1 23- 1 24- 43 11 25- 45 14 0 26- 45 0 27- 10[...]

31 28- 14 29- 13 30- 16 31- 15 1 32- 1 1 33- 1 1 34-44 40 1 2 35- 45 2 36- 30 37- 43 35 40 38-43, 33 40 25 39-43, 33 25 3 40- 45 3 41- 45 13 42- 10 4 43- 44 4 3 44- 45 3 45- 13 1 46- 1 3 47- 44 3 3 48- 45 3 49- 31 4 50- 45 4 1 51- 1 0 52- 45 0 1 53- 45 1 54- 21 55- 10[...]

32 1. Key in the program. 56- 20 57- 16 58- 42 14 59- 14 60- 31 61- 15 62- 15 63- 42 14 64- 31 65- 16 66- 13 1 67- 1 3 68-44 40 3 1 69-44 30 1 1 70- 45 1 71- 43 35 74 72-43, 33 74 48 73-43, 33 48 4 74- 45 4 75- 16 76- 31 76 77-43, 33 76 REGISTERS n: Used i: i/12 PV : Used PMT : Used FV : Used R 0 : Used R 1 : Used R 2 : Used R 3 : Used R 4 : Level [...]

33 2. Press CLEAR . 3. Key in the term of the loan and press . 4. Key in the annual intere st rate and press . 5. Key in the total loan amount and press . 6. Key in the rate of graduation (as a percent) and press . 7. Key in the number of years for wh ich the loan gradu ates and press . The following informatio n will be displayed for each ye ar un[...]

34 V ariable Rate Mortgages As its name sugge sts, a varia ble rate mortgage is a mortgage loan which provides for adjustment of it s interest rate as market interest rates change. As a result, the current inter est rate on a variable rate mortgage may dif fer from its or igination rate (i.e., the rate when the loan was made). This is the diff eren[...]

35 2. Key in the remaining balance of the loan and press . The remaining balance is the difference between the loan amount and the total principal from the payments which have been made. T o calculate the remaining bala nce, do the following: a. Key in the previous remaining balan ce. If this is the first mortgage adjustment, this value is the orig[...]

36 Skipped Payment s Sometimes a loan (or lease) may be negotiated in which a specific set of monthly payment s are going to be skipped each yea r . Seasonally is usually the reason for such an agree m ent. For example, because of heavy rainfall, a bulldozer canno t be operated in Oreg on during December , January , and February , and the lessee wi[...]

37 8. Key in the loan amount and press 0 to obtain the monthly payment amount when the pa yment is made at the end of the month. 9. Press 0 1 . 10. Key in the annual intere st rate as a percent and press to find the monthly payment amount when the payment is made at the beginning of the month. Example: A bulldozer wor th $100,000 is being purchased[...]

38 Savings Initial Deposit with Periodic Deposit s Given an initial deposit into a savings account, and a serie s of periodic deposits coincident with the compoun ding period, the future value (or accumulated amount) may be calculated as follows: 1. Press and press CLEAR . 2. Key in the initial investment and press . 3. Key in the number of additio[...]

39 Number of Periods to Deplete a Savings Account or to Reach a S pecified Balance. Given the c urrent valu e of a savin gs account, the periodi c interest rate , the amount of the perio dic withdrawa l, and a specified balance, this procedur e determines th e number of per iods to reach tha t balance (the balance is zero if th e account is dep let[...]

40 The cash flow diagram looks like this : Now suppose th at at the beginnin g of the 6th month yo u withdrew $80. What is the new balance? Y ou increase your monthl y deposit to $65. How much will you have in 3 months? The cash flow diagram looks like this : Keystrokes Display CLEAR 50 5.5 1023.25 5 1,299.22 Amount in account. Keystrokes Display 8[...]

41 Suppose that for 2 months you de cide not to make a periodic deposit. What is the balance in the account? This type o f procedur e may be c ontinued fo r any lengt h of time, a nd may be modified to me et the user's p articular needs. Savings Account Compounded Daily This HP 12C program determines th e value of a savings account when intere[...]

42 calculate the total amount re maining in the account after a series of transactions on specified dates. KEYSTROKES DISPLA Y CLEAR 00- 01- 16 02- 13 03- 33 3 04- 3 6 05- 6 5 06- 5 07- 10 08- 12 09- 33 0 10- 44 0 11- 15 13 12- 16 13- 31 2 14- 44 2 15- 33 1 16- 44 1 0 17- 45 0 1 18- 45 1 19- 43 26 20- 11 21- 15 22- 42 14 23- 15 24- 36 25- 45 13[...]

43 1. Key in the program 2. Press CLEAR and press . 3. Key in the date (MM.DDYYYY) of the first transaction and press . 4. Key in the annual nominal in terest rate as a percentage and press . 5. Key in the amount of the initial deposit and press . 6. Key in the date of the next transaction and press . 7. Key in the amount of the transacti on (posit[...]

44 10. For a new case press and go to step 2. Example: Compute the amo unt remaining in this 5.25% account af ter the following transactions: 1. January 19, 1981 de posit $125.00 2. February 24, 1981 deposit $60.00 3. March 16, 1981 deposit $70.00 4. April 6, 1981 withdraw $50.00 5. June 1, 1981 deposit $175.00 6. July 6, 1981 with draw $100.00 Com[...]

45 I savings plans however , money may become available for deposit or investment at a frequency dif ferent fro m the compounding frequencie s offere d. The HP 12C can easily be used in these calculations. However , because of the assumptions mention ed the periodic interest rate must be adjusted to correspo nd to an equivalent rate for th e paymen[...]

46 Example 2: Solving for payment a mount. For 8 years you wish to make weekly deposit s in a savings account p aying 5.5% compounded quarterly . What amount must you deposit each week to accumulate $60 00. Example 3: Solving for number of payment periods. Y ou can make weekly deposits of $10 in to an account paying 5.25% compounded daily (365- day[...]

47 Investment Analysis Lease vs. Purchase An investment decision frequently encou ntered is the decision to lease or purchase capit al equipment or buildi ngs. Although a thor ough evaluation of a complex acquisition usually r equ ires the servic es of a q ualified accountant, it is po ssible to simp lify a number of the as sumptions to produce a f[...]

48 15- 45 11 1 16-44 48 1 17- 45 12 2 18-44 48 2 5 19- 45 5 20- 13 6 21- 45 6 22- 11 7 23- 45 7 24- 12 0 25- 45 0 26- 42 24 1 27-44 40 1 9 28- 45 9 29- 13 0 30-45 48 0 31- 14 1 32-45 48 1 33- 11 2 34-45 48 2 35- 12 1 36- 45 1 3 37- 45 3 38- 20 39- 45 14 40- 30 8 41- 45 8 42- 30[...]

49 Instructions: 1. Key in the program. -Select the depreciation function and key in at line 26. 2. Press and press CLEAR . 3. Input the following information for the purchase of the lo an: -Key in the number of years for amortization and press . -Key in the annual interest rate and press . -Key in the loan amount (purchase price) and press . -Pres[...]

50 8. For declining ba lance depreciation, ke y in the depreciati on factor (as a percentage) and press 7. 9. Key in the total first lease payment (including any advance payments) and press 1 3 2. 10. Key in the first year's maintenance expen se that would be anticipated if the asset was owned and press . If the lease contract does not include[...]

51 2 3 4 5 6 7 8 9 10 200 200 200 1500 300 300 300 300 300 1700 1700 1700 1700 1700 1700 1700 0 0 1000 750 Keystrokes Display CLEAR 0.00 10 12 10000 -10,000.00 Always use negati ve loan amount. 1,769.84 Purchase payment. .48 3 0.48 Marginal tax rate. .05 1 4 1.05 Discounting factor . 10000 1500 5 8,500.00 Depreciable value. 10 6 10.00 Depreciable l[...]

52 Break-Even Analysis Break-even analysis is basically a techniqu e for analyzing the relationships among fixed costs, va riable costs, and income . Until the break even point is reached at the intersection of th e total income an d total cost lines, the prod ucer operates at a loss. After the break-e ven point each unit produced and so ld makes a[...]

53 The variables are: fixed costs ( F ), Sales p rice per unit ( P ), variable cost per unit ( V ), number of unit s sold ( U ), and gross profit ( GP ). One can readily evaluate GP , U or P given the four other variables. T o calculate the break-even volume, simply let the gross profit eq ual zero and calculate the number of units so ld ( U ). T o[...]

54 T o calculate the sales volum e needed to achieve a specified gros s profit: 1. Key in the desired gross profit and press . 2. Key in the fixed cost and press . 3. Key in sales price per unit and press . 4. Key in the variable cost per unit and press . 5. Press to calculate the sales volume. T o calculate the require d sales price to achieve a g[...]

55 For repeated calculation th e following HP-12C program can be used . 12000 12,000.00 Fixed cost. 4500 16,500.00 2500 6.60 6.75 13.35 Sales price per unit to achieve desired gross profit. KEYSTROKES DISPLA Y CLEAR 00- 3 01- 45 3 2 02- 45 2 03- 30 00 04-43, 33 00 4 05- 45 4 06- 20 1 07- 45 1 08- 30 00 09-43, 33 00 5 10- 45 5 1 11- 45 1 12- 40 13- [...]

56 1. 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 and press 2. c. Key in the unit price, P (if known) and press 3. d. Key in the sales volume, U , in units (if known) and press 4. e. Key in the gross profit, GP , (if known) and press 5. 2. T o calcula[...]

57 Example 2: A manufacturer of automotive accessories pr oduces rear view mirrors. A new line of mirrors will require fixed cost s of $35,00 to produce. Each mirror has a variable cost o f $8.25. The price of mirrors is tentatively set at $12.50 each. What volume is needed to break even? What would be the gross profit if t he price is r aised to $[...]

58 3. 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 in example 1 of the Brea k-Even Analysis section, calculate the op erating leve rage at 20 00 units a nd at 5000 unit s when the sales price is $13 a copy For repeated calculations the foll owing HP-12C pro[...]

59 1. Key in the program. 2. Key in and store input variables F , V and P as described in the Break-Even Analysis progra m. 3. Key in the sales volume and press to calculate the operating leverage. 4. T o calculate a new operating leve rage at a different sales volume, key in the new sales volume and press Example 2: For the figures given in exampl[...]

60 Any of the five variables : a) list price, b ) discount ( as a percen tage of list price), c) manufacturing cost, d) operating expense (as a percen tage), e) net profit af ter t ax (as a percent age) ma y be calculated if the other four are known. Since the tax rage varies fr om company to compa ny , provision is made for inputting your applicab[...]

61 23- 16 1 24- 1 25- 40 0 26- 45 0 27- 20 00 28-43, 33 0 29- 10 30- 16 1 31- 45 1 32- 40 1 33- 45 1 34- 10 0 35- 45 0 36- 20 00 37-43, 33 00 5 38- 45 5 6 39- 45 6 40- 10 41- 30 00 42-43, 33 00 4 43- 45 5 44- 30 6 45- 45 6 46- 20 00 47-43, 33 00 REGISTERS n: Unused i: Unused PV : Unused PMT : Unused[...]

62 1. 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 and press 6. 3. a. Key in the list price in dolla rs (if known) and press 1. b. Key in the discount in percent (if known) and press 2. c. Key in the ma nufacturing cost in dollars (if known) and press 3.[...]

63 b. Press 12 43 . Example: What is the net return on an item that is sold for $1 1.98, discounted throug h distribution an average of 35% and has a manufacturing cost of $2.50? The standar d compan y operating expense is 32% of ne t shipping ( sales) price and tax rate is 48%. If manufacturing expenses increase to $3.25, what is the ef fect on ne[...]

64 What reduction in m anufacturing co st would achieve the same result without necessit ating an increase in list price above $1 1.98? 13 7.79 01 2.30 Manufacturing cost ($).[...]

65 Securities Af ter-T ax Y ield The following HP-12C program calculate the af ter tax yi eld to maturity of a bond held for more than one ye ar . The calculations assumes an actual/ actual day basis. For after-t ax comp ut ations, the interest or coupon payment s are considered income, while the dif ference betwe en the bond or note face value and[...]

66 1. Key in the program. 2. Key in the purchase price and pre ss 1. 3. Key in the sales price and press 2. 4. Key in the annual coupon rate (as a percentage) and press 3. 5. Key in capital gains tax rate (as a percent age) and press 4. 6. Key in the income tax rate (as a percentage) and press 5. 7. Press . 19- 25 20- 30 0 21- 45 0 22- 10 23- 14 1 [...]

67 8. 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 percentage). 10. For the same bond but different date return to step 8. 1 1. For a new case retu rn to step 2. Example: Y ou can buy a 7% bond on Octob er 1, 1981 for $70 and expect to sell it in 5 years fo[...]

68 2 02- 45 2 03 - 43 26 3 04- 45 3 05- 10 5 06- 45 5 07- 25 1 08- 1 09- 34 10- 30 4 11- 45 4 12- 20 5 13- 44 5 14- 31 1 15- 45 1 2 16- 45 2 17 - 43 26 3 18- 45 3 19- 34 20- 10 4 21- 45 4 5 22- 45 5 23- 10 1 24- 1 25- 30 26- 20 27- 26 2 28- 2 29- 20 00 30-43, 33 00[...]

69 1. Key in the program. 2. Press . 3. Key in the settlement da te (MM.DDYYYY) and press 1. 4. Key in the maturity date (MM.DDYYYY) and press 2. 5. Key in the number of days in a year (360 or 365) and press 3. 6. Key in the redemption value per $100 and press 4. 7. T o calculate the p urchase price: a. Key in the discount rate a nd press 5. b. Pre[...]

70 Example 2: Determine the yield of this security; settlement date June 25, 1980; maturity date Septemb er 10, 1980; price $99.45; redemption value $101.33. Assume 360 da y basis. 3.21 1981 2 3.21 Maturity dtae. 360 3 360.00 360 day basis. 100 4 100.00 Redemption valu e per $100. 7.8 5 7.80 Discount rate. 96.45 Price. 8.09 Y ield. Keystrokes Displ[...]

71 Forecasting Simple Moving A verage Moving averages are of ten useful in recording of fore casting sales figures, expenses or manufacturing volume. There are many differe nt types of moving average calculations. An of ten used, straightfor ward method of calculation is presente d here. In a moving average a speci fied number of data points are av[...]

72 For repeated calculations the following HP 12C program can be used for up to a 12 element moving average: CLEAR 0.00 21 1570 1.00 1 12550 2.00 190060 3.00 171,393.33 3-month average for March. 21 1570 2.00 131760 3.00 144,790.00 3-month average for April. 1 12550 2.00 300500 3.00 207,440.00 3-month average for May . 190060 2.00 271 120 3.00 234,[...]

73 4 10- 40 5 11- 45 5 4 12- 44 4 5 13- 40 6 14- 45 6 5 15- 44 5 6 16- 40 7 17- 45 7 6 18- 44 6 7 19- 40 8 20- 45 8 7 21- 44 7 8 22- 40 9 23- 45 9 24- 44 8 9 25- 40 0 26-45 48 0 9 27- 44 9 10 28- 4 0 1 29-45 48 1 0 30-44 48 0 11 31- 40 2 32-45 48 2 1 33-44 48 1 12 34- 4 0 0 35- 45 0 36- 10[...]

74 *At step 38, m =number of eleme nts in the movin g average , i.e. fir a 5 element moving aver age line 38 would be 5 and for a 12 -element average line 38 would b e 2 This program can b e used for a moving average of 2 to 12 element s. It may be shortened considerably for moving aver ages with less than 12 elements. T o do this, key in the progr[...]

75 5. Continue as above, keying in and storing each d ata point in its appropriate register until m data points have been stored. 6. Press 00 to calculate the first moving average. 7. Key in the next data point and press to calculate the next moving average. 8. Repeat step 7 for each new data point. Example 2: Calculate the 3-element moving aver ag[...]

76 Seasonal V ariation Factors Based on Centered Moving A verages. Seasonal variation factors are usef ul concepts in ma ny types of forecasting. There ar e several methods of developing seasonal moving averages, on the of more co mmon wa ys being to calculate them as a ration of the periodic value to a centered movi ng average for the same period.[...]

77 1. 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 1. 2 08- 44 2 09- 40 4 10- 45 4 3 11- 44 3 12- 40 5 13- 45 5 4 14- 44 4 2 15- 2 16- 10 17- 40 4 18- 4 19- 10 20- 31 2 21- 45 2 22- 23 23- 31 5 24- 44 5 01 25-43, 33 01 REGISTERS n: Unused i: Unused [...]

78 b. Key in 2nd quarter sale s 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 quarter sales for the next year and press 5. 4. Press 00 to calculate the centered moving average for the 3rd quarter of the first year . 5. Press to calculate the seasonal variation for this qua rter . 6.[...]

79 Now average each quarter's seasona l variation for the two year s? 390 449.75 4th quarter , 1978. 111 . 4 0 530 460.25 1st quarter , 1979. 98.86 560 476.38 2nd quarter , 1979. 81.87 513 490.00 3rd quarter , 1979. 107.94 434 503.75 4th quarter , 1979. 111 . 1 7 562 513.25 1st quarter , 1979. 99.95 593 521.38 2nd quarter , 1980. 83.24 Keystro[...]

80 An HP-12C program to calculate a centered 12-mon th moving average and seasonal variation facto r is as follows: CLEAR 0.00 111 . 4 1.00 111 . 1 7 2.00 111 . 2 9 4th quarter average seasonal variation, %. KEYSTROKES DISPLA Y CLEAR 00- 1 01- 45 1 2 02-2 03- 10 2 04- 45 2 1 05- 44 1 06- 40 3 07- 45 3 2 08- 44 2 09- 40 4 10- 45 4 3 11- 44 3 12- 40 [...]

81 6 20- 44 6 21- 40 8 22- 45 8 7 23- 44 7 24- 40 9 25- 45 9 8 26- 44 8 27- 40 0 28-45 48 0 9 29- 44 9 30- 40 1 31-45 48 1 0 32-44 48 0 33- 40 2 34-45 48 2 1 35-44 48 1 36- 40 3 37-45 48 3 2 38-44 48 2 2 39- 2 40- 10 41- 40 0 42- 45 0 43- 10 44- 31 6 45- 45 6 46- 23 47- 31[...]

82 1. 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 registers 1 through .3; i.e. Key in the 1st month and press 1. Key in the 2nd month and press 2, etc., Key in the 10th month and press 0, etc., Key in the 13th month and press 3. 5. Press 00 to calculate t[...]

83 A useful c urve for ev aluating sale s tr ends, etc., is the Gompertz curve. This is a "growth" curve h aving a general "S" shape and may b e used to describe series of dat a where the early rate of growth is small, then accelerates for a period of time and then slows again as the time grows long. The sales curve for many pro[...]

84 18- 30 19- 10 4 20- 45 4 21- 22 22- 21 6 23- 44 6 1 24- 45 1 3 25- 45 3 26- 20 2 27- 45 2 28- 36 29- 20 30- 30 1 31- 45 1 3 32- 45 3 33- 40 2 34- 45 2 2 35- 2 36- 20 37- 30 38- 10 4 39- 45 4 40- 10 41- 43 22 7 42- 44 7 6 43- 45 6 1 44- 1 45- 30[...]

85 6 46- 45 6 4 47- 45 4 48- 21 1 49- 1 50- 30 51- 36 52- 20 53- 10 6 54- 45 6 55- 10 2 56- 45 2 1 57- 45 1 58- 30 59- 20 60- 43 22 5 61- 44 5 62- 31 63- 45 6 64- 34 65- 21 5 66- 45 5 67- 34 68- 21 7 69- 45 7 70- 20 62 71-43, 33 62 REGISTERS n: Unused i: Unused[...]

86 1. 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 convenience. 3. Key in the first point of group I and press . 4. Key in the first point of group II and press . 5. Key in the first point of group III and press . 6. Repeat steps 3, 4, and 5 for the b[...]

87 present trend continues? What an nual sales rate would the curve have predicted for the 5th year of the product's life? (Arra nge the data as follows:) Forecasting with Exponential Smoothing A common method for analyzing trends in sa les, inventory and securitie s is the moving averag e. Exponential sm oothing is a version of the weig hted [...]

88 Exponentia l smoothing is o ften used for shor t term sales and inventor y forecast s. T ypical forecast periods are monthly or quarterly . Unlike a moving average, exponential smoo thing does not require a g reat deal of historical data. However , it should not be used with dat a which has more than a mode rate amount of u p or down tre nd. Whe[...]

89 2 14- 45 2 1 15- 45 1 16- 20 17- 40 2 18- 45 2 19- 16 20- 34 2 21- 44 2 22- 40 0 23- 45 0 24- 20 1 25- 45 1 3 26- 45 3 27- 20 28- 40 3 29- 44 3 1 30- 45 1 31- 20 0 32- 45 0 33- 10 2 34- 45 2 35- 40 36- 44 5 3 37- 45 3 0 38- 45 0 39- 10 2 40- 45 2 41- 40[...]

90 Selecting 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 "trial " and press 0 1. 4. Key in the first historical value ( X 1 ) and pr ess 2. 5. Key in the second historical value ( X 2 ) and press 6 . The result is the error betw een the forecast [...]

91 1. 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 smoothed average S t-1 and press 2. o Key in the trend T t-1 and press 3. o Key in the forecast t+1 and press 6 . 4. Key in the current data value and press . The output is the error in forecasting the [...]

92 The proc edure is rep eated for several α 's. Smoothing Constant ( α ) . 5 .1 .25 .2 Cumulative Error ( Σ e 2 ) 23.61 25.14 17.01 18.0 3 For the selected α = .2 5 S t+1 = 24.28 T t-1 = 0.34 D t+1 = 25.64 Forecasting: Note: At least 4 periods of current dat a should be entered befor e forecasting is a ttempted. 4 23.61 Cumulative error ([...]

93 Pricing Calculations Markup and Margin Calculations Sales work often involves calculating the various relations between markup, margin, selling price and costs. Markup is defined as the diff erence between selling price and cost, divided by the cost. Margin is defined as the difference between selling price and cos t, divided by selling price. I[...]

94 Example 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 help ful for repetitive calcu lations of selling price and costs as well as conversions between markup and margin. Keystrokes Displa y 21 21.00 Selling price. 1 50 50.00 Markup (%). 14.00 Cost. 50 50.00 1 33.3[...]

95 1. Key in program. 2. T o calculate selling price, given the markup, key in the cost, press , key in the markup and press 00 . 3. T o calculate cost, given the markup, key in the selling price, press , key in the markup and press 00 . 4. T o calculate selling price, given the margin, key in the cost, press , key in the margin a nd press 03 . 5. [...]

96 list and new and several discounts are known it may be de sirable to calculate a missing discount. The following series of keystro kes may be used: 1. Key in 1, press 1. 2. Key in the first discount (as a percentage) and press 1 . 3. Repeat step 2 for each of the remaining known discount rates. 4. T o calculate the list price, key in the net pri[...]

97 1. 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 remaining discount rates. 5. T o calculate the list price, key in the net price and press 1 . 6. T o calculate the net price, key in the list price and press 1 . 7. T o calculate the unknown discount ra[...]

98 1 1 1.00 48 0.52 5 0.95 1.45 3.28 07 10.51 3rd discount rate (%). 0.89 Include 3rd discoun t rate in calculation. 3.75 1 1.66 New net price.[...]

99 S t atistics Curve Fitting Exponential Curve Fit Using the function of the HP-12C, a leas t squa res exponential curve fit may be easily calculate d according t o the equa tion y = Ae Bx . The exponential curve fitting technique is o ften used to determine the g rowth rate of a variable such as a stock's value over time, when it is suspecte[...]

100 5. Press to obtain B. 6. Press 1 to obtain the effective growth rate (as a decimal). 7. T o make a y-estimate, key in the x-value and press . Example 1: A stock's price in history is lis ted below . What effective growth rate does this repres ent? If the stoc k continues this grow th rate, what is the price projected to be at the end of 19[...]

101 CLEAR 00- 01- 34 02- 43 23 03- 34 04- 49 00 05-43, 33 00 06- 43 2 07- 34 08- 31 1 09- 1 10- 43 2 11- 43 22 0 12- 0 13- 43 2 14- 43 22 15- 31 16- 34 17- 33 18- 10 19- 43 23 20- 31 21- 43 22 1 22- 1 23- 30 24- 31 25- 43 2 26- 43 22 00 27-43, 33 00[...]

102 1. Key in the program and pres s CLEAR . 2. For each input p air of va lues, key in the y-value and press , key in the corresponding x -value and press . 3. After all dat a pairs are input, press 06 to obtain the correlation coefficient (between ln y and x ). 4. Press to obtain A . 5. Press to obtain B . 6. Press to obtain th e effective growth[...]

103 Logarithmic Curve Fit If your data doe s not fit a line or an exponential cu rve, try the following logarithmic curve fit. This is ca lculated according to the equation y = A + B (ln x ), and all x values must be positive. A typical logarithmic curve is shown below . The proced ure is as follows : 27.34 A 0.31 B 0.36 Effective growth ra te. 7 2[...]

104 1. Press CLEAR . 2. Key in the first y -value an d press . Key in the first x -value and press . Repeat this step for each data p air . 3. After all data p airs are input, press to obtain the correlation coefficient (between y and ln x ). 4. Press 1 0 to obtain A in the equation above. 5. Press to obt ain B . 6. T o make a y -estimate, key in t[...]

105 Power Curve Fit Another method of analysis is the power cu rve or geometric curve. The equation of the po wer curve is y = Ax B , and the values for A and B are computed by calculations similar to linear r egression. Some examples of power curves are shown below . The following keystrokes fi t a power curve according t o the equatio n ln y = ln[...]

106 levels of the T ower of Pisa (which was leaning even then) and timed its descent by counting his pulse. Th e following data a re measurements Galileo might have made. Find the power curve formulas that best expresses h as a function of t ( h = At B ). The formula that best expresse s h as a function of t is We know , as Galileo did not, that in[...]

107 1. 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. If you are summing two sets of numbers, key in the y -value and press , key in the x -value and press . Continue until you have entered all of the values. 4. Press to obtain the mean of the x -valu[...]

108 this procedure computes the mea n, standard deviation, an d standard error of the mean. 1. Press CLEAR . 2. Key in the first value and press . 3. Key in the respective frequency and press 0 . The display shows the number of data points entered. 4. Repeat steps 2 and 3 for each data point. 5. T o calculate the mean (average) press 0 1 6 3 . 6. P[...]

109 1. Key in the program. 2. Press CLEAR . 3. Key in the first value and press . CLEAR 00- 0 01-44 40 0 02- 20 03- 49 00 04-43, 33 00 0 05- 45 0 1 06- 44 1 6 07- 45 6 3 08- 44 3 09- 43 0 10- 31 11- 43 48 12- 31 0 13- 45 0 14- 43 21 15- 10 00 16-43, 33 00 REGISTERS n: Unused i: Unused PV : Unused PMT : Unused FV : Unused R 0 : Σ f i R 1 : Σ f i R[...]

110 4. 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. T o calculate th e mean, press 05 . 7. Press to find the standard deviation. 8. Press to find the standard error of the mean. 9. For a new ca se, go to step 2. Chi-Square St atistics The chi-sq uare[...]

111 If there is a clo se agreement bet ween the observed and expe cted frequencies, x 2 will be small. If the agreement is poor , x 2 will be large. The following keystrokes calculate the x 2 statist ic: 1. Press CLEAR . 2. Key in the first O i value and press . 3. Key in the first E i value and press 0 0 . 4. Repeat steps 2 and 3 for all data pair[...]

112 The number o f degrees of freedom is ( n -1). Since n = 6 , the degrees of freedom = 5. Consulting statistical t ables, you look up x 2 to a 0.05 significance level with 5 degrees of freedom, and see that x 2 0.05,5 = 1 1.07. Since x 2 = 5 is within 1 1.07, we may conclude that to a 0.05 significance level (probability = .95), the die is fair .[...]

113 1. Key in the program. 2. Press CLEAR . 3. Key in the first O i value and press . 4. Key in the first E i value and press . 5. Repeat steps 3 and 4 for all data pairs. The x 2 value is displa yed. 6. For a new ca se, go to step 2. Normal Distribution The normal (or Gaussian) distribution is an important tool in st atistics and business analysis[...]

114 Relative error less than 0.042% over the range 0 < x < 5.5 Reference: S teph en E. Derenzo, "Approximations for Hand Calcu lators Using Small Integer Coef ficients," Mathe matics of Computation , V ol. 31, No. 137, page 214-225; Jan 1977. KEYSTROKES DISPLA Y CLEAR 00- 0 01- 44 0 8 02- 8 3 03- 3[...]

115 04- 20 3 05- 3[...]

116 1. Key in program. 2. Key in x and press to computed Q ( x ). 5 06- 5 1 07- 1 08- 40 0 09- 45 0 10- 20 5 11- 5 6 12- 6 2 13- 2 14- 40 7 15- 7 0 16- 0 3 17- 3 0 18- 45 0 19- 10 1 20- 1 6 21- 6 5 22- 5 23- 40 24- 10 25- 16 26- 43 22 2 27- 2 28- 10 00 29-43, 33 00 REGISTERS n: Unused i: Unused PV : Unused PMT : Unused FV : Unused R 0 : x R 1 -R .6[...]

117 3. Repeat step 2 for each new case. Example: Find Q ( x ) for x = 1.18 and x = 2.1. Covariance Covariance is a measure of the interd ependence between p aired variabl es ( x and y ). Like sta ndard deviation, covar iance may be defined for either a sample (S xy ) or a population (S' xy ) as follows: S xy = r * s x * s y S' xy = r * s&[...]

118 T ry the previous examp le using the following HP-12C program: 54 62 51 68 40 74 -354.14 S xy 1 1 1 -303.55 S' xy KEYSTROKES DISPLA Y CLEAR 00- 01- 49 00 02-43, 33 00 03- 43 48 04- 20 05- 36 06- 43 2 07- 33 08- 20 09- 31 1 10- 45 1 1 11- 1 12- 30 13- 45 1 14- 10 15- 20 00 16-43, 33 00 REGISTERS[...]

119 1. Key in the program. 2. Press CLEAR . 3. Key in the y -value and press . 4. Key in the x -value and p ress . Repeat steps 3 an d 4 for all data pairs. 5. Press 03 . to obtain the value of S xy . 6. Press to obtain S' xy . 7. For a new ca se, go to step 2. Permut ation A permutation is an ordered subset of a set of distinc t objects. The [...]

120 where m , n are integers and 69 ≥ m ≥ n ≥ 0. Use the following HP-12C p rogram to calculate the number of po ssible permut ations. 1. Key in the program. 2. Key in m and press . 3. Key in n and press to calculate m P n . 4. For a new case go to step 2. Example: How many ways can 10 people be seated on a bench if only 4 seats ar e availabl[...]

121 Combination A combination is a selection of one or more of a set of distinct obje cts without regard to order . The number of possible combin ations, each conta ining n object s, that can be formed from a collection of m distinct objects is given by: Where m , n are integers and 69 ≥ m ≥ n ≥ 0. Use the following HP-12C to calculate the nu[...]

122 1. Key in the program. 2. Key in m and press . 3. Key in n and press to calculate m C n . 4. For a new ca se, go to step 2. Example: A manager want s to choose a committee of three people fro m the seven en gineers working for hi m. In how many diffe rent ways can the committee be selected? Random Number Generator This HP-12C program calculates[...]

123 1. Key in the program. 2. T o generate a rando m number , press . 3. Repeat step 2 as many times as desired. Example: Generate a seq uence of 5 random numb ers. 2 03- 2 8 04- 8 4 05- 4 1 06- 1 6 07- 6 3 08- 3 0 09- 44 0 9 10- 9 9 11- 9 7 12- 7 13- 20 14- 43 24 0 15- 44 0 16- 31 10 17-43, 33 10 REGISTERS n: Unused i: Unused PV : Unused PMT : Unu[...]

124 Personal Finance Homeowners Monthly Payment Estimator It is often useful, when compar ison shopp ing for a mortgage or determining the appropria te price range of houses to consider , to be able to quickly est imate the mon thly payment given the purchase price, tax rate per $1000, percent down, interest ra te and term of the loan. The calculat[...]

125 The following HP-12C program may be used instead of the above. -672.16 Approximate monthly payment. KEYSTROKES DISPLA Y CLEAR 00- 01- 43 8 1 02- 45 1 2 03- 45 2 04- 25 05- 30 06- 13 07- 36 08- 43 36 09- 40 3 10- 45 3 11- 20 1 12- 1 2 13- 2 14- 26 3 15- 3 16- 10 17- 16 18- 36 19- 14 20- 14 21- 40 00 22-43, 33 00 REGISTERS[...]

126 1. Key in the program. 2. Press CLEAR . 3. Key in the annual intere st rate and press . 4. Key in the term of the loan in years and press . 5. Key in the purchase price and pre ss 1. 6. Key in the percent down and press 2. 7. Key in the tax rate in dollars per thousand and press 3. 8. T o calculate the a pproximate monthly payment, press . 9. F[...]

127 T ax-Free Individual Retirement (IRA) of Keogh Plan. The advent of tax-free retirement ac counts (IRA or Keogh) has resulted in considerable benefit s for many person who are no t able to particip ate in group profit sharing o r retirement pl ans. The savings d ue to ta x-free st atus are often consi derable, but complex to calculate. Required [...]

128 06- 31 1 07- 45 1 08- 48 5 09- 5 10- 25 11- 16 1 12- 1 13- 40 14- 45 15 15- 20 16- 31 1 17- 1 18- 48 1 19- 1 0 20- 0 21- 45 11 22- 21 23- 10 24- 31 25- 45 12 1 26- 1 1 27- 45 1 28- 25 29- 30 30- 20 31- 12 32- 15 33- 31 17 34-43, 33 17[...]

129 1. 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 . 5. Key in the interest rates as a percentage and press . 6. Key in the annual payment and press . 7. Press to calculate the future va lue of the tax free investment. 8. Press to compute th e total cash [...]

130 6. 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 be the total tax-p aid cash at retirement? 7. What is the purchasing power of that figure in terms of today's dollars? Stock Port folio Evaluation and Analysis This program evaluates a port fo[...]

131 • Prices are input in the form XXX.ND wh ere N is the numerator and D is the Denominator of the fractional portion of the price, e.g. 25 5/8 is input as 25.58. • The beta coefficient analysis is optional. Key in 1.00 if bet a is not to be analyzed. KEYSTROKES DISPLA Y CLEAR 00- 6 01- 44 6 02- 43 24 03- 43 35 15 04-43, 33 15 1 05- 1 0 06- 0 [...]

132 0 25-44 40 0 26- 34 7 27- 45 7 28- 20 1 29-44 40 1 30- 33 31- 20 3 32-44 40 3 5 33- 45 5 34- 43 36 35- 24 36- 31 01 37-43, 33 01 38- 40 39- 34 7 40- 44 7 41- 20 5 42- 44 5 2 43-44 40 2 1 44- 1 4 45- 44 4 46- 31 01 47-43, 33 01 2 48- 45 2 49- 31 0 50- 45 0 51- 31 52- 24[...]

133 Instructions: 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 the initial purchase of the stock an d press . 5. Key in the beta coefficient of the stock and press . 6. Key in the annual dividen d of the stock and press . 7. Key in the present price of the stock[...]

134 9. Next, to evaluate the entire portfolio, press 48. 10. Press to see the initial portfolio value. 1 1. Press to see the present portfolio value. 12. Press to see the percent change in value. 13. Press to see the total yearly dividend. 14. Press to see the annual dividend yield as a percent of the current market value. 15. Press to see the beta[...]

135 89.78 1.00 1.3 1.30 4.55 4.55 96.18 6.95 Percent chang e in S tock's value. 500 500.00 N. W . Sundial 65.14 1.00 .6 0.60 3.50 3.50 64.38 -1.34 Percent change in Stock's value. 48 45,731.25 Original value. 46,418.75 Present value. 1.50 Percent change in value. 2,567.50 T otal yearly dividend. 5.53 Annual dividend yield. 0.77 Portfolio [...]

136 Canadian Mortgages In Canada, interest is compounded semi- annually with payment s made monthly . This resu lts in a different mo nthly mortgage factor than is use d in the United S tates and preprogramme d into the HP-12C. This dif ference can be easily hand led by the addition of a few keystrokes. Fo r any problem requiring an input for , the[...]

137 Number of Periodic Payment s to Fully Amortize a Mortgage Example 2: An investor can afford to pay $44 0 per month on a $56,000 Canadian Mortgage. If the annual interest rate is 9 1/4 %, how long will it take to completely amortize this mortgage? Effective Interest Rate (Y ield) Example 3: A Canadian mortgage has mo nthly payment s of $612.77 w[...]

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

139 Miscellaneous Learning Curve for Manufacturing Cost s Many production process cost s vary wit h output accordin g to the "learning curve" equation. The prod uction t eam becomes more p roficient in manufacturing a given item as more and more of them are fabricated and costs ma y be expected to decrease by a pred ictable amoun t. The l[...]

140 CLEAR 00- 01- 43 23 2 02- 2 03- 43 23 04- 10 2 05- 44 2 06- 33 07- 34 1 08- 44 1 09- 10 10- 43 23 2 11- 45 2 12- 10 13- 43 22 2 14- 44 2 00 15-43, 33 00 2 16- 45 2 17- 43 23 2 18- 2 19- 43 23 20- 10 21- 21 1 22- 45 1 23- 20 00 24-43, 33 00 3 25- 44 3 26- 34[...]

141 4 27- 44 4 2 28- 45 2 29- 43 23 2 30- 2 31- 43 23 32- 10 1 33- 1 34- 40 0 35- 44 0 36- 21 3 37- 45 3 0 38- 45 0 39- 21 40- 30 0 41- 45 0 42- 10 4 43- 45 4 3 44- 45 3 45- 30 46- 10 1 47- 45 1 48- 20 00 49-43, 33 00 REGISTERS n: Unused i: Unused PV : Unused PMT : Unused FV : Unused R 0 : K +1 R 1 : C 1 R 2 : r R 3 : i R 4 : j[...]

142 1. 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. T o calculate r , the learning fa ctor , if C 1 and C n are know n: a. Key in C 1 , the cost of the first unit and press . b. Key in C n , the cost of the n th unit an d press . c. Key in n , the number of units and [...]

143 Queuing and W aiting Theory W aiting lines, or queues, ca use proble ms in many marketing situations. Customer goodwill, business efficiency , labor and space considerations are only some of the problems which may be minimized by prop er application of queuing theory . Although queuing theory ca n be complex and complicated su bject, handheld c[...]

144 Richard E T rueman, "An Introduction to Quantitative Methods for Decision Making," Holt, Rinehart and Winston, New Y ork, 1977 Example 1: Bank customers arrive at a bank on an average of 1.2 customers per minute . They join a common queue for three te llers. Each teller completes a transaction at th e rate of one customer every 2 min [...]

145 What is the average n umber of cust omers in th e waiting line at any time ? The average wa iting time? What is the ave rage total time for a customer to wait and be checke d out? The average number of custom ers in the system? With an HP-12C program on can readily calculate the necessar y probabilities for this type of problem (dispensing with[...]

146 14- 49 01 15-43, 33 01 0 16-45 48 0 7 17- 45 7 18- 21 1 19- 1 0 20-45 48 0 7 21- 45 7 22- 10 23- 30 24- 10 7 25- 45 7 26- 43 3 27- 10 6 28- 44 6 2 29- 45 2 30- 40 31- 22 1 32- 44 1 6 33- 45 6 34- 20 2 35- 44 2 0 36-45 48 0 37- 20 7 38- 45 7 0 39-45 48 0 40- 30 41- 10[...]

147 3 42- 44 3 0 43-45 48 0 44- 40 4 45- 44 4 8 46- 45 8 47- 10 5 48- 44 5 3 49- 45 3 8 50- 45 8 51- 10 6 52- 44 6 53- 31 8 54- 45 8 7 55- 45 7 9 56- 45 9 57- 20 58- 30 59- 20 60- 43 22 2 61- 45 2 62- 20 53 63-43, 33 53 REGISTERS n: Unused i: Unused PV : Unused PMT : Unused FV : Unused R 0 : K R 1 : P 0 R 2 : P b R 3 : L q R 4 : L R 5 : T R 6 : Use[...]

148 1. 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 press 8. 4. Key in the service rate of each server , µ , and press 9. 5. Press 0 to calculate and store ρ , the intensity factor . 6. Press to see T q , the average waiting time in the queue. Display P 0 [...]

149 2 0.65 P b probability all servers are busy . 3 2.59 L q average # waiting in que ue. 4 4.99 L , average # waiting in system. 5 4.16 T , average total time in system. 2 0.36 Probability of having to wait 2 minutes or more.[...]

150 Appendix Real Est ate Wrap- Around Mortgage • n 1 = number of years remaining in original mortgage. • PMT 1 = yearly payment of original mortgage. • PV 1 = remaining balance of original mo rtgage. • n 2 = number of years in wrap-around mortgage. • PMT 2 = yearly payment of wrap-around mortgage. • r = interest rate of wrap-around mor[...]

151 Lending Loans with a const ant amount p aid towards Princip al • BAL k = remaining balance after time period k. • CPMT = Constant payment to principal. • BAL k = PV - ( k x CPMT ) • K th payment to in terest = i ( BAL k ) = ( PMT i ) k • K th total payment = CPMT + ( PMT i ) k Add-On Interest Rate to APR • r = add-on rate as a deci [...]

152 • FC = ( G - AMT - CL ) Rule of 78's Rebate • PV = finance charge. • I k = interest charged at month k . • n = number of months in loan. • • • BAL k = ( n - k ) x PMT - Rebate k Skipped Payment s • A = number of payments per year . • B = number of years. • C = annual percentage rate as decimal. • D = periodic payment [...]

153 Compounding Periods Different Fr om Payment Periods • C = number of compounding periods per year . • P = number of payments periods per year . • i = periodic interest rate, expressed as a percen tage. • r = i / 100, periodic interest rate expressed as a deci mal. • i PMT = ((1 + r / C) C/P - 1) 100 Investment Analysis Lease vs. Pu rch[...]

154 Profit and Loss Analysis • Net income = (1 - tax)(net sales pr ice - manufacturing expense - operating expense) • Net sales price = list price(1 - discount rate) • where operating expense represents a percentage of net sales price. Securities Discounted Notes Price (given discount rate) • B = number of days in year (annual basis). • D[...]

155 Simple Moving A verage • X = moving average. • m = number of elements in moving average. • • •e t c . Seasonal V ariation Factors Based on a Centered Mov ing A verage • X c = centered moving a verage • m = number of elements in the centered moving averag e. • • SV = Seasonal variation factor . • x i = value of the ith data p[...]

156 • • •W h e r e S 1 , S 2 , and S 3 are: • • • • a , b and c are determined by solving the three equations above simulta- neously . Forecasting With Ex ponential Smoothing • a = smoothing constant (0 < a < 1) • X t = actual current period usage c 1 n -- - S 1 S 3 S 2 2 – S 1 S 3 2S 2 – + ------------------------------[...]

157 • Smoothed average S t = α X t + (1 - α ) S t - 1 • Change, C t = S t - S t - 1 • T rend, T t = α C t + (1 - α ) T t - 1 • Current period expected usage, • Forecast of next period expected usage, • Error , e t = t - X t • Cumulative error = • Initial conditions: S t-1 = X t-1 T t-1 = 0 Pricing Calculations Markup and Margin [...]

158 • • • • • • • • M a 100 SC – S ------------- - = M u 100 SC – C ------------- - = S C 1 Ma 100 --------- - – ------------------ - = SC 1 Mu 100 --------- - +   = CS 1 Ma 100 --------- - –   = C S 1 Mu 100 --------- - + ------------------- - = Ma Mu 1 Mu 100 --------- - + ------------------- - = Mu[...]

159 Calculations of List and Net Prices with Dis count s • L = List price. • N = Net price. • D = Discount(%). • • • St atistics Exponential Curve Fit • y = Ae Bx • • • = - Ae Bx Logarithmic Curve Fit • y = A + B (ln x ) D ' 1 D 100 --------- - – = L N D ' 1 D ' 2 SSDDF × × ----------------------------------[...]

160 • • • = A + B (ln x ) Power Curve Fit • y = Ax B ( A >0) •l n y = ln A + B ln x • • • = Ax B St andard Error of the Mean • Mean, St andard Deviation, S t andard Error fo r Grouped Dat a B Σ y i x i ln 1 n -- - Σ x i Σ y i ln ln – Σ x i ln () 2 1 n -- - Σ x ln () 2 – -------------------------------------------------[...]

161 • mean • standard deviation • standard er ror Personal Finance T ax-Free Retirement Account (IRA) or Keogh Plan • n = the number of years to retirement. • i = the compunded annual interest. • PMT = the earnings used for investment (and taxes). • FV = future value. • tax = the percent tax expressed as a decimal. For ordinary t ax[...]

162 Port folio bet a coefficien t: • Canadian Mortgages • r = annual interest rate expressed as a decimal. • monthly factor Miscellaneous Learning Curve for Manufac turing Cost • C n = Cost of the n th unit. • C 1 = Cost of the first unit. • n = number of units. • r = learning factor . • k = ln r / ln 2 • C n = C 1 n k C ij = the [...]

163 Queuing and W aiting Theo ry • n = number of servers. • λ = arrival rate of customers (Poisson input). • µ = service rate for each server (exponen tial service). • ρ = Intensity factor = λ / µ ( ρ , n for valid results). • P 0 = Probability that all servers are idle. • P b = Probability that all servers are busy . • L q = Av[...]

164 • where: • • A = number of payments per year • B = number of years that payments increase • C = percentage increase in periodic payments (as a decimal) • PMT 1 = amount of the first payment PV PMT 1 1 1I + () A I --------------- - 1Q + () B 1 Q --------------------- -          1 [...]