Abstract
This paper discusses techniques for conducting break-even analyses. A break-even analysis determines the quantity, at which costs are equal to revenue, or profits are equal to zero. The break-even quantity is then used to decide on whether a particular product line should be continued or stopped, depending on whether the sales volume of that particular product is above or below the break-even point. Equations for calculating break-even points and profits or net contribution are provided. Profits are achieved when Sales levels exceed the break-even point, while losses are incurred when sales levels are below the break-even point. Methods of classifying costs involved in these break-even analysis methods are also discussed. Comparisons have been made between the break-even point under the current system and when the new machine is purchased; profits under the current system and when the new machine is purchased; and also profits under the current system and when the new machine is purchased if half of the patients have Medicare coverage.
Introduction
Wilkinson (2005) demonstrates that the break-even quantity is the quantity at which the organization neither makes profits or losses. For our large U.S health care organization, the break-even point is the number of auto-immunity tests that have to be performed by the array machine for the organization to be able to cover all costs without making any profit. It can be computed using the following formula:
- Break even point = Fixed costs / contribution margin.
Literature review
Break-even analysis can be used to determine the number of auto-immunity tests that have to be performed by the array machine to enable the organization to cover all costs without making any profit (Hansen, D., and Mowen, M., 2006, Garrison, R., Noreen, E., and Brewer, P. 2009, Wilkinson, N. 2005). Excess capacity can also be measured using Break-even analysis (Maher, M., Stickney, C., and Weil, R. 2007, Salvatore, D. 2006, Warren, C., Reeve, J., and Duchac, J. 2008). Break-even analysis can also be used to support decisions on whether to invest in particular projects or to terminate a project (Bhattacharyya, A. 2008, Upchurch, A. 1998, Baugh, H. 1915).
Methods
The break even point is the number of auto-immunity tests which are required to be performed by the array machine so as to enable the organization to cover all costs without making any profit or loss. The following formula can be used to calculate the Break even point:
- Break even point = Fixed costs / contribution margin.
From the data given in the question, if the organization purchases the array machine, the contribution margin can be computed as follows:
- Charges to patients per test $ 20
- Average variable costs
- Costs of reagents $ 2
- Average variable costs per unit $ 2
- Contribution margin $18
- Fixed costs are as follows
- Depreciation $ 10,000
- Technician time $ 4,680
- Total fixed costs $14,680
- Break even quantity = 14,680 / 18
Therefore the breakeven quantity would be 815.6 auto-immunity tests, which we can round off to 816 auto-immunity tests. We round up because it would not be practical for the organization to charge for an incomplete test, and if we round down to 815 auto-immunity tests, the organization would make a loss.
Proof of breakeven quantity:
- Profit, = 20 Q – ($14,680 + 2 Q)
- Profit = $ 20 * 816 – ($14,680 + $ 2 * 816)
- Profit = $ 16,312 – ($14,680 + $ 1,632)
- Profit = $ 16,312 – $ 16,312
- Profit = $ 0
From the computation of breakeven quantity above, total revenue from performing tests at the break even quantity is $ 16,312, given by the Charges to patients per test, 20, multiplied by the breakeven quantity, 816 auto-immunity tests. Therefore when the organization performs 816 auto-immunity tests using the array machine, it does not make any profit or loss. When the organization performs less than 816 auto-immunity tests using the array machine, it would make a loss because the fixed costs would still be incurred. However when the organization performs more than 816 auto-immunity tests using the array machine, it would make a profit. This breakeven point is needed in order to decide on whether or not to purchase the array machine. The organization should only purchase the array machine if it can perform more than 816 auto-immunity tests.
Under the current system, the organization’s break even point can be computed as follows:
- Charges to patients per test $ 20
- Average variable costs
- Costs of reagents $10
- Average variable costs per unit $ 10
- Contribution margin $ 10
- Fixed costs are as zero
- Break even quantity = 0 / 10 = 0
Therefore the breakeven quantity would be zero auto-immunity tests, which means that the organization can continue in operation even without the auto-immunity tests. This is because there are no fixed costs.
- Proof of breakeven quantity:
- Profit, = 20 Q – ($ 0 + 10 Q)
- Profit = $ 20 * 0 – ($0 + $ 2 * 0)
- Profit = $ 0 – ($0 + $ 0)
- Profit = $ 0 – $ 0
- Profit = $ 0
The volume of auto-immunity tests that are currently performed are 5 per day, giving 30 per week from Monday to Saturday, and 1,560 per year of 52 weeks. Given this number of auto-immunity tests, the profits that would be realized by the organization at the current level of activity would be as follows:
- Profit, = 20 Q – ($14,680 + 2 Q)
- Profit = $ 20 * 1,560 – ($14,680 + $ 2 * 1,560)
- Profit = $ 31,200 – ($14,680 + $ 3,120)
- Profit = $ 31,200 – $ 17,800
- Profit = $ 13,400
Therefore given the volume of tests that are performed currently, the organization would realize an annual net contribution of $ 13,400.
Currently the profits that are realized by the organization at the current level of activity can be computed as follows:
- Profit, = 20 Q – ($ 0 + 10 Q)
- Profit = $ 20 * 1,560 – ($ 0 + $ 10 * 1,560)
- Profit = $ 31,200 – ($ 0 + $ 15,600)
- Profit = $ 31,200 – $ 15,600
- Profit = $ 15,600
From the above calculation, we can see that the organization would make less profit if it purchases the array machine, as compared to the profit it is making presently. This is evidenced by the fact that if the array machine is purchased and the number of auto-immunity tests remains at the current level that is five tests per day, the profit realized by the organization would be $ 13,400 per year. On the other hand, if the current system is continued without purchasing the array machine, then the profit realized by the organization would be $ 15,600 per year.
Half of the patients having Medicare coverage (DRG reimbursement includes all tests) would mean that half of the current 1,560 auto-immunity tests would still pay $ 20 per test, while the other half that have Medicare coverage would pay $ 2 per test. The net contribution in such a case would be as follows:
- Profit, = 20 Q – ($14,680 + 2 Q)
- Profit = $ 20 * 1,560 / 2 + $ 2 * 1,560 / 2 – ($ 14,680 + $ 2 * 1,560)
- Profit = $ 15,600 + $ 1,560 – ($14,680 + $ 3,120)
- Profit = $ 17,160 – $ 17,800
- Loss = $ 640
The above calculation shows that if the array machine is purchased, the organization would make a loss of $ 640 if the number of tests performed remains the same as current and half of the patients have Medicare coverage.
In a case where half of the patients have Medicare coverage, the break even point would be as follows:
- 0 = $ 20 * Q / 2 + $ 2 * Q / 2 – ($ 14,680 + $ 2 * Q)
- 0 = $ 20 * Q / 2 + $ 2 * Q / 2 – $ 14,680 – $ 2 * Q
- $ 14,680 = 20 * Q / 2 + 2 * Q / 2 – 2 * Q
- $ 14,680 = 10 Q + $ Q – $ 2 Q
- $ 14,680 = 9 Q
- Q = 14,680 / 9
- Q = 1631.1
Therefore the breakeven quantity would be 1631.1 auto-immunity tests, which we can round off to 1632 auto-immunity tests. We round up because it would not be practical for the organization to charge for an incomplete test, and if we round down to 1631 auto-immunity tests, the organization would make a loss.
Proof of breakeven quantity:
- Profit, = 20 Q – ($14,680 + 2 Q)
- Profit = $ 20 * 1,632 / 2 + $ 2 * 1,632 / 2 – ($14,680 + $ 2 * 1,632)
- Profit = $ 16,320 + $ 1,632 – ($14,680 + $ 3,264)
- Profit = $ 17,952 – $ 17,944
- Profit = $ 8
The profit of $ 8 comes as a result of the rounding off from 1631.111 to 1632.
If the machine is not purchased, and half of the patients have Medicare coverage, the profits made by the organization would be as follows:
- Profit, = 20 Q – ($ 0 + 10 Q)
- Profit = $ 20 * 1,560 / 2 + $ 10 * 1,560 / 2 – ($ 0 + $ 10 * 1,560)
- Profit = $ 15,600 + $ 7,800 – ($ 0 + $ 15,600)
- Profit = $ 23,400 – $ 15,600
- Loss = $ 7,800
From the above calculation, we can see that if the array machine is not purchased, the organization would still make a profit of $ 7,800 if the number of tests performed remains the same as current and half of the patients have Medicare coverage.
Therefore in a scenario where the number of tests performed remains the same as current and half of the patients have Medicare coverage, the organization would not break even and the array machine should not be purchased. The decision would however change if the apolipoprotein cardiac profiles that the array machine can perform in addition to the auto-immunity tests are also chargeable to patients. This is because the machine would have been purchased anyway, and the income from the apolipoprotein cardiac profiles would just be additional revenue.
The fact that the clinical chemistry department’s current equipment only gives a positive or negative indicator while the array machine can provide a quantitative measure as well as the positive or negative indicator should not be considered if there is no charge to patient for the quantitative measure, because the organization has been comfortable with the results given, so it is not necessary to purchase the array machine just to get the quantitative measure.
Results
If the array machine is purchased, the breakeven quantity would be 816 auto-immunity tests, meaning that when the organization performs 816 auto-immunity tests using the array machine, it does not make any profit or loss. If the machine is not purchased, the breakeven quantity would is zero auto-immunity tests, meaning that any auto-immunity test performed translates into profits for the organization.
At the current level of auto-immunity tests performed by the organization, if the array machine is purchased, the organization would make a profit of $ 13,400 per year. This is lower than the $ 15,600 level of profits that the organization currently makes, without purchasing the array machine.
At the current level of auto-immunity tests performed by the organization, if half of the patients have Medicare coverage, the organization would not break even. The organization would make a loss of $ 640. This means that the organization would make a loss if it purchases the array machine. The break even point in such a scenario would be 1631 auto-immunity tests. If the array machine is not purchased, the organization would still make a profit of $ 7,800 if the number of tests performed remains the same as current and half of the patients have Medicare coverage.
Conclusion
The array machine should only be purchased if the number of auto-immunity tests would increase significantly as a result of the purchase. If the number of auto-immunity tests does not increase significantly, then the organization would be better off with the current system without the array machine. This is because under the current system, any number of tests performed would result in profits for the organization since the break even point is zero. If the number of tests performed remains the same as current and half of the patients have Medicare coverage, the organization would still make profits if the array machine is not purchased, but would incur losses under the same scenario if the array machine is purchased.
Reference
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