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	$	620		$	180		850
Retest		950			500		100
Vital		4,360			2,980		50

Variable costs include the labor costs of the medical technicians at the lab. Fixed costs of $450,000 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? (Do not round your intermediate calculation.)

(c)	At what sales revenue will the company earn $192,000 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 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 $480,000 per year. What would be the effect of this change in product mix on Limitless Labs's earnings after taxes per year?

Answer 1

a) Calculation of Earning after taxes (Amount in $)

Particulars	Basic (A)	Retest (B)	Vital (C)	Total (A+B+C)
Revenue	($620*850) = 527,000	($950*100) = 95,000	($4,360*50) = 218,000	840,000
Less: Variable Cost	($180*850) = (153,000)	($500*100) =(50,000)	($2,980*50) = (149,000)	(352,000)
Contribution	374,000	45,000	69,000	488,000
Less: Fixed cost				(450,000)
Profit before taxes				38,000
Less: Income tax (@40%)				(15,200)
Profit after tax				22,800

b) Total units sold = 850+100+50 = 1,000

Sales mix percentage of the three tests

Basic = (Units sold of basic/Total units sold)*100 = (850/1,000)*100 = 85%

Retest = (100/1,000)*100 = 10%

Vital = (50/1,000)*100 = 5%

Weighted Average Revenue per unit = ($620*85%)+($950*10%)+($4,360*5%)

= $527+$95+$218 = $840

Weighted Average contribution per unit = [($620-$180)*85%]+[($950-$500)*10%]+[($4,360-$2,980)*5%]

= $374+$45+$69 = $488

Weighted Average contribution ratio = (weighted average contribution/Weighted average revenue)*100

= ($488/$840)*100 = 58.09524%

Break even revenue = Fixed cost/Weighted average contribution ratio

= $450,000/58.09524% = $774,590

c) After tax income = $192,000

Before tax income = $192,000/(1-0.40) = $320,000

Break even revenue = (Fixed cost + Required Profit)/Weighted average contribution ratio

= ($450,000+$320,000)/58.09524% = ($770,000/58.09524%)

= $1,325,410

d-1) Calculation of  Earning after taxes after change (Amount in $)

Particulars	Basic (A)	Retest (B)	Vital (C)	Total (A+B+C)
Revenue	($620*100) = 62,000	($950*400) = 380,000	($4,360*200) = 872,000	1,314,000
Less: Variable Cost	($180*100) = (18,000)	($500*400) =(200,000)	($2,980*200) = (596,000)	(814,000)
Contribution	44,000	180,000	276,000	500,000
Less: Fixed cost				(480,000)
Profit before taxes				20,000
Less: Income tax (@40%)				(8,000)
Profit after tax				12,000

Total units sold = 100+400+200 = 700

Sales mix percentage of the three tests

Basic = (Units sold of basic/Total units sold)*100 = (100/700)*100 = 14.2857%

Retest = (400/700)*100 = 57.1429%

Vital = (200/700)*100 = 28.5714%

Weighted Average Revenue per unit = ($620*14.2857%)+($950*57.1429%)+($4,360*28.5714%)

= $88.5713+$542.8575+$1,245.7130 = $1,877.1418

Weighted Average contribution per unit

= [($620-$180)*14.2857%]+[($950-$500)*57.1429%]+[($4,360-$2,980)*28.5714%]

= $62.8571+$257.1430+$394.2853 = $714.2854

Weighted Average contribution ratio = (weighted average contribution/Weighted average revenue)*100

= ($714.2854/$1,877.1418)*100 = 38.05175%

Break even revenue = Fixed cost/Weighted average contribution ratio

= $480,000/38.05175% = $1,261,440