Question

A plant is operating at its normal capacity of 50,000 units per year. The annual fixed costs are $20,000 and the variable cost is $0.12 per unit.

a. What must be the minimum unit selling price if a loss situation is to be prevented?

b. If the demand increases to 70,000 units per year, the plant can operate on an overtime basis at an additional cost of $0.03 per unit (total cost = $.15 per unit) for only those additional items. Assuming the selling price calculated in part (a), what would be the annual profit?

Answer 1

(a)

Annual demand, D = 50,000 units
Unit variable cost, v = $0.12 per unit
Annual fixed cost, F = $20,000

Let the selling price be 's' when the total annual profit is zero. In other words,

D * (s - v) - F = 0

or, 50000*(s - 0.12) - 20000 = 0

or, s - 0.12 = 0.40

or, s = 0.52

So, the selling price has to be at least equal to $0.52 per unit in order to avoid profit.

(b)

Total annual revenue = selling price * volume = 0.52*70000 = $36,400

Total variable cost to produce the first 50000 units = 50000*0.12 = $6,000

Total variable cost to product the next 20000 units = 20000*0.15 = $3,000

So, the total variable cost for all the 70000 units = 6000+3000 = $9,000

The annual fixed cost is same as above i.e. $20,000

So,

Total profit = Total revenue - Total variable cost - Total fixed cost

= 36400 - 9000 - 20000

= $7,400