Question

Caspian Sea Drinks is considering the purchase of a new water filtration system produced by Rube Goldberg Machines. This new equipment, the RGM-7000, will allow Caspian Sea Drinks to expand production. It will cost $15.00 million fully installed and will be fully depreciated over a 15 year life, then removed for no cost. The RGM-7000 will result in additional revenues of $2.65 million per year and increased operating costs of $695,644.00 per year. Caspian Sea Drinks' marginal tax rate is 29.00%. The internal rate of return for the RGM-7000 is _____.

Answer 1

To calculate the internal rate of return (IRR) for the RGM-7000 water filtration system, we first need to analyze the cash flows produced by the investment over its useful life. Here’s a step-by-step breakdown:

1. Initial Investment: The initial cost of the RGM-7000 is $15.00 million.

2. Depreciation: The system will be fully depreciated over a 15-year life. \[ \text{Annual Depreciation} = \frac{\text{Initial Cost}}{\text{Life}} = \frac{15,000,000}{15} = 1,000,000 \text{ per year} \]

3. Additional Revenues and Operating Costs:

   • Additional Revenues: $2.65 million per year
   • Increased Operating Costs: $695,644 per year

   This gives us the net cash flows before tax: \[ \text{Net Cash Flow Before Tax} = \text{Additional Revenues} - \text{Increased Operating Costs} \] \[ \text{Net Cash Flow Before Tax} = 2,650,000 - 695,644 = 1,954,356 \text{ per year} \]

4. Tax Impact: Since the company has a marginal tax rate of 29%, we need to account for taxes: \[ \text{Tax} = \text{Net Cash Flow Before Tax} \times \text{Tax Rate} = 1,954,356 \times 0.29 = 568,762.24 \]

   The after-tax cash flow is then: \[ \text{After-Tax Cash Flow} = \text{Net Cash Flow Before Tax} - \text{Tax} + \text{Depreciation Tax Shield} \] Where the depreciation tax shield is given by: \[ \text{Depreciation Tax Shield} = \text{Annual Depreciation} \times \text{Tax Rate} = 1,000,000 \times 0.29 = 290,000 \]

   Therefore, the after-tax cash flow can be calculated as follows: \[ \text{After-Tax Cash Flow} = 1,954,356 - 568,762.24 + 290,000 = 1,675,593.76 \]

5. Cash Flows Over Time: The cash flows are as follows:

   • Year 0 (Initial Investment): -$15,000,000
   • Year 1-15: $1,675,593.76 per year

6. Calculating IRR: To find the IRR, we can use the formula for the net present value (NPV) and set it equal to zero: \[ 0 = -15,000,000 + \sum_{t=1}^{15} \frac{1,675,593.76}{(1 + r)^t} \]

   You'll typically solve this equation iteratively or using a financial calculator or software that can compute IRR.

Using a financial calculator or software to compute IRR with the cash flow structure (initial outflow of $15 million followed by fifteen years of inflow of $1,675,593.76), we arrive at the internal rate of return.

For approximate values, you can use the IRR function in Excel or any financial calculator. The IRR for this scenario is around 7.14%.

Thus, the internal rate of return for the RGM-7000 investment is approximately 7.14%.