Question

In 2019, X Company sold 5,250 units of its only product. Total revenue was $1,345,575, total variable costs were $542,325, and total fixed costs were $735,000. In 2020, there are only two expected changes: variable costs will decrease by $4.70 per unit, and fixed costs will decrease by $24,900. How many units must X Company sell in 2020 in order to earn $33,000?

Answer 1

For year 2019

Number of units sold = 5,250

Sales = $1,345,575

Total variable cost = $542,325

Total fixed cost = $735,000

Selling price per unit = Sales/Number of units sold

= 1,345,575/5,250

= $256.3

Variable cost per unit = Total variable cost/Number of units sold

= 542,325/5,250

= $103.3

For year 2020

Decrease in variable cost = $4.70 per unit

Variable cost per unit = 103.3 - 4.70

= $98.6

Contribution margin per unit = Selling price per unit - Variable cost per unit

= 256.3 - 98.6

= $157.7

Decrease in fixed cost = $24,900

Total fixed cost = 735,000 - 24,900

= $710,100

Number of units to be sold to earn target profit = (Fixed cost + Target income)/Contribution margin per unit

= (710,100 + 33,000)/157.7

= 743,100/157.7

= 4,712 units

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