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Hi sir can you help me with the concept of this as i know the concept of fixed cost when semi fixed are introduced at a certain output level. I have the answer but i am not able to understand its concept. Could you please explain the solution of this.
Output level(units) 5000 10,000
Total Overhead Cost($) 14,000 27,000The variable element of total overhead cost is known to increase by $1 per unit at output levels above 7000 units.
What is the variable element of total overhead cost at an output level of 5,000 units?
Thank you,
Kamal BishtYou need to use a little simple algebra.
Suppose the variable cost per unit at the lower level is V, then at the higher level it is V + 1.
The difference between the two total costs (13,000) is the difference in the total variable costs (because the fixed cost does not change).
The total variable cost for 10,000 units = 10,000 (V+1) = 10,000V + 10,000
The total variable cost for 5,000 units = 5,000VSo the difference = 10,000V + 10,000 – 5,000V = 13,000
So, subtracting 10,000 from both sides, 10,000V – 5,000V = 13,000 – 10,000
Therefore 5,000V = 3,000
V = 3,000/5,000 = 0.60.I have a question on this Mr Moffat.
I thought that as the change in unit variable cost was not specified to have occured from zero units, we should have added the increment only to the remaining units above 7, 000.I mean,
27,000 = F + 7,000v + 3,000 (v + 1)How is this sir ?
I understand the point you are making, but the wording of the question implies that the extra $1 per unit will apply to all units if the output is above 7,000 units.
(Think about it from a practical point of view (this is a practical exam, not an arithmetic exam 🙂 ) – it would be very strange to produce units and the cost for some of those units to be different to the cost of others of the units 🙂 )
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