Willamette Forests is considering a new software package that may improve productivity over the next 2 years. There is a sixty percent chance that the project will be a success in year 1 earning 2 million and a forty percent change that the venture will fail during the first year resulting in a 1 million loss due to worse asset management than under the current system. The original system would be reinstalled, resulting in no additional losses during the second year.

If the project is a success in the first year, there is an eighty percent chance that it will earn 3 million in the second year. There is a twenty percent chance that the software will be ineffective in year 2, despite success in year 1, in which case there would be a loss of 500,000. Assuming a nine percent required rate of return on these, and a total cost of the software system of 500,000, should Willamette install the new system?

To determine whether Willamette Forests should install the new software system, we can perform a financial analysis using the Net Present Value (NPV) method. NPV calculates the present value of cash flows, taking into account the required rate of return.

First, let's identify the cash flows associated with the project. We have the following possibilities:
- Year 1:
- 60% chance: $2 million (success)
- 40% chance: -$1 million (failure)

- Year 2 (if Year 1 was a success):
- 80% chance: $3 million (success)
- 20% chance: -$500,000 (ineffective)

Now, let's calculate the NPV. We'll start by calculating the expected cash flows for each year, discounting them at the required rate of return, and then summing them up. We'll subtract the initial cost of the software system ($500,000) from the NPV to get the final answer.

Year 1 NPV:
Expected Cash Flow = (0.6 * $2 million) + (0.4 * -$1 million)
Discounted Cash Flow = Expected Cash Flow / (1 + 0.09)^1

Year 2 NPV (if Year 1 was a success):
Expected Cash Flow = (0.8 * $3 million) + (0.2 * -$500,000)
Discounted Cash Flow = Expected Cash Flow / (1 + 0.09)^2

Final NPV = Year 1 NPV + Year 2 NPV - Initial Cost

To calculate the NPV, let's plug in the numbers into the formula:

Year 1 NPV = (0.6 * $2 million) + (0.4 * -$1 million) / (1 + 0.09)^1
Year 2 NPV = (0.8 * $3 million) + (0.2 * -$500,000) / (1 + 0.09)^2

Now, we can calculate the final NPV:

Final NPV = Year 1 NPV + Year 2 NPV - Initial Cost

If the final NPV is positive, it indicates that the project is expected to generate a positive return and should be pursued. If the final NPV is negative, it suggests that the project is expected to generate a negative return and should be avoided.

By plugging in the numbers and performing the calculations, we can find the answer to whether Willamette should install the new system.