Final answer:
To calculate the NPV of the investment, discount each of the $46,000 annual cash inflows at a 9% rate back to their present value, sum these values, and subtract the initial investment of $232,000.
Step-by-step explanation:
The question asks to calculate the net present value (NPV) of an investment that requires an initial outlay of $232,000 and promises annual cash inflows of $46,000 for the next 6 years with the first cash inflow occurring one year from today.
Given a discount rate of 9%, we need to discount each of the cash inflows back to their present value and then subtract the initial investment to find the NPV. The formula to calculate the present value of a future cash flow is PV = CF / (1 + r)^n, where CF is the cash flow for the year, r is the discount rate, and n is the number of periods.
Here is a step-by-step calculation:
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- Calculate the present value of each of the $46,000 cash inflows.
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- Sum the present values of all cash inflows to find the total present value of the cash inflows.
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- Subtract the initial investment of $232,000 from the total present value of cash inflows to arrive at the NPV of the investment.
For example, the present value of the first $46,000 cash inflow at a 9% discount rate is $46,000 / (1 + 0.09)^1. You would repeat this calculation for cash inflows in years 2 through 6, and then sum all the present values before subtracting the initial investment.