Managerial Accounting Assignment
Cost estimation and management of overhead costs
Pauline Raphael, executive assistant to the principal of Ecole Superieure des Mines de St Etienne, is concerned about the overhead costs at her university. Cost pressures are severe, so controlling and reducing overheads is very important. Raphael believes overhead costs incurred are generally a function of the number of different academic programmes (including different specializations, degrees and research programmes) that the university has and the number of enrolled students. Both have grown significantly over the years. She collects the following data:
|
Year
|
Overhead costs ('000)
|
Number of academic programmes
|
Number of enrolled students
|
|
1
|
£ 13500
|
29
|
3400
|
|
2
|
19200
|
36
|
5000
|
|
3
|
16800
|
49
|
2600
|
|
4
|
20100
|
53
|
4700
|
|
5
|
19500
|
54
|
3900
|
|
6
|
23100
|
58
|
4900
|
|
7
|
23700
|
88
|
5700
|
|
8
|
20100
|
72
|
3900
|
|
9
|
22800
|
83
|
3500
|
|
10
|
29700
|
73
|
3700
|
|
11
|
31200
|
101
|
5600
|
|
12
|
38100
|
103
|
7600
|
She finds the following results for two separate simple regression models:
Regression 1: Overhead costs = a + (b* Number of academic programmes)
|
Variable
|
Coefficient
|
Standard error
|
t-value
|
|
Constant
|
£ 7127.75
|
£ 3335.34
|
2.14
|
|
Independent variable 1: number of academic programmes
|
£ 240.64
|
£ 47.33
|
5.08
|
R2 = 0.72; Durbin-Watson statistic = 1.81
Regression 2: Overhead costs = a + (b* Number of enrolled students)
|
Variable
|
Coefficient
|
Standard error
|
t-value
|
|
Constant
|
£ 5991.75
|
£ 5067.88
|
1.18
|
|
Independent variable 1: number of enrolled students
|
£ 3.78
|
£ 1.07
|
3.53
|
R2 = 0.55; Durbin-Watson statistic = 0.77
REQUIRED
1. Plot the relationship between overhead costs and each of the following variables: (a) number of academic programmes, and (b) number of enrolled students.
2. Compare and evaluate the two simple regression models estimated by Raphael.
3. What insights do the analyses provide about controlling and reducing overhead costs at the Ecole Superieure?
4. Given the findings from the simple regression analysis, should Raphael use multiple regression analysis to better understand the cost drivers of overhead costs? Explain your answer.
5. Suppose that Raphael decides that the simple regression analysis should be extended to a multiple regression analysis. She finds the following result:
Regression 3: Overhead costs = a + (b1*Number of academic programmes) + (b2*Number of enrolled students)
|
Variable
|
Coefficient
|
Standard error
|
t-value
|
|
Constant
|
£ 2779.62
|
£ 3620.05
|
0.77
|
|
Independent variable 1: number of academic programmes
|
£ 178.37
|
£ 51.54
|
3.46
|
|
Independent variable 2: number of enrolled students
|
£ 1.87
|
£ 0.92
|
2.03
|
R2 = 0.81; Durbin-Watson statistic = 1.84
The coefficient of correlation between number of academic programmes and number of students is 0.60. Evaluate the multiple regression models. Assume linearity and constant variance and normality of residuals. Should Raphael choose the multiple regression models over the two simple regression models?
6. How might the principal of the Ecole Superieure use these regression results to manage overhead costs?