Question

Question - 4 (4-2003) An industrial product may be manufactured by two methods of production Using Method X, fixed costs are £5,500,000 per period and variable costs are £535 per unit of product. Using Method Y, fixed costs are £8,260,000 per period and variable costs are £420 per unit of product. (a) Calculate the level of output per period for which the total costs are the same for the two methods of production. Produced by Method X the product has unit costs during a period as follows: Components £275 Labour £180 Production overheads £85 Distribution expenses £120 The figures include variable costs and apportioned fixed costs. (b)Calculate the number of units produced in the period. (c) Compare the total costs of Methods X and Y at the level of output in (b) above.​

Answer 1

(a) To calculate the level of output per period for which the total costs are the same for the two methods of production, we can set the total costs of each method equal to each other and solve for output.

Code snippet
Total cost of Method X = Total cost of Method Y

(5,500,000 + 535x) = (8,260,000 + 420y)

535x = 8,260,000 - 5,500,000

535x = 2,760,000

x = 5,144
Therefore, the level of output per period for which the total costs are the same for the two methods of production is 5,144 units.

(b) The number of units produced in the period is given as 5,144 units.

(c) The total costs of Methods X and Y at the level of output in (b) above are as follows:

Code snippet
Method X:

Total cost = (5,500,000 + 535 * 5,144) = £29,078,440

Method Y:

Total cost = (8,260,000 + 420 * 5,144) = £34,055,680

As you can see, the total cost of Method X is lower than the total cost of Method Y at the level of output in (b) above. This is because Method X has lower variable costs than Method Y.