To calculate the incremental cash flows produced by the RGM-7000, we will follow these steps:
- Calculate the annual depreciation.
- Determine the operating income.
- Calculate the tax impact.
- Compute the after-tax cash flow.
Step 1: Calculate the annual depreciation
The RGM-7000 costs $15 million and will be fully depreciated over 18 years:
\[ \text{Annual Depreciation} = \frac{\text{Cost}}{\text{Lifespan}} = \frac{15,000,000}{18} \approx 833,333.33 \]
Step 2: Determine operating income
We need to account for the additional revenues and the increased operating costs:
\[ \text{Revenue} = 3,230,000 \] \[ \text{Operating Costs} = 738,759 \] \[ \text{Operating Income} = \text{Revenue} - \text{Operating Costs} - \text{Depreciation} \]
Now substituting the values:
\[ \text{Operating Income} = 3,230,000 - 738,759 - 833,333.33 \approx 1,657,907.67 \]
Step 3: Calculate the tax impact
Now, we calculate the tax on the operating income:
\[ \text{Tax} = \text{Operating Income} \times \text{Tax Rate} = 1,657,907.67 \times 0.24 \approx 397,908.84 \]
Step 4: Compute after-tax cash flow
Finally, we calculate the after-tax cash flows:
\[ \text{After-Tax Operating Income} = \text{Operating Income} - \text{Tax} \]
\[ \text{After-Tax Operating Income} = 1,657,907.67 - 397,908.84 \approx 1,259,998.83 \]
To find the total incremental cash flow, we should add back the depreciation (since it is a non-cash charge):
\[ \text{Incremental Cash Flows} = \text{After-Tax Operating Income} + \text{Depreciation} \]
\[ \text{Incremental Cash Flows} \approx 1,259,998.83 + 833,333.33 \approx 2,093,332.16 \]
Conclusion
The incremental cash flows produced by the RGM-7000 is approximately $2,093,332.16 per year.
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