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

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. Forecast personnel expenses for fiscal year 20X5 using moving averages, weighted moving averages, exponential smoothing, and time series regression.

Moving Averages

Fiscal Year Expenses

20X2 $5,500,000

20X3 $6,000,000

20X4 $6,750,000

20X2-4 $18,250,000

20X5 $18,250,000/3 = $6,083,333

Weighted Averages

Fiscal Year Expenses Weight Weighted 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 6 $37,750,000 20X5 $37,750,000/6 = $6,291,667

Exponential Smoothing

Given:

Last Forecast (LF) = $6,300,000Last Data (LD) = $6,750,000α = 0.95 I used the 0.95 alpha because I strongly believe that the new forecast will be based on the last data.

NF = LF + α (LD – LF)

NF = $6,300,000 + 0.95 ($6,750,000 – $6,300,000)

NF = $6,300,000 + 0.95 (450,000)

NF = $6,300,000 + 427,500

NF = $6,727,500

20X5 = $6,727,500

Time Series Regression

Computer Output

Constant = 4,625,000

Variable = 500,000

R-Square = 0.95

Y = 4,625,000 + 500,000X

20X5 = 4,625,000 + 500,000 (5)

20X5 = 4,625,000 + 2,500,000

20X5 = $7,125,000

Which forecast will you use? Why?

Over the past year expenses have clearly been growing. The R-square in the time series regression makes this more evident. From the 4 different forecasts, the Time Series Regression reveals that the expenses will grow, on 20X5. Because of this, I choose to use the Time Series Regression.

Reference

Martin, L. (2001). Financial management for human service administrators. Boston, MA: Allyn and Bacon.

Exercise 9.3

The following data represent total revenues (from all sources) for the Palmdale Human Service Agency for the past four fiscal years:

20X1 $15,000,000

20X2 $14,250,000

20X3 $14,000,000

20X4 $13,500,000

Forecast total revenues 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 $13,000,000. 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 $14,250,000

20X3 $14,000,000

20X4 $13,500,000

20X2-4 $41,750,000

20X5 $41,750,000/3= $13,916,667 (rounded-up)

Weighted Averages

Fiscal Year Expenses Weight Weighted Score 20X2 $14,250,000 1 $14,250,000 20X3 $14,000,000 2 $28,000,000 20X4 $13,500,000 3 $40,500,000...