# CT Scan Financial Analysis – Step-by-Step ## Data (Restated) ### Fixed Costs (Annual Total) - Supervisor Wages and Benefits: $14,275 - Radiology Equipment Service Contract: $88,102 - Office Equipment Service Contract: $2,599 - Other Repair and Maintenance: $2,150 - CT Lease Costs: $180,000 - Janitorial Services: $12,500 - Building Maintenance: $1,000 - Fixed Building Costs: $15,000 - Insurance: $10,421 - Marketing Expense: $1,000 - Miscellaneous Expenses: $9,300 - **Total Fixed Costs:** **$336,347** ### Per Scan (Unit) Data - Revenue per scan: **$390.13** - Variable Costs per scan: - Labor: $50.00 - Facility: $2.00 - Supplies: $40.00 - Other: $10.00 - **Total Variable Costs per scan:** **$102.00** --- ## 1. Contribution Margin (CM) in Dollars **Formula:** \[ \text{Contribution Margin (CM)} = \text{Revenue per scan} - \text{Variable Costs per scan} \] \[ \text{CM} = \$390.13 - \$102.00 = \boxed{\$288.13} \] --- ## 2. Contribution Margin as a Percent **Formula:** \[ \text{CM\%} = \frac{\text{CM}}{\text{Revenue per scan}} \times 100 \] \[ \text{CM\%} = \frac{288.13}{390.13} \times 100 = 73.9\% \] **Rounded to one decimal place:** \[ \boxed{73.9\%} \] --- ## 3. P&L Statement in Increments of 100 Scans (–200) | Volume | Total Revenue | Total Variable Costs | Total Fixed Costs | Total Costs | Profit (Loss) | |--------|--------------|---------------------|------------------|-------------|---------------| | | $ | $ | $336,347 | $336,347 | -$336,347 | | 100 | $39,013 | $10,200 | $336,347 | $346,547 | -$307,534 | | 200 | $78,026 | $20,400 | $336,347 | $356,747 | -$278,721 | | 300 | $117,039 | $30,600 | $336,347 | $366,947 | -$249,908 | | 400 | $156,052 | $40,800 | $336,347 | $377,147 | -$221,095 | | 500 | $195,065 | $51,000 | $336,347 | $387,347 | -$192,282 | | 600 | $234,078 | $61,200 | $336,347 | $397,547 | -$163,469 | | 700 | $273,091 | $71,400 | $336,347 | $407,747 | -$134,656 | | 800 | $312,104 | $81,600 | $336,347 | $417,947 | -$105,843 | | 900 | $351,117 | $91,800 | $336,347 | $428,147 | -$77,030 | | 100 | $390,130 | $102,000 | $336,347 | $438,347 | -$48,217 | | 110 | $429,143 | $112,200 | $336,347 | $448,547 | -$19,404 | | 120 | $468,156 | $122,400 | $336,347 | $458,747 | $10,591 | | 130 | $507,169 | $132,600 | $336,347 | $468,947 | $38,222 | | 140 | $546,182 | $142,800 | $336,347 | $479,147 | $67,035 | | 150 | $585,195 | $153,000 | $336,347 | $489,347 | $95,848 | | 160 | $624,208 | $163,200 | $336,347 | $499,547 | $124,661 | | 170 | $663,221 | $173,400 | $336,347 | $509,747 | $153,474 | | 180 | $702,234 | $183,600 | $336,347 | $519,947 | $182,287 | | 190 | $741,247 | $193,800 | $336,347 | $530,147 | $211,100 | | 200 | $780,260 | $204,000 | $336,347 | $540,347 | $239,913 | --- ## 4. Total Revenues at 500 Scans \[ \text{Total Revenue} = 500 \times \$390.13 = \$195,065 \] --- ## 5. Total Fixed Costs at 500 Scans Fixed costs do **not** depend on volume: \[ \boxed{\$336,347} \] --- ## 6. Total Variable Costs at 1,000 Scans \[ \text{Total Variable Costs} = 1,000 \times \$102.00 = \$102,000 \] --- ## 7. Total Costs at 1,500 Scans \[ \text{Total Variable Costs} = 1,500 \times \$102 = \$153,000 \] \[ \text{Total Costs} = \$336,347 + \$153,000 = \$489,347 \] --- ## 8. Expected Profit or (Loss) at 1,000 Scans From table: - Profit = Total Revenue – Total Costs = $390,130 – $438,347 = **-$48,217** --- ## 9. Expected Profit or (Loss) at 1,500 Scans From table: - Profit = $585,195 – $489,347 = **$95,848** --- ## 10. Break-Even Point - Profit is negative at 1,100 scans (–$19,404) - Profit is positive at 1,200 scans ($10,591) **Break-even is between 1,100 and 1,200 scans** **Answer:** \[ \boxed{\text{b) Between 1,100 and 1,200 scans}} \] --- # **Summary Table** | Question | Answer | |--------------------------------------------------------------------------------|-------------------------| | 1. Contribution to Margin (dollars) | $288.13 | | 2. Contribution to Margin (%) | 73.9% | | 3. P&L in increments of 100 (see above) | See table | | 4. Total revenues at 500 scans | $195,065 | | 5. Total fixed costs at 500 scans | $336,347 | | 6. Total variable costs at 1,000 scans | $102,000 | | 7. Total costs at 1,500 scans | $489,347 | | 8. Expected profit (loss) at 1,000 scans | –$48,217 | | 9. Expected profit (loss) at 1,500 scans | $95,848 | | 10. Break-even point | **b) 1,100–1,200 scans**| --- ## Visual: Break-Even Chart  --- ## Key Takeaways - **Contribution margin per scan:** $288.13 (73.9%) - **Break-even volume:** Between 1,100 and 1,200 scans per period (year) - **At 1,500 scans:** Profit is $95,848 - **At 1,000 scans:** Loss is $48,217 - **Fixed costs remain constant regardless of scan volume** This structured approach helps you analyze the impact of volume changes on profit and identify the scan volume needed to break even.

## Contribution Margin as a Percent (Step-by-Step) ### Formula To calculate the Contribution Margin as a percent, use the following formula: \[ \text{CM\%} = \frac{\text{Contribution Margin}}{\text{Revenue per scan}} \times 100 \] ### Step 1: Calculate Contribution Margin From the previous calculation, we know: - Contribution Margin (CM) = $288.13 - Revenue per scan = $390.13 ### Step 2: Substitute Values into the Formula Substituting the values into the formula: \[ \text{CM\%} = \frac{288.13}{390.13} \times 100 \] ### Step 3: Perform the Calculation Calculating the above expression: \[ \text{CM\%} \approx 73.9\% \] ### Final Result **Contribution Margin as a Percent:** \[ \boxed{73.9\%} \]

## Contribution Margin as a Percent – Summary Steps ### Step 1: Calculate Contribution Margin The Contribution Margin (CM) is determined by subtracting total variable costs from revenue per scan. In this case, CM is calculated as $288.13. ### Step 2: Substitute Values into the Formula We use the formula \(\text{CM\%} = \frac{\text{CM}}{\text{Revenue per scan}} \times 100\) to find the percentage. The revenue per scan provided is $390.13. ### Step 3: Perform the Calculation By substituting the values into the formula, we compute \(\text{CM\%} \approx 73.9\%\). This indicates that approximately 73.9% of the revenue contributes to covering fixed costs and profit. ### Final Result The Contribution Margin as a Percent is reported as 73.9%. This figure highlights the efficiency of revenue generation relative to variable costs.

# Contribution Margin Analysis – 10 Steps Summary ### Step 1: Data Collection Collect all relevant financial data such as fixed costs, variable costs, and revenue per scan. This foundational information is essential for accurate calculations. ### Step 2: Calculate Fixed Costs Sum all fixed costs associated with operating the imaging facility. In this case, total fixed costs amount to $336,347. ### Step 3: Determine Revenue per Scan Identify the revenue generated from each CT scan, which is $390.13. This figure provides a basis for further financial analysis. ### Step 4: Calculate Variable Costs per Scan List all variable costs incurred for each scan, totaling $102.00. These costs fluctuate based on the volume of scans performed. ### Step 5: Calculate Contribution Margin (CM) Use the formula \( \text{CM} = \text{Revenue} - \text{Variable Costs} \) to determine the contribution margin per scan. The resulting CM is $288.13. ### Step 6: Calculate Contribution Margin as a Percent Apply the formula \( \text{CM\%} = \frac{\text{CM}}{\text{Revenue}} \times 100 \) to find the contribution margin percentage. The calculated percentage is 73.9%. ### Step 7: Project Total Revenues Estimate total revenue for a specific volume of scans, e.g., 500 scans. The expected revenue at this volume is $195,065. ### Step 8: Assess Total Fixed Costs Recognize that total fixed costs remain constant regardless of the volume of scans. Thus, fixed costs at any volume, including 500 scans, are still $336,347. ### Step 9: Calculate Total Variable Costs Determine the total variable costs for a specified volume, such as 1,000 scans. The total variable costs at this volume are $102,000. ### Step 10: Analyze Expected Profit or Loss Evaluate the profit or loss by comparing total revenue against total costs for given volumes. For 1,000 scans, the loss is $48,217, while at 1,500 scans, the profit is $95,848. --- This structured summary encapsulates the key steps and findings in analyzing the financial impact of CT scans, highlighting profitability and operational efficiency.