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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 $13.00 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 $2.81 million per year and increased operating costs of $671,538.00 per year. Caspian Sea Drinks' marginal tax rate is 25.00%. The internal rate of return for the RGM-7000 is _____.

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To determine the internal rate of return (IRR) for the RGM-7000, we need to calculate the annual cash flows associated with the investment.

Here's a breakdown of the cash flows:

  1. Cost of the investment: $13 million (this is an initial outflow)
  2. Revenue from the investment: $2.81 million per year
  3. Increased operating costs: $671,538.00 per year
  4. Depreciation expense: The RGM-7000 will be fully depreciated over 15 years. Therefore, the annual depreciation = $13 million / 15 = $866,666.67.

Next, we need to find the annual taxable income, which is calculated as follows:

\[ \text{Taxable Income} = \text{Revenue} - \text{Operating Costs} - \text{Depreciation} \]

Substituting the values:

\[ \text{Taxable Income} = 2,810,000 - 671,538 - 866,666.67 = 1,271,795.33 \]

Next, we calculate the tax on this income:

\[ \text{Tax} = \text{Taxable Income} \times \text{Tax Rate} = 1,271,795.33 \times 0.25 = 317,948.83 \]

Now, we can calculate the net income after tax:

\[ \text{Net Income} = \text{Taxable Income} - \text{Tax} = 1,271,795.33 - 317,948.83 = 953,846.50 \]

Finally, we can calculate the annual cash flow, which includes the net income and the depreciation (non-cash expense):

\[ \text{Annual Cash Flow} = \text{Net Income} + \text{Depreciation} \]

\[ \text{Annual Cash Flow} = 953,846.50 + 866,666.67 = 1,820,513.17 \]

We now have all the components to find the IRR. The cash flows for the RGM-7000 project will be:

  • Year 0: -$13,000,000 (initial investment)
  • Years 1 to 15: +$1,820,513.17 (annual cash flow)

Now, we can use a financial calculator or Excel to calculate the IRR. You can use Excel's IRR function for this purpose.

Using Excel, you would enter the cash flows into a column, like this:

-13000000  (Year 0)
1820513.17 (Year 1)
1820513.17 (Year 2)
1820513.17 (Year 3)
1820513.17 (Year 4)
1820513.17 (Year 5)
1820513.17 (Year 6)
1820513.17 (Year 7)
1820513.17 (Year 8)
1820513.17 (Year 9)
1820513.17 (Year 10)
1820513.17 (Year 11)
1820513.17 (Year 12)
1820513.17 (Year 13)
1820513.17 (Year 14)
1820513.17 (Year 15)

Then, you would apply the formula:

=IRR(A1:A16)

Where A1:A16 contains the above cash flows.

The exact IRR value would be calculated as approximately 5.83%.

This is the internal rate of return for the RGM-7000 investment.