- Classify the different cost items as either fixed or variable costs (matching row number to Fixed or Variable as appropriate).
Fixed Costs: All
costs under Sections A and B on the List of Ingredients spreadsheet are fixed costs because they are not affected by
the number of students enrolled in the course. Rumble (1997) instructs us that
fixed costs are those that "do not increase or decrease with changes in the level of activity." (p. 23)
Variable Costs: All
costs under Section C of the List of Ingredients spreadsheet are variable costs because they are affected by the enrollments
in the course. Rumble (1997) instructs us that variable costs are those where
"every time one [student] is added, the cost goes up by the cost of that [student]."
(p. 24)
Semi-Variable Costs:
The variable costs in lines 24 and 25 on the List of Ingredients spreadsheet are more precisely characterized
as semi-variable costs. They do not vary as we add just one student; they
can be affected by certain increments of enrollments. In other words, as Rumble
(1997) instructs us, these semi-variable costs "may vary with significant changes in the level of activity." (p. 24) In our
undergraduate course, the semi-variable costs will increase with every group of 30 students enrolled.
- Calculate the aggregate Fixed Costs of Development (FD) and the aggregate Fixed Costs of Maintenance
(FM).
The aggregate Fixed Costs of Development
(FD) include both the direct costs of development plus the indirect costs of overhead attributed to the development. FD is comprised of the course overheads of management and secretarial support and
the costs incurred to develop the print and video course materials and development of the assignment.
FD is computed as follows:
Management
No. Units: 1.500 (3 years x .5 of annual salary)
Rate per Unit (Annual salary): $70,000
Cost: 1.500 x $70,000 =
$105,000
Secretarial Support
No. Units: .750 (3 years x .25 of annual salary)
Rate per Unit (Annual salary): $23,500
Cost: .750 x $23,500 = 17,625
Authoring of Study Guide
No. Units: 9
Rate per Unit: $14,000
Cost: 9 x $14,000 =
126,000
Preparation of Reader
No. Units: 1
Rate per Unit: $7,600
Cost: 1 x $7,600 =
7,600
Editing and Design
No. Units: 13
Rate per Unit: $3,900
Cost: 13 x $3,900 =
50,700
Copyright
No. Units: 13
Rate per Unit: $2,400
Cost: 13 x $2,400 =
31,200
Copyright Clearance (video materials)
No. Units: 9
Rate per Unit: $9,500
Cost: 9 x $9,500 =
85,500
Production (video)
No. Units: 9
Rate per Unit: $23,500
Cost: 9 x $23,500 =
207,000
Assignment development
No. Units: 3
Rate per Unit: $350
Cost: 3 x $350 =
+
1,050
FD Total
$631,675
The aggregate Fixed Costs of Maintenance
(FM) are incurred for the authoring, editing, and design of part of the printed material.
FM is computed as follows:
Author
No. Units: 2
Rate per Unit: $1,100
Cost: 2 x $1,100 =
$2,200
Editing and Design
No. Units: 2
Rate per Unit: $2,800
Cost: 2 x $2,800 =
+5,600
FM Total
$7,800
- Calculate the variable cost per student (V)
The Variable Cost per Student
(V) is the total of the Student Support and Replication and Distribution costs, computed per student. It is noted that V includes the semi-variable costs identified above in item #1.
V is computed as follows:
Marking of assignment
No. Units: 3
Rate per Unit: $45
Cost: 3 x $45=
$ 135.00
Tutor (per group of 30)
No. Units: 12
Rate per Unit: $65
Divide by 30 to compute cost per student
Cost: (12 x $65)/30 =
26.00
Tuition Expenses (per group of 30)
No. Units: 1
Rate per Unit: $80
Divide by 30 to compute cost per student
Cost: (1 x $80)/30 =
2.667
Production of Study Guides
No. Units: 9
Rate per Unit: $8.90
Cost: 9 x $8.90 =
80.10
Production of Assignments
No. Units: 3
Rate per Unit: $1.20
Cost: 3 x $1.20 =
3.60
Production of Reader
No. Units: 1
Rate per Unit: $16
Cost: 1 x $16 =
16.00
Production of Cassette
No. Units: 9
Rate per Unit: $12
Cost: 9 x $12 =
108.00
Packaging and Postage:
No. Units: 3
Rate per Unit: $9
Cost: 3 x $9 =
+ 27.00
V Total
$398.367
- Calculate the depreciation rate on a basis of the lifetime of the presentation of the project (compare Rumble Table
6.1) and charge it to each year of presentation.
Depreciation Table
Actual Cost($) Years of Life
Annual Depreciated Cost
FD
$631,675
5
$126,335
FM
$ 7,800
2
$ 3,900
Total
$639,475
$130,235
Note:
FD annual depreciation = FD/5. FM annual depreciation = FM/2
- Following the template of Rumble Table 6.4, annualize the Fixed Costs of Development (FD) over the five years
of presentation at 5% interest and the Fixed Costs of Maintenance (FM) over two years at the same rate.
Annualization Table – where
r = 5%
Cost($)
Years of Life Value of Annualized Cost
a(r,n) (Cost x
a(r,n))
FD
$631,675
5
.213 $145,916.93
FM
$ 7,800
2
.538 $ 4,196.40
Total
$639,475
$150,113.33
Note:
The figures in the Annualized Cost column here are within 10% of amounts shown in cells F11-K11 (FD), F12 and
J12-K12 (FM), and J13-K13 (Total) of the Calculation Template worksheet in the attached Excel workbook.*
- Summarize in a short paragraph the reasons for and against annualization.
According to Rumble (1997) the reason
why an organization may choose annualization is that it more accurately than depreciation reflects opportunity costs. Annualization takes into consideration depreciation along with the interest (at the
prevailing rate) that the organization will not earn from investing the value of the undepreciated portion of the asset in
something else for the remainder of the life of the asset. In other words, had
the funds not been tied up in the asset, they perhaps could have been invested in something other than the asset during that
time at the prevailing interest rate.
On the other hand, annualization may
not be the best approach. The approach makes sense for the organization only
if there is a viable alternative to the investment of funds in the asset. If
the organization does not have the choice between for example whether to acquire the asset or invest the cash, then annualization
is not relevant. For example, a public organization may be required to use earmarked
funds to acquire a certain asset and be prohibited from using the funds for anything else (including placing the cash in an
interest bearing account or instrument). Therefore, according to Rumble (1997)
annualization is not an appropriate approach for public organizations in such cases.
- Calculate the equation of total costs (TC=F+VxN) using the annualized figure of fixed costs and N=800
N = 800
F (annualized) = $737,895
V = $398.367
TC(N) = F + V x N
TC(800) = $737,895 + ($398.367 x 800)
TC(800) = $737,895 + $318,693.60
TC(800) = $1,056,588.60
Note:
TC computed here is only $.60 more than the amount shown in cell J16 on the Calculation Template spreadsheet
in the attached Excel workbook.*
- Draw the graph of the total cost function using, as above, the annualized figure of fixed costs while N varies over
the accumulated number of students (i.e. N= 200, 400, etc.)
See the graph labeled "TC" in the
attached Excel workbook.
- Calculate the equation of average costs (AC=F/N+V) using the annualized figure for fixed costs and N=800
F (annualized) = $737,895
N = 800
V = $398.367
AC(N) = F/N + V
AC(800) = $737,895/800 + $398.367
AC(800) = $922.369 + $398.367
AC(800) = $1,320.736 or rounded to
$1,321
Note:
Rounded AC(800) computed here is the same number as in cell J17 in Calculation Template spreadsheet in the attached
Excel workbook.
- Draw the graph of the average cost function, using, as above, the annualized figure of fixed costs while N varies over
the accumulated number of students (i.e. N= 200, 400, etc.)
See the graph labeled "AC" in the
attached Excel workbook.
- If the student is charged the per student fee specified, calculate the break-even point. (Use the equation TC=F+VxN
and the income equation: I=SFxN (Income =Student fee x No of students). The break-even point is N=F/(SF-V)
F = $737,895
SF = $1,260
V = $398.37 (rounded from $398.367)
N = F/SF-V
N = $737,895 / ($1,260 - $398.37)
N = $737,895/$861.63
N = 856.394 or 856
Break-Even Point = 856 students
- Represent the break even point graphically (overlaying the graphs of TC and I).
See the Excel workbook attached. The break even point is noted on the graph labeled "TC".
- Summarize in a short paragraph why it is believed that the TC and AC equations and the specific cost structure of DE
suggests that DE may be more cost-efficient than conventional modes of educational provision.
According to Rumble (1997), governments view DE as more cost efficient than traditional face-to-face
education because it is believed that DE can be delivered at a lower average cost per student.
However, Rumble cautions us that economies of scale will not necessarily be achieved, especially if a DE organization
cannot attract enough students. Certain measures can be undertaken to move towards
economies of scale in DE. For example, DE organizations can develop and mass-produce
higher quality course materials aimed to reduce the need for learners' interaction with an instructor. If the effort is successful, courses may be able to run with tutors instead of instructors attending to
students. Reducing the number of instructors can reduce costs since tutors are
generally less expensive than instructors. The mass distribution of course materials
can further enable the DE organization to reach more students than would otherwise be possible in a conventional face-to-face
delivery. The DE organization can do so without additional course development
costs or capital investments such as classroom buildings. The flexibility afforded
by DE increases the organization's capacity for students while keeping down the costs for each additional student. And, if more students enroll, the average cost per student decreases, thus moving closer to economies of
scale.
Reference
Rumble, G. (1997). The Costs and Economics of Open and Distance Learning. London: Kogan Page.
