A car component can be produced by either of two manufacturi

A car component can be produced by either of two manufacturing methods, method A or method B. For method A the fixed costs are £90000 per year and the variable costs are £15 per component. For method B the fixed costs are £99000 per year and the variable costs are £10 per component. Calculate the break-even quantity per year, for which the cost of manufacture is the same whichever method is used Give your answer as an exact value Break-even quantity

Solution

Total Cost = Fixed Costs per year + Variable costs per year

Total Cost = Fixed Costs per year + [ (Variable Cost per component) * (Number of components) ]

Let the break even quantity be X.

At Break even,

Total Cost under Method A = Total Cost under Method B

Now, Total Cost under Method A = 90000 + 15X

Total Cost under Method B = 99000 + 10X

At Break even,

90000 + 15X = 99000 + 10X

15X - 10X = 99000 - 90000

5X = 9000

X = 9000 / 5

X = 1800 units

Therefore, break even quantity per year for which cost of manufacture is same whichever method is used is 1800 units.