Question

In 2018, X Company's revenue-based profit function was 0.35R - $76,800. Only one change is expected in 2019, a 10% decrease in total fixed costs. What must revenue be in 2019 for X Company to earn $38,000?

In 2018, X Company sold 5,000 units of its only product for $35.70 each. Unit costs were as follows:

Variable manufacturing			$15.30
Fixed manufacturing			3.21
Variable selling			5.13
Fixed selling			3.43
Total			27.07

In 2019, the selling price, variable costs per unit, and total fixed costs are not expected to change. Assuming a tax rate of 31%, how many units must X Company sell in 2019 in order to earn $64,000 after taxes?

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X Company, a merchandiser, had the following income statement for 2018:

Sales	$210,418
Cost of goods sold	116,728
Gross margin	$93,690
Other operating expenses	45,123
Profit	$48,567

$97,828 of the cost of goods sold were variable, and $28,423 of the other operating expenses were variable. If cost behavior in 2019 is expected to continue as it did in 2018, what must total sales be in 2019 in order for X Company to break even?

Answer 1

1.profit = 0.35r -76800

here r is revenue and 76800 is fixed cost

decrease in fixed cost =76800-10%=69120$

profit = 0.35R -69120

38000 = 0.35R - 69120

R =69120+38000/0.35

=306057$

revenue be in 2019 for X Company to earn $38,000? = 306057$

2.64000$ is after tax profit so before tax profit required is = 64000/ (1-t)

=64000 / (1-0.31)

=92754$

contribution margin per unit = sales- variable

=35.70-15.30-5.13

=15.27$

total fixed cost = (3.21*5000units+3.43*5000units) As the fixed cost remains same at any level of sales.

=33200$

target sales = profit+fixed cost /contribution margin per unit

=92754+33200/15.27$

=125954/15.27

=8248 units must be sold to earn 64000$ after tax profit.

3.

break even = fixed cost /contribution margin ratio

contribution margin = sales-variable cost

=210,418 - (97828+28423)

=210418-126251

=84167$

contribution margin ratio =contribution margin /sales

=84167/210418

=40%

sales required= fixed costs /contribution margin ratio

fixed cost =116728+45123-97828-28423

=35600$

total sales be in 2019 in order for X Company to break even = 35600/40%

=89000$