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The following data represent total personnel expenses for the Palmdale Human
Service Agency for past four fiscal years:
20X1 $5,250,000
20X2 $5,500,000
20X3 $6,000,000
20X4 $6,750,000
Forecast personnel expenses for fiscal year 20X5 using moving averages, weighted
moving averages, exponential smoothing, and time series regression. For moving
averages and weighted moving averages, use only the data for the past three fiscal
years. For weighted moving averages, assign a value of 1 to the data for 20X2, a
value of 2 to the data for 20X3, and a value of 3 to the data for 20X4. For exponential
smoothing, assume that the last forecast for fiscal year 20X4 was $6,300,000.
You decide on the alpha to be used for exponential smoothing. For time series
regression, use the data for all four fiscal years. Which forecast will you use? Why?
130 C H A P T E R 9
Financial Management

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    E X E R C I S E S

    Exercise 9.1

    The following data represent total personnel expenses for the Palmdale Human
    Service Agency for past four fiscal years:
    20X1 $5,250,000
    20X2 $5,500,000
    20X3 $6,000,000
    20X4 $6,750,000
    Forecast personnel expenses for fiscal year 20X5 using moving averages, weighted
    moving averages, exponential smoothing, and time series regression. For moving
    averages and weighted moving averages, use only the data for the past three fiscal
    years. For weighted moving averages, assign a value of 1 to the data for 20X2, a
    value of 2 to the data for 20X3, and a value of 3 to the data for 20X4. For exponential
    smoothing, assume that the last forecast for fiscal year 20X4 was $6,300,000.
    You decide on the alpha to be used for exponential smoothing. For time series
    regression, use the data for all four fiscal years. Which forecast will you use? Why?
    Moving averages
    Fiscal Year Expenses
    20X2 $5,500,000
    20X3 $6,000,000
    20X4 $6,750,000
    20X5 $6,083,333

    To get the moving average, we add the last three years then divide by 3 to get the forecasted expenses for fiscal year 20X5.
    Weighted moving averages
    Fiscal Year Expenses Weight Weight Score
    20X2 $5,500,000 1 $5,500,000
    20X3 $6,000,000 2 $12,000,000
    20X4 $6,750,000 3 $20,250,000
    20X5 $6,291,667

    To get weighted moving average for fiscal year 20X5, we add weight to the expenses to get a weight score. We then add the weight score and divide by number of weight added all together, to get fiscal year expenses for 20X5.


    Exponential smoothing
    Fiscal Year Expenses
    20X2 $5,500,000
    20X3 $6,000,000
    20X4 $6,750,000
    20X5 $6,210,000

    Exponential smoothing uses the formula NF = LF + a (LD - LF) to calculate a forecast.
    NF=$6,300,000+.3($6,000,000-$6,300,000)

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