07-44 | HP 12C guide

Exponential smoothing is often used for short term sales and inventory forecasts. Typical forecast periods are monthly or quarterly. Unlike a moving average, exponential smoothing does not require a great deal of historical data. However , it should not be used with data which has more than a moderate amount of up or down trend.

When using exponential smoothing, a smoothing factor is chosen which affects the sensitivity of the average much the same way as the length of the standard moving average period. The correspondence between the two techniques can be represented by the formula:

α2

=-----------

n + 1

where α is the exponential smoothing factor (with values from 0 to 1) and n is the length of the standard moving average. As the equation shows, the longer the moving average period, the smaller the equivalent and the less sensitive the average becomes to fluctuations in current values.

Forecasting with exponential smoothing involves selecting the best smoothing factor based on historical data and then using the factor for updating subsequent data and forecasting. This procedure uses the following HP 12C program:

KEYSTROKES		DISPLAY

CLEAR	00-
	01-		36

	02-		36

6	03-	45	6
	04-		30

	05-		36

	06-		20

4	07-44	40	4
	08-	43	36

	09-		31

	10-		33

	11-		33

0	12-	45	0
	13-		20

88

Image 89

HP 12C manual 07-44

Contents

Page Introduction Refinancing Real Estate Wrap-Around Mortgage PMT Rate of return to lender Cash flow occurs 39 timesFinal cash flow Number of periods and monthly Derivation of these cash flows follows a set sequence Income Property Cash Flow AnalysisBefore-Tax Cash Flows Derivation of these reversions are as follows Vacancy LossBefore-Tax Reversions Resale Proceeds After-Tax Cash Flows Keystrokes Display 30-43 33-44 35-43 40-44 42-45 48-44 53-44 Registers 3291.75 ATCF1 After-Tax Net Cash Proceeds of Resale 18-44 33-44 39-44 48-43 Key in the number of years after purchase and press Atncpr Loan Reduction Schedule LendingLoan With a Constant Amount Paid Towards Principal Add-On Interest Rate Converted to APR APR Converted to Add-On Interest Rate Add-On Rate Loan with Credit Life Page 53-43 77-45 78-43 PMT PMT Credit life Interest Rebate Rule of 78s 26-43 Graduated Payment Mortgages Keystrokes Display 34-44 38-43 39-43 68-44 69-44 72-43 73-43 77-43 Keystrokes Display Variable Rate Mortgages Keystrokes Display Skipped Payments Group of payments is skipped Initial Deposit with Periodic Deposits Savings Periodic Deposits and Withdrawals FV = ? Cash flow diagram looks like this PV = Savings Account Compounded Daily Keystrokes Display 27-44 37-43 Compounding Periods Different From Payment Periods Clear 519.61 Future value Lease vs. Purchase Investment Analysis 16-44 18-44 27-44 30-45 32-45 34-45 Instructions Year Maintenance Lease Payment Tax Credit Buy Back 200 1700 1000 1500 300 750 Break-Even Analysis Profit To calculate the gross profit at a given volume Find the gross profit if 2500 units are sold 04-43 09-43 15-43 23-43 Gross Profit Operating Leverage 10-43 Profit and Loss Analysis 11-43 28-43 37-43 42-43 47-43 Page 100.00 48% tax rate Manufacturing cost $ After-Tax Yield Securities Purchase price Discounted Notes 30-43 Settl. date Maturity dtae Simple Moving Average Forecasting Keystrokes Display 26-45 29-45 30-44 32-45 33-44 Unused PV Unused PMT Unused FV Unused R .4 Unused 12-43 Seasonal Variation Factors Based on Centered Moving Averages 25-43 Sales in $K Quarterly 1st 2nd 3rd 4th 98.86 99.95 99.41 1st quarter average seasonal Variation, % 02-2 28-45 31-45 32-44 34-45 35-44 37-45 38-44 Gompertz Curve Trend Analysis 02-44 05-44 08-44 10-44 12-43 Page 71-43 Year III Forecasting with Exponential Smoothing 07-44 Page Forecasting Selecting the best smoothing constant α 22.00 23.00 23.25 25.25 23.69 27.13 25.95 Procedure is repeated for several αs Markup and Margin Calculations Pricing Calculations 02-43 14-43 Calculations of List and Net prices With Discounts 100 10.51 3rd discount rate % 05-44 06-43 16-43 Page Exponential Curve Fit StatisticsCurve Fitting 100 101 102 Logarithmic Curve Fit 104 Power Curve Fit Formula that best expresses h as a function of t is Standard Error of the Mean Mean, Standard Deviation, Standard Error for Grouped Data 108 Use the following HP-12C program for the previous example 109 Chi-Square Statistics 111 112 Normal Distribution 114 Relative error less than 0.042% over the range 0 xReference 115 116 117 CovarianceExample Find Qx for x = 1.18 and x = 118 Try the previous example using the following HP-12C program Permutation 120 121 Combination 122 Random Number Generator 123 Example Generate a sequence of 5 random numbers 124 Personal FinanceHomeowners Monthly Payment Estimator 125 Following HP-12C program may be used instead of the above 126 Example Solve the previous example using the HP-12C programWhat if the down payment is increased to 20%? 127 Tax-Free Individual Retirement IRA of Keogh Plan 128 129 Stock Portfolio Evaluation and Analysis 131 132 133 134 Example Evaluate the following portfolio 135 136 Canadian MortgagesPeriodic Payment Amount Effective Interest Rate Yield Number of Periodic Payments to Fully Amortize a MortgageBalance Remaining at End of Specified Period 137 138 139 MiscellaneousLearning Curve for Manufacturing Costs 140 141 142 143 Queuing and Waiting Theory Intensity factor 145 146 147 148 149 Real Estate AppendixWrap-Around Mortgage 150 Loans with a constant amount paid towards Principal LendingAdd-On Interest Rate to APR Add-On to APR with Credit Life Rule of 78s Rebate SavingsSkipped Payments 152 Compounding Periods Different From Payment Periods Investment AnalysisLease vs. Purchase Break-Even Analysis and Operating Leverage Forecasting SecuritiesProfit and Loss Analysis Discounted Notes Price given discount rate 155 Simple Moving AverageGompertz Curve Trend Analysis 156 Forecasting With Exponential Smoothing Forecast of next period expected usage Pricing CalculationsMarkup and Margin Calculations 157 158 159 StatisticsCalculations of List and Net Prices with Discounts 160 Tax-Free Retirement Account IRA or Keogh Plan Personal FinanceFor ordinary taxable investment For tax-free investment Miscellaneous Canadian MortgagesPortfolio beta coefficient Learning Curve for Manufacturing Cost 163 Queuing and Waiting TheoryGraduated Payment Mortgage + C 164