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
Please note that we don't do students' homework for them. Be sure to go back into your textbook or use a good search engine. http://hanlib.sou.edu/searchtools/
Once YOU have come up with attempted answers to YOUR assignment, please re-post and let us know what you think. Then someone here will be happy to comment on your thinking.
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)
To forecast personnel expenses for fiscal year 20X5 using different methods, let's go step by step:
1. Moving Average:
- Calculate the average of personnel expenses for the past three fiscal years: (5,500,000 + 6,000,000 + 6,750,000) / 3 = 6,083,333
- This average will be your forecast for fiscal year 20X5 using moving averages.
2. Weighted Moving Average:
- Assign weights to the data for the past three fiscal years: 20X2 = 1, 20X3 = 2, 20X4 = 3
- Multiply each data point by its corresponding weight: (5,500,000 * 1) + (6,000,000 * 2) + (6,750,000 * 3) = 42,750,000
- Calculate the total weights: 1 + 2 + 3 = 6
- Calculate the weighted moving average by dividing the total by the sum of the weights: 42,750,000 / 6 = 7,125,000
- This weighted moving average will be your forecast for fiscal year 20X5.
3. Exponential Smoothing:
- Assume that the last forecast for fiscal year 20X4 was $6,300,000.
- Choose a value for alpha, which determines the weighting given to recent observations. Common values for alpha range from 0.1 to 0.3.
- Multiply the previous forecast by (1 - alpha) and add the actual observation for the last fiscal year multiplied by alpha: (6,300,000 * (1 - alpha)) + (6,750,000 * alpha) = forecast for fiscal year 20X5
- Repeat the calculation by adjusting the alpha value until you find the most accurate forecast. Compare the results for different alpha values and choose the one that gives the best fit for the historical data.
4. Time Series Regression:
- Use all four years of data to derive a regression equation that predicts personnel expenses based on the fiscal year.
- Fit a linear regression model to the data, where the dependent variable (expenses) is regressed against the independent variable (fiscal year).
- Based on the regression equation, input the value for fiscal year 20X5 to obtain the forecasted personnel expenses.
Which forecast to use depends on various factors such as the accuracy of each method in predicting future expenses and the specific requirements or preferences of the Palmdale Human Service Agency. It is recommended to compare the forecasts from different methods and choose the one that aligns best with historical trends and provides the most accurate prediction in the given context.