Question

A 9-year project is expected to provide annual sales of $189,000 with costs of $93,500. The equipment necessary for the project will cost $320,000 and will be depreciated on a straight-line method over the life of the project. You feel that both sales and costs are accurate to +/−15 percent. The tax rate is 21 percent. What is the annual operating cash flow for the worst-case scenario?


Multiple Choice

$69,372


$31,875


$49,435


$35,472


$96,947

Answer 1

To calculate the annual operating cash flow (OCF) for the worst-case scenario, we first need to find the worst-case values for sales and costs, along with the depreciation expense. Here's a breakdown of the calculation:

### Step 1: Calculate the Worst-case Sales and Costs
Sales and costs are both subject to +/− 15% variations:

- **Actual Sales**: $189,000
- Worst-case Sales (down 15%):
\[
\text{Sales}_{\text{worst}} = 189,000 \times (1 - 0.15) = 189,000 \times 0.85 = 160,650
\]

- **Actual Costs**: $93,500
- Worst-case Costs (up 15%):
\[
\text{Costs}_{\text{worst}} = 93,500 \times (1 + 0.15) = 93,500 \times 1.15 = 107,525
\]

### Step 2: Calculate Depreciation
The equipment costs $320,000 and is depreciated straight-line over 9 years:
\[
\text{Depreciation Expense} = \frac{320,000}{9} \approx 35,555.56
\]

### Step 3: Calculate EBIT (Earnings Before Interest and Taxes)
Using the worst-case sales and costs:
\[
\text{EBIT} = \text{Sales}_{\text{worst}} - \text{Costs}_{\text{worst}} - \text{Depreciation}
\]
\[
\text{EBIT} = 160,650 - 107,525 - 35,555.56 \approx 17,569.44
\]

### Step 4: Calculate Taxes
Calculate the tax based on the EBIT:
\[
\text{Taxes} = \text{EBIT} \times 0.21 = 17,569.44 \times 0.21 \approx 3,691.58
\]

### Step 5: Calculate Net Income
\[
\text{Net Income} = \text{EBIT} - \text{Taxes}
\]
\[
\text{Net Income} = 17,569.44 - 3,691.58 \approx 13,877.86
\]

### Step 6: Calculate Operating Cash Flow (OCF)
To find the OCF, we add back the depreciation to the net income:
\[
\text{OCF} = \text{Net Income} + \text{Depreciation}
\]
\[
\text{OCF} = 13,877.86 + 35,555.56 \approx 49,433.42
\]

### Conclusion
The annual operating cash flow for the worst-case scenario is approximately **49,435 (rounding to two decimal places)**.

Thus, the answer is:
\[
\boxed{49,435}
\]