Answer:
Explanation:
To determine the net present value (NPV) of Project A over a 4-year life with salvage value, you can follow these steps. The formula for NPV is:
\[NPV = \sum_{t=0}^{n} \frac{CF_t}{(1 + r)^t}\]
Where:
- \(NPV\) is the net present value.
- \(CF_t\) is the cash flow at time \(t\).
- \(r\) is the discount rate.
- \(n\) is the number of years.
In this case:
- The original investment (\(CF_0\)) for Project A is -$64,200 (negative because it's an initial outflow).
- Cash flows for the next four years (\(CF_1\) to \(CF_4\)) are $19,400 per year.
- The salvage value (\(CF_5\)) is $14,800 at the end of the fourth year.
- The discount rate (\(r\)) is 12% or 0.12.
- \(n\) is 4.
Now, calculate the NPV for Project A:
\[NPV = \frac{-64,200}{(1 + 0.12)^0} + \frac{19,400}{(1 + 0.12)^1} + \frac{19,400}{(1 + 0.12)^2} + \frac{19,400}{(1 + 0.12)^3} + \frac{19,400 + 14,800}{(1 + 0.12)^4}\]
\[NPV = -64,200 + \frac{19,400}{1.12} + \frac{19,400}{1.12^2} + \frac{19,400}{1.12^3} + \frac{34,200}{1.12^4}\]
Now, calculate each term:
\[NPV = -64,200 + 17,321.43 + 15,483.99 + 13,841.07 + 24,028.99\]
Now, add all these values to find the NPV:
\[NPV = -64,200 + 17,321.43 + 15,483.99 + 13,841.07 + 24,028.99\]
\[NPV = 6,475.48\]
So, the net present value of Project A over a 4-year life with a salvage value, assuming a minimum rate of return of 12%, is approximately $6,475.48.