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?
Forecasting 131
Financial Management for Human Service Administrators, by Lawrence L. Martin. Copyright © 2001 by Allyn and Bacon, a Pearson Education Company.
ISBN: 0-
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)
Haven't figured out time seriers yet
How do financial tren impact forecasting
To forecast total revenues for fiscal year 20X5 using different methods, we have the following options: moving averages, weighted moving averages, exponential smoothing, and time series regression.
1. Moving Averages:
For moving averages, we will use the data for the past three fiscal years. We calculate the average of these three years and use that as the forecast for fiscal year 20X5.
Average = (20X2 revenue + 20X3 revenue + 20X4 revenue) / 3
Average = ($14,250,000 + $14,000,000 + $13,500,000) / 3
Average = $41,750,000 / 3
Average = $13,916,667
So, the moving average forecast for fiscal year 20X5 is $13,916,667.
2. Weighted Moving Averages:
For weighted moving averages, we assign different weights to each year's data. In this case, we will 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. We calculate the weighted average using these weights.
Weighted Average = (20X2 revenue × 1 + 20X3 revenue × 2 + 20X4 revenue × 3) / (1 + 2 + 3)
Weighted Average = ($14,250,000 × 1 + $14,000,000 × 2 + $13,500,000 × 3) / (1 + 2 + 3)
Weighted Average = ($14,250,000 + $28,000,000 + $40,500,000) / 6
Weighted Average = $82,750,000 / 6
Weighted Average = $13,791,667
So, the weighted moving average forecast for fiscal year 20X5 is $13,791,667.
3. Exponential Smoothing:
For exponential smoothing, we assume that the last forecast for fiscal year 20X4 was $13,000,000. We also need to decide on the value of alpha (α) to be used. Alpha is a smoothing constant that determines the weight given to the most recent data point. A higher value of α gives more weight to recent observations.
Let's assume α = 0.5 (you can choose a different value if desired).
Forecast for 20X5 = Last Forecast + α × (Current Data - Last Forecast)
Forecast for 20X5 = $13,000,000 + 0.5 × ($13,500,000 - $13,000,000)
Forecast for 20X5 = $13,000,000 + 0.5 × $500,000
Forecast for 20X5 = $13,000,000 + $250,000
Forecast for 20X5 = $13,250,000
So, the exponential smoothing forecast for fiscal year 20X5 is $13,250,000.
4. Time Series Regression:
For time series regression, we use the data for all four fiscal years to build a regression model. This model will help us estimate the relationship between total revenues and time. We can then use this model to forecast total revenues for fiscal year 20X5.
Without the data for all four fiscal years, it is not possible to provide a specific forecast using time series regression.
Considering the available options, we can choose the forecast based on the specific requirements or preferences of the Palmdale Human Service Agency. Each method has its own assumptions and limitations, so it ultimately depends on which method is considered the most appropriate for the agency's needs and context.