Break-Even Analysis
Using the information provided below, please assign each value with its appropriate variable.

1. How many autoimmunity tests per year will have to be performed on the array machine to break even?

Question 1: Breakeven =Fixed Cost/Price-Variable Costs

2. Given the present volume of tests, would there be an annual net contribution and, if so, how much?

Question 2: P(x) = FC + VC(x) + NC

Where:
P= price
x=quantity
FC=Fixed Costs
VC= Variable Costs
NC=Net Contribution

Break-Even Analysis

Machine price: $50,000
Cost of reagents: $2 / test
Charge to patients: $20 / test (Average)
Saving per test: $18

The array machine can process a maximum of 40 samples at a time and perform 20 tests on each sample per two hours.
Maximum possible speed of machine operation: (40 x 20) / 2 = 400 tests / hour
Days of operation: 6 per week
Maintenance schedule: 1 hour / day
Maintenance cost: $15 / hour
Assuming that the number of tests performed each working day is the highest possible as the hospital needs to cover the cost of buying the array as quickly and economically as possible. Time of machine operation per working day: 23 hours
Maximum number of tests carried out per day: 400 x 23 = 9200
Maximum revenue from one day of operation (excluding maintenance costs):
9200 x 18 = $165,600
It is clear that the machine would only need to run at full speed and capacity for one day, (assuming the patient demand is correspondingly high,) in order to break even.
If n’ is the number of tests required to break even then,
50,000 + 15 = 18n
n = 50,015 / 18 = 2778.61 ~ 2779 tests
The number of days of operation for achieving the desired break-even profits has been kept as low as possible because each day of operation incurs a cost in maintenance of $15.
Alternately, if the machine is run every working day of the year, and the required break-even revenue is spread over five years, then
Days of operation in five years: 365 x 5 x (6/7) = 1564.29 ~ 1564
Total Maintenance cost: 1564 x 15 = $23,460
Therefore,
Overall cost: 50,000 + 23,460 = $73,460
Then,
If n’ is the total number of test required to break-even,
18n = 73,460
n = 4081.11 ~ 4082
And,
Number of tests per year: 4082 / 5 = 816.4 ~ 817
Expected Volume and Net Contribution
Given the present volume of testing, which is approximately five tests per day, and assuming operation for all working days of the year,
Expected total number of tests over five years: 365 x 5 x 5 x (6/7) = 7821.43 ~ 7821 tests
Subtracting the break-even number of tests from the expected number of tests,
Profit earned: (7821 €“ 4082) x 18 = $67,302
Gross revenue generated: (7821/2) x 20 = $78,210
Total cost of reagents: 2 x 7821 = $15,642
Total maintenance cost: $23,460
Hence,
Overall cost: 50,000 + 23,460 + 15,642 = $89,102
Therefore,
Net Balance: 78,210 €“ 89,102 = €“ $10,892
So, the facility, in this scenario, is incurring a net cost of over $10,000 over the five years of operation and is failing to break even.