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 $ 660 $ 200 700 Retest 1,000 540 250 Vital 4,480 3,040 50 Variable costs include the labor costs of the medical technicians at the lab. Fixed costs of $470,000 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 30 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? (Do not round your intermediate calculation.) (c) At what sales revenue will the company earn $196,000 per year after taxes assuming the above sales mix? (Do not round your intermediate calculation.) (d-1) Limitless Labs is considering becoming more specialized in retests and vital cases. What would be the company's break-even revenues per year if the number of retests increased to 550 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 $500,000 per year. What would be the effect of this change in product mix on Limitless Labs's earnings after taxes per year? (d-2) If the laboratory's managers seek to maximize the company's after-tax earnings, would this change be a good idea? Yes No rev: 06_25_2014_QC_50760, 08_01_2014_QC_50760

Answer 1

(a):

	Basic	Retest	Vital		Total
Revenue	700*$660	250*$1000	50*$4480	=	936,000.00
less: Variable costs	700*$200	250*$540	50*$3040	=	427,000.00
Contribution margin				=	509,000.00
less: Fixed costs				=	470,000.00
Profit before tax				=	39,000.00
less: Tax @ 30%				=	11,700.00
Profit				=	27,300.00

Thus profit = $27,300

(b): Here we will compute weighted average contribution margin percentages for each product.

	Price	VC	Contribution margin = Price - VC	Weights (as per no. of tests)
Basic	660.00	200.00	460.00	0.70
Retest	1,000.00	540.00	460.00	0.25
Vital	4,480.00	3,040.00	1,440.00	0.05

Weighted average revenue = 0.70*660 + 0.25*1000 + 0.05*4480 = $936

Weighted average CM = 0.70*460 + 0.25*460 + 0.05*1440 = $509

Weighted average CM% = 509/936 = 54.38%

Thus break even revenue = fixed costs/CM%

= 470,000/54.38%

= $864,282.91

This can be rounded off to $864,283 (if required)

(c): After tax income = $196,000. Thus before tax income = 196,000/(1-tax rate) = 196,000/(1-30%) = $280,000

Now Revenue = (Fixed costs + required profit)/weighted average CM%

= (470,000+280,000)/54.38%

= $1,379,174.85

This can be rounded off to $1,379,175 if required.

(d-1):

	Basic	Retest	Vital		Total
Revenue	100*$660	550*$1000	200*$4480	=	1,512,000.00
less: variable costs	100*$200	550*$540	200*$3040	=	925,000.00
Contribution margin				=	587,000.00
less: Fixed costs				=	500,000.00
Profit before tax				=	87,000.00
less: Tax @ 30%				=	26,100.00
Profit				=	60,900.00

Thus profit = $60,900

(d-2): YES, as after tax profits increases.