Question

Supply the missing data for three service companies shown in the table below:

Note: Loss amounts should be indicated by a minus sign. Round your percentage answers to nearest whole percent.

Sales: Company A- $9 mil
Sales: Company B- $7 mil
Sales: Company C- $4.5 mil
Net operating income: Company A [blank]
NOI: Company B: 280k
NOI: Company C [blank]
Average operating assets : Company A: 3mil
Average operating assets: Company B: [blank]
Average operating assets: Company C: 1.8mil
ROI: Company A: 18%
ROI: Company B: 14%
ROI: Company C: [blank]

Percentage: Company A: 16%
Percentage: Company B: [blank]
Percentage: Company C: 15%
Dollar Amount: Company A [blank]
Dollar Amount:: Company B: 320k
Dollar amount: Company C [blank]

Residual Income: Company A: [blank]
Residual Income: Company B: [blank]
Residual Income: Company C: 90k

Answer 1

To fill out the missing data for the three service companies, we can use the formulas for Return on Investment (ROI), Residual Income (RI), and operating income. Here's the breakdown of how to derive the missing values:

1. **Net Operating Income (NOI) Calculation:**
\[
\text{ROI} = \frac{\text{Net Operating Income}}{\text{Average Operating Assets}} \times 100
\]
Rearranging this formula gives us:
\[
\text{Net Operating Income} = \text{ROI} \times \frac{\text{Average Operating Assets}}{100}
\]

For Company A:
\[
\text{Net Operating Income} = 18\% \times 3,000,000 = 0.18 \times 3,000,000 = 540,000 \text{ or } 540k
\]

For Company B:
\[
\text{Net Operating Income} = 280,000 \text{ (given)}
\]

For Company C, we can calculate NOI using the percentage and sales values:
\[
\text{ROI for Company C} = 15\%
\]
So:
\[
\text{Net Operating Income} = \text{ROI} \times \text{Average Operating Assets} = 15\% \times 1,800,000 = 0.15 \times 1,800,000 = 270,000 \text{ or } 270k
\]

2. **Average Operating Assets for Company B:**
Using the ROI formula:
\[
14\% = \frac{280,000}{\text{Average Operating Assets}}
\]
Rearranging gives:
\[
\text{Average Operating Assets} = \frac{280,000}{0.14} = 2,000,000 \text{ or } 2 million
\]

3. **ROI Calculation for Company C:**
Since we already calculated the NOI and Average Operating Assets for Company C:
\[
\text{ROI for Company C} = \frac{270,000}{1,800,000} \times 100 = 15\%
\]

4. **Dollar Amounts:**
- **Company A's Dollar Amount:** This is the profit based on the percentage given (16%):
\[
16\% = \frac{\text{Dollar Amount}}{9,000,000}
\]
This gives:
\[
\text{Dollar Amount} = 0.16 \times 9,000,000 = 1,440,000 \text{ or } 1.44 million
\]

- **Company B's Dollar Amount:** This is already given:
\[
320,000 \text{ (given)}
\]
- **Company C's Dollar Amount:** This can be calculated with the percentage:
\[
15\% = \frac{\text{Dollar Amount}}{4,500,000}
\]
Thus:
\[
\text{Dollar Amount} = 0.15 \times 4,500,000 = 675,000 \text{ or } 675k
\]

5. **Residual Income Calculation:**
\[
\text{Residual Income} = \text{Net Operating Income} - (\text{Minimum required return} \times \text{Average Operating Assets})
\]
We need to calculate the minimum required return which we can derive from the percentages and operations:

- **For Company A:** The minimum required return @ 16%:
\[
\text{Minimum required return} = 0.16 \times 3,000,000 = 480,000
\]
Residual Income:
\[
540,000 - 480,000 = 60,000
\]
- **For Company B:** The minimum required return @ 14%:
\[
\text{Minimum required return} = 0.14 \times 2,000,000 = 280,000
\]
Residual Income:
\[
280,000 - 280,000 = 0
\]
- **For Company C:** The minimum required return @ 15%:
\[
\text{Minimum required return} = 0.15 \times 1.8 million = 270,000
\]
Residual Income:
\[
270,000 - 270,000 = 0
\]

Now we can summarize the missing information:

| Data | Company A | Company B | Company C |
|-----------------------------|--------------|---------------|--------------|
| Net Operating Income | 540k | 280k | 270k |
| Average Operating Assets | 3 million | 2 million | 1.8 million |
| ROI | 18% | 14% | 15% |
| Percentage | 16% | 14% | 15% |
| Dollar Amount | 1.44 million| 320k | 675k |
| Residual Income | 60k | 0 | 0 |

This completes the missing data for the three service companies.