Final answer:
To evaluate Project X using a 7% discount rate, the NPV, ROI, and payback year are calculated. The payback diagram visualizes when the project's cumulative cash flow becomes positive. The recommendation to invest relies on a positive NPV and an acceptable payback period, taking other factors into account.
Step-by-step explanation:
When evaluating Project X, we must calculate the Net Present Value (NPV), Return on Investment (ROI), and determine the payback year. The discount rate is given as 7%, which we will use to discount future cash flows. To calculate the NPV, we apply the formula:
NPV = ∑ (Benefits - Costs) / (1 + r)^t
where r is the discount rate and t is the time period.
For ROI, we use the formula:
ROI = (Total Benefits - Total Costs) / Total Costs
To determine the payback year, we calculate the cumulative net cash flow for each year until it becomes positive.
Yearly costs and benefits are as follows:
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- Year 1: Costs = $100,000; Benefits = $0
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- Year 2-5: Costs = $30,000 each; Benefits = $75,000 each
Performing the calculations, we find:
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- NPV: $(100,000 / 1.07^1) + (∑ from t=2 to t=5 ($75,000 - $30,000) / 1.07^t)
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- ROI: ($75,000 * 4 - $100,000 - $30,000 * 4) / $100,000
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- Payback Year: We track the cumulative cash flow until it becomes positive
The payback diagram is a visual representation of the payback year and would include a plot of cumulative cash flow over time, showing the point where it crosses from negative to positive.
As for recommending this project, whether to invest would be based on the results of the NPV (positive NPV indicates a potentially good investment) and whether the payback period is acceptable given the investor's tolerance for recouping their initial outlay. Care should be taken to consider any additional factors not presented here, such as risk, competition, and market conditions.