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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)