Answer:
To determine if the project is economically justified using present worth (PW) analysis and a minimum acceptable rate of return (MARR) of 10%, we need to calculate the present worth of the cash flows associated with the project.
The initial cost of the project is $200,000. The annual maintenance cost is $5,000, and we need to calculate the present worth of this cost for the five-year life of the project. Using a 10% discount rate, we can calculate the present worth as follows:
PW maintenance = $5,000 * [(1 - 1/(1 + 0.1)^5)/0.1] = $20,890
The annual revenue for the project is $40,000 in year 1, increasing by $10,000 each year through year 5. We need to calculate the present worth of these cash flows using a 10% discount rate.
PW revenue = [$40,000 * (1/(1 + 0.1)^1)] + [$50,000 * (1/(1 + 0.1)^2)] + [$60,000 * (1/(1 + 0.1)^3)] + [$70,000 * (1/(1 + 0.1)^4)] + [$80,000 * (1/(1 + 0.1)^5)] PW revenue = $227,025
The total present worth of the cash flows is the present worth of the revenue minus the present worth of the maintenance cost minus the initial cost of the project.
PW total = PW revenue - PW maintenance - initial cost PW total = $227,025 - $20,890 - $200,000 PW total = $6,135
Since the PW total is positive, the project is economically justified using PW analysis and a MARR of 10% per year. Therefore, the project is profitable and is expected to generate a positive return on investment.
Step-by-step explanation: