Conduct Break-Even Analysis in the following two scenarios:
R Squared is a mobile diagnostic imaging company that performs MRI scans of patients at hospitals and clinics that cannot afford their own scanners. General Hospital has contacted R Squared regarding a contract for services. Accountants at R Squared have calculated the variable cost per scan at $1,200. The fixed cost per month is $90,000 (Cost of MRI lease payments and service). The accepted price charged in the community for an MRI scan is $2,100.
R Squared must charge General Hospital $200 less than the community price in order to get the contract.
1. Approximately how many patients must R Squared scan at General Hospital to break even for a given month?
2. Approximately how many patients will General Hospital have to guarantee for R Squared to make a monthly profit of $10,000?
3. Assuming that General Hospital can guarantee 125 patients per month, will R squared accept the contract?
4. If not, what can General Hospital or R Squared do to reach an agreement?
Take a shot. Questions 1 and 2 are simple algebra.
To conduct a break-even analysis in these scenarios, we need to find the number of patients needed for R Squared to cover its costs (break-even point) and the number of patients needed for R Squared to make a monthly profit.
1. To find the break-even point for a given month:
The formula for break-even point is: Break-even point = Fixed costs / (Selling price per unit - Variable cost per unit)
In this case, the fixed cost per month is $90,000, the variable cost per scan is $1,200, and the price charged to General Hospital is $2,100 - $200 = $1,900.
Using the formula, the break-even point can be calculated as:
Break-even point = $90,000 / ($1,900 - $1,200)
Break-even point = $90,000 / $700
Break-even point ≈ 128.57
Therefore, R Squared needs to scan approximately 129 patients at General Hospital to break even for a given month.
2. To find the number of patients needed for R Squared to make a monthly profit of $10,000:
The formula to calculate the profit is: Profit = (Selling price per unit - Variable cost per unit) * Number of units - Fixed costs
In this case, the profit desired is $10,000, the variable cost per scan is $1,200, and the price charged to General Hospital is $1,900.
Using the formula, the number of patients needed for profit can be calculated as:
$10,000 = ($1,900 - $1,200) * Number of patients - $90,000
Simplifying the equation:
$10,000 = $700 * Number of patients - $90,000
$700 * Number of patients = $100,000
Number of patients ≈ 142.86
Therefore, General Hospital will need to guarantee approximately 143 patients for R Squared to make a monthly profit of $10,000.
3. Assuming General Hospital can guarantee 125 patients per month:
In this case, since the guaranteed number of patients is less than the break-even point of 129 patients, R Squared will not be able to cover its costs. Therefore, R Squared will not accept the contract.
4. To reach an agreement:
General Hospital could increase the number of guaranteed patients to at least 129 or more. Alternatively, R Squared could negotiate a higher price per scan with General Hospital. These options would allow R Squared to cover its costs and make a profit, making the contract acceptable.