(make a cash flow diagram)
A project your firm is considering for implementation has these estimated costs and revenues: an investment cost of $50,000; maintenance costs that start at $5,000 at the end of year (EOY) 1 and increase by $1,000 for each of the next 4 years, and then remain constant for the following 5 years; savings of $20,000 per year (EOY 1–10); and finally a resale value of $35,000 at the EOY 10. If the project has a 10-year life and the firm’s MARR is 10% per year, what is the present worth of the project? Is it a sound investment opportunity? make a
Cannot diagram on these posts.
For Activity
To determine the present worth of the project and whether it is a sound investment opportunity, we need to create a cash flow diagram and then calculate the net present value (NPV).
First, let's create the cash flow diagram:
-50,000 (Investment) +35,000 (Resale Value)
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+5,000 | +6,000 +7,000 +8,000 +9,000 +10,000 +20,000 +20,000 +20,000 +20,000
(maintenance costs) (Annual Savings)
In this cash flow diagram, the investment cost of $50,000 is represented as a cash outflow at time zero (beginning of year 1). The maintenance costs increase by $1,000 each year for years 1-5 and then remain constant for the following 5 years. These costs are represented by the positive cash flows at the end of each year. The savings of $20,000 per year over the 10-year project life are represented by the positive cash flows at the end of each year. Finally, the resale value of $35,000 at the end of year 10 is represented as a cash inflow.
To calculate the present worth of the project, we need to discount each cash flow to its present value using the project's minimum attractive rate of return (MARR), which is given as 10% per year.
The formula to calculate the present worth (PW) is as follows:
PW = (C1 / (1 + r)^1) + (C2 / (1 + r)^2) + ... + (Cn / (1 + r)^n)
Where:
C1, C2, ..., Cn = Cash flows at each time period
r = Discount rate (MARR)
n = Number of time periods
In this case, there are 10 time periods (years) and the discount rate is 10%.
Now let's calculate the present worth of the project:
PW = (-50,000 / (1 + 0.10)^0) + (5,000 / (1 + 0.10)^1) + (6,000 / (1 + 0.10)^2) + (7,000 / (1 + 0.10)^3) + (8,000 / (1 + 0.10)^4) + (9,000 / (1 + 0.10)^5) + (10,000 / (1 + 0.10)^6) + (20,000 / (1 + 0.10)^7) + (20,000 / (1 + 0.10)^8) + (20,000 / (1 + 0.10)^9) + (20,000 / (1 + 0.10)^10) + (35,000 / (1 + 0.10)^10)
Calculating this expression will give us the present worth of the project.
Once we have the present worth, we can determine whether it is a sound investment opportunity. If the present worth is positive, it means the project is expected to generate more cash inflows than outflows, making it a sound investment. If the present worth is negative, it means the project is expected to generate more cash outflows than inflows, indicating a potential loss and making it an unsound investment.
Now you can plug in the values into the formula and calculate the present worth.