User manual HP 12C

[. . . ] Introduction This Solutions Handbook has been designed to supplement the HP-12C Owner's Handbook by providing a variety of applications in the financial area. Programs and/or step-by-step keystroke procedures with corresponding examples in each specific topic are explained. We hope that this book will serve as a reference guide to many of your problems and will show you how to redesign our examples to fit your specific needs. 1 Real Estate Refinancing It can be mutually advantageous to both borrower and lender to refinance an existing mortgage which has an interest rate substantially below the current market rate, with a loan at a below-market rate. The borrower has the immediate use of tax-free cash, while the lender has substantially increased debt service on a relatively small cash outlay. [. . . ] Your modified program listing will look like this: KEYSTROKES DISPLAY CLEAR 1 2 1 000102030445 45 44 1 2 1 40 45 44 3 2 40 45 0 10 31 44 3 01 3 2 3 0 050607080910- 3 01 11- 12-43, 33 Keystrokes CLEAR 3 211570 112550 190060 0 1 2 3 Display 0. 00 3. 00 211, 570. 00 112, 550. 00 190, 060. 00 75 00 131760 300500 271120 171, 393. 33 144, 790. 00 207, 440. 00 234, 460. 00 3-month average for March. 3-month average for June. Seasonal Variation Factors Based on Centered Moving Averages. Seasonal variation factors are useful concepts in many types of forecasting. There are several methods of developing seasonal moving averages, on the of more common ways being to calculate them as a ration of the periodic value to a centered moving average for the same period. For instance, to determine the sales for the 3rd quarter of a given year a centered moving average for that quarter would be calculated from sales figures from the 1st, 2nd, 3rd and 4th quarters of the year and the 1st quarter of the following year. The seasonal variation factor for that 3rd quarter would then be the ration of the actual sales in the 3rd quarter to the centered moving average for that quarter. While quarterly seasonal variations are commonly used, the HP 12C can also be programmed to calculate monthly seasonal variations using a centered 12 month moving averages. Programs for both of these calculations are represented here: An HP 12C program to calculate the quarterly seasonal variations based on a centered 4-point moving average is: KEYSTROKES DISPLAY CLEAR 1 2 0001020345 1 2 10 45 44 2 1 40 45 3 2 1 040506- 3 07- 76 2 0809- 44 2 40 4 3 101112- 45 44 4 3 40 5 4 2 1314151617- 45 44 5 4 2 10 40 4 10 31 4 1819202 2122235 01 2444 45 2 23 31 5 01 25-43, 33 n: Unused PV: Unused FV: Unused R1: X1 R3: X3 R5: X5 1. Press CLEAR . REGISTERS i: Unused PMT: Unused R0: n R2: X2 R4: X4 R6-R. 6: Unused Key in the quarterly sales figures starting with the first quarter: a. Key in 1st quarter sales and press 1. 77 b. Press Press Key in 2nd quarter sales and press Key in 3rd quarter sales and press Key in 4th quarter sales and press 2. 5. Key in the 1st quarter sales for the next year and press 00 to calculate the centered moving average for the 3rd quarter of the first year. to calculate the seasonal variation for this quarter. to calculate the moving Key in the next quarter's sales and press average for the next quarter. Press to calculate the seasonal variation. Repeat steps 6 and 7 for the balance of the data. Example: Econo-Wise Home Appliance Company had quarterly sales for the years 1978 thru 1980 as follows: Quarterly 1978 1979 1980 Sales (IN $K) 1st 2nd 3rd 397 376 460 455 390 530 513 434 562 4th 501 560 593 Find the centered 4-quarter moving average and seasonal variation factor for each quarter. Keystrokes CLEAR 397 376 460 501 455 1 2 3 4 5 00 Display 0. 00 397. 00 376. 00 460. 00 501. 00 455. 00 440. 75 104. 37 Centered 4-element average for 3rd quarter, 1978 seasonal variation factor. 78 390 449. 75 111. 40 4th quarter, 1978. 530 460. 25 98. 86 1st quarter, 1979. 560 476. 38 81. 87 2nd quarter, 1979. 513 490. 00 107. 94 3rd quarter, 1979. 434 503. 75 111. 17 4th quarter, 1979. 562 513. 25 99. 95 1st quarter, 1979. 593 521. 38 83. 24 2nd quarter, 1980. Now average each quarter's seasonal variation for the two years? Keystrokes CLEAR 98. 86 99. 95 Display 0. 00 1. 00 2. 00 99. 41 CLEAR 81. 87 83. 24 0. 00 1. 00 2. 00 82. 56 CLEAR 104. 37 107. 94 0. 00 1. 00 2. 00 106. 16 3rd quarter average seasonal variation, %. 2nd quarter average seasonal variation, %. 1st quarter average seasonal variation, %. 79 CLEAR 111. 4 111. 17 0. 00 1. 00 2. 00 111. 29 4th quarter average seasonal variation, %. An HP-12C program to calculate a centered 12-month moving average and seasonal variation factor is as follows: KEYSTROKES DISPLAY CLEAR 1 2 000102-2 0310 45 44 2 1 40 45 44 3 2 40 45 44 4 3 40 45 44 5 4 40 45 44 6 5 40 45 7 45 1 2 1 040506- 3 2 070809- 4 3 101112- 5 4 131415- 6 5 161718- 7 19- 80 6 2021- 44 6 40 8 7 222324- 45 44 8 7 40 9 8 2526270 28-45 29301 0 31-45 32-44 332 1 34-45 35-44 363 2 37-45 38-44 394041- 45 44 9 8 40 48 44 0 9 40 9 48 48 1 0 40 48 48 2 1 40 48 48 3 2 2 10 40 2 0 424344- 45 0 10 31 6 454647- 45 6 23 31 81 3 01 48-44 48 3 01 48-43, 33 n: Unused PV: Unused FV: Unused R1: X1 R3: X3 R5: X5 R7: X7 R9: X9 R. 1: X11 R. 3: X13 1. Press CLEAR . REGISTERS i: Unused PMT: Unused R0: n R2: X2 R4: X4 R6: X6 R8: X8 R. 0: X10 R. 2: X12 Key in 12 and press 0. 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 Key in the 2nd month and press Key in the 10th month and press Key in the 13th month and press 1. Press 00 to calculate the centered moving average for to calculate the seasonal variation for that month. to calculate the Key in the value for the next month (14th) and press moving average for the next month (8th). Repeat steps 6 and 7 for the balance of the data. These programs may be customized by the user for different types of centered moving averages. [. . . ] m = number of elements in moving average. Seasonal Variation Factors Based on a Centered Moving Average Gompertz Curve Trend Analysis · · · S3 ­ S2 b = ------------------ S 2 ­ S 1 1 -n y = ca(bx) where x, y, a, b, and c are positive. (1 ­ a) D t = S t + ---------------- Tt 155 · 1 S 1 S 3 ­ S 2 - c = exp -- ----------------------------------- n S 1 + S 3 ­ 2S 2 · ( b ­ 1 ) ( S2 ­ S1 ) a = exp ----------------------------------------2 n b(b ­ 1) · · Where S1, S2, and S3 are: 2 1 1 t + 1 = S t + -- T t n S1 = i=1 b ­1 Iny i = n ln c + b ( ln a ) -------------b­1 n · 2n S2 = i = n+1 Iny i = n ln c + b n+1 b ­1 ( ln a ) -------------b­1 n · · a, b and c are determined by solving the three equations above simultaneously. a = smoothing constant (0 < a < 1) Xt = actual current period usage Forecasting With Exponential Smoothing · · 156 3n S3 = i = 2n + 1 Iny i = n ln c + b 2n + 1 b ­1 ( ln a ) -------------b­1 n · · · · Smoothed average St = Xt + (1 - )St - 1 Change, Ct = St - St - 1 Trend, Tt = Ct + (1 - )Tt - 1 Current period expected usage, · Forecast of next period expected usage, · · Error, et = t - Xt Cumulative error = t=1 2 et · Initial conditions: St-1 = Xt-1 Tt-1 = 0 Pricing Calculations Markup and Margin Calculations · · · · Ma = margin(%). C = cost. 157 · S­C Ma = 100 ------------S · S­C Mu = 100 ------------C · C S = -----------------Ma 1 ­ --------100 · Mu S = C 1 + --------- 100 · Ma C = S 1 ­ --------- 100 · S C = ------------------Mu 1 + --------100 · Mu Ma = ------------------Mu 1 + --------100 · Ma Mu = ------------------Ma 1 + --------100 158 Calculations of List and Net Prices with Discounts · · · · D D' = 1 ­ --------100 · N L = -------------------------------------------------D' 1 × D' 2 × SSDDF . . . [. . . ]