Doctor J. is considering purchasing a new blood analysis machine to test for HIV

Question

Doctor J. is considering purchasing a new blood analysis machine to test for HIV; it will cost $10,000. He estimates that he could charge $150.00 for an office visit to have a patient's blood analyzed, while the actual cost of a blood analysis would be $10.00.
How many HIV blood analyses would he have to perform in order to break even?
What would be his profit if he were to perform 6,000 HIV blood analyses?
How many HIV blood analyses would he have to perform in order to make a profit of $35,000?

Explanation / Answer

Contribution margin earned from each blood analysis

= Charge for office visit - Actual cost of blood analysis

= $ 150 - $10

= $140

Let number of analysis to be performed to breakeven = N

Total contribution margin at breakeven point = $140.N

At breakevenpoint, Total cost = Total contribution margin

10,000 = 140.N

Or, N = 10,000/140

Or, N = 71.43

71.43 NUMBERS OF BLOOD ANALYSIS NEEDS TO BE PERFORMED IN ORDER TO BREAKEVEN

Total profit at 6000 blood analysis , $

= Total contribution margin – Purchasing cost of machine

= 6000 x 140 – 10,000

= 840,000 – 10,000

= $830,000

PROFIT AT 6000 BLOOD ANALYSIS = $830,000

Let required number of blood analysis needs to be performed to make a profit of$35,000 = N1

In such case,

Total contribution margin = $140.N1

Cost = $10,000

Profit = $35,000

Since , Profit = Total contribution margin – machine purchase cost

35,000 = 140.N1 – 10,000

Or, 140.N1 = 45,000

Or, N1 = 45,000/140

Or, N1 = 321.43

REQUIRED NUMBER OF BLOOD ANALYSIS NEEDS TO BE PERFORMED TO MAKE A PROFIT OF $35,000 = 321.43

71.43 NUMBERS OF BLOOD ANALYSIS NEEDS TO BE PERFORMED IN ORDER TO BREAKEVEN

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