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Cost
behaviour case study
The DK Pizza House has
provided you with the following information on its costs at various levels of
monthly sales.
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Monthly sales units |
3,000 |
6,000 |
9,000 |
|
Cost of food |
3,500 |
5,000 |
6,500 |
|
Supplies |
600 |
1,200 |
1,800 |
|
Utilities |
360 |
420 |
480 |
|
Other operating costs |
1,500 |
3,000 |
4,500 |
|
Building rent |
1,000 |
1,000 |
1,000 |
|
Depreciation |
200 |
200 |
200 |
Required
1 Identify each cost as variable, fixed or
mixed.
2 Develop an equation to estimate total cost at
various levels of activity
3 Project total cost with monthly sales of 8,000
units.
What follows is just the solution to this question:
for a detailed explanation of the methods on which the solutions are based,
please see other pages in this series:
1 We could
identify the behaviour of costs in a number of ways. However, I believe the most effective way of cost behaviour
identification in cases such as this is to use the scattergraph method. The six graphs we need follow:
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In summary, these graphs tell us the following:
| Cost | Cost Behaviour |
| Cost of food | semi variable cost |
| Supplies | variable cost |
| Utilities | semi variable cost |
| Other Operating Costs | variable cost |
| Building Rent | fixed cost |
| Depreciation | fixed cost |
2 The graphs contain equations that enable us to predict what that cost would be for any level of activity (within the relevant range, of course). However, the question asks for one equation and this must be based on total costs. We can use the high low method to derive the cost function y = a + bx here:
| Sales | Total Costs |
| 9,000 | 14,480 |
| 3,000 | 7,160 |
| 6,000 | 7,320 |
the value of 'b' is 7,320/6,000 = 1.22
the value of 'a' is 14,480 - (9,000 * 1.22) = 3,500
therefore, y = a + bx = 3,500 + 1.22x
Check
on cost
behaviour if you have any queries with what I have presented
here.
3 Using the function we found in question 2, when x = 8,000
y = 3,500 + 1.22 * 8,000 = 13,260
The costs at
a level of output of 8,000 units are, using the equations given on the graphs
above are:
| Monthly sales units | 8,000 |
| Cost of food sold | 6,000 |
| Supplies | 1,600 |
| Utilities | 460 |
| Other operation costs | 4,000 |
| Building rent | 1,000 |
| Depreciation | 200 |
| Total | 13,260 |
August 2000
This
case came to me as an e-mail message as a problem to solve. I don’t know who sent it to me and I don’t
know whether it comes from copyright material.
If anyone recognises the case as their own then I would happily give
them the recognition they deserve.
