Question

1. In 2019, X Company sold 5,650 units of its only product. Total revenue was $1,415,890, total variable costs were $773,485, and total fixed costs were $616,000. In 2020, there are only two expected changes: variable costs will increase by $4.60 per unit, and fixed costs will decrease by $21,200. How many units must X Company sell in 2020 in order to earn $32,000?

2. In 2019, X Company's profit function was 0.40R - $93,700, where R is revenue. In 2020, the relationship between revenue and variable costs will not change, but fixed costs will increase by $16,866. Assuming a tax rate of 30%, what will revenue have to be in order for X Company to earn $43,900 after taxes in 2020?

Answer 1

1.

for 2019

Number of units sold = 5,650

Sales = $1,415,890

Total variable cost = $773,485

Total fixed cost = $616,000

Selling price per unit = Sales/Number of units sold

= 1,415,890/5,650

= $250.60

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

= 773,485/5,650

= $136.90

For 2020

Increase in variable cost = $4.60 per unit

Variable cot per unit = 136.90+4.60

= $141.50

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

= 250.60-141.50

= $109.10

Decrease in fixed cost = $21,200

Total fixed cost = 616,000-21,200

= $594,800

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

= (594,800+32,000)/109.10

= 5,745 units

2.

Tax rate = 30%

Profit after tax = $43,900

Profit before tax = Profit after tax/ (1- tax rate)

= 43,900/ (1-0.30)

= 43,900/0.7

= $62,714

Increase in fixed cost = $16,866

In the profit function, 0.40R - $93,700, $93,700 is the fixed cost.

fixed cost will become = 93,700+16,866= $110,566

Profit function = 0.40R - 110,566

62,714 = 0.40R - 110,566

R = $433,200

Hence, revenue of $433,200 is needed to earn profit of $43,900, after taxes.

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