Question

Assume that Limitless Labs, Inc., offers three basic drug-testing services for professional athletes. Here are its prices and costs: Price per Unit Variable Cost per Unit Units Sold per Year Basic $ 500 $ 120 850 Retest 800 400 100 Vital 4,000 2,800 50 Variable costs include the labor costs of the medical technicians at the lab. Fixed costs of $390,000 per year include building and equipment costs and the costs of administration. A basic "unit" is a routine drug test administered. A retest is given if there is concern about the results of the first test, particularly if the test indicates that the athlete has taken drugs that are on the banned drug list. Retests are not done by the laboratory that performed the basic test. A "vital" test is the laboratory's code for a high-profile case. This might be a test of a famous athlete and/or a test that might be challenged in court. The laboratory does extra work and uses expensive expert technicians to ensure the accuracy of vital drug tests. Limitless Labs is subject to a 40 percent tax rate.

Required:

a. How much will Limitless Labs earn each year after taxes?

b. Assuming the above sales mix is the same at the break-even point, at what sales revenue does Limitless Labs break even?

c. At what sales revenue will the company earn $180,000 per year after taxes assuming the above sales mix?

d-1. Limitless Labs is considering becoming more specialized in retests and vital cases. Assume the number of retests increased to 400 per year and the number of vital tests increased to 200 per year, while the number of basic tests dropped to 100 per year?

With this change in product mix, the company would increase fixed costs to $420,000 per year. What would be the effect of this change in product mix on Limitless Labs's earnings after taxes per year?

Answer 1

Answer a:

Limitless Lab's earnings each year after taxes = $19,800

Workings are as follows:

Basic Retest Vital Total Per Unit Total (850 units) Per Unit Total (100 units) Per Unit Total (50 units $200,000 $705,000 $140,000 $282,000 $60,000 $423,000 $390,000 $33,000 $13,200 $19,800 $500 $120 $380 $425,000$800 $102,000 $400 $323,000$400 $80,000 $4,000 $40,000 $2,800 $40,000 $1,200 Sales value Variable cost Contribution Fixed cost Earnings before tax Tax at 40% Earnings after tax
Answer b:

Limitless Lab's contribution margin ratio = Total contribution / Total sales = 423000/705000 = 60%

Assuming sales mix is the same at the break-even point:

Limitless Lab's break even sales revenue = Fixed cost / Contribution ratio

= $390,000 /60%

= $650,000

Assuming sales mix is the same at the break-even point, Limitless Lab's break even sales revenue = $650,000

Answer c:

Sales revenue required for target earnings = [Fixed cost + Target earnings / (1 - Tax rate)] / Contribution ratio

Sales revenue that will the company earn $180,000 per year after taxes = ($390,000 + $180,000/ (1 - 40%)) / 60%

= $1,150,000

Sales revenue that will the company earn $180,000 per year after taxes = $1,150,000

Answer d:

Change in contribution due to change in sales mix = (100 - 850) * $380 + (400 - 100) * $400 + (200 - 50) * $1200 = $15,000

Effect of this change in product mix on Limitless Lab's earnings after taxes per year = (Change in Contribution - Change in Fixed cost) * (1 - Tax rate)

= [($15,000 - ($420,000 - $390,000)] * (1 - 40%)

= - $9,000

Limitless Lab's earnings after taxes per year reduces by $9,000

Effect of this change in product mix on Limitless Lab's earnings after taxes per year = - $9,000