Final answer:
The net present value (NPV) of the 5-year capital budgeting project, after discounting the expected cash flows at the given rates of return and subtracting the initial outlay, is $56,835.31. This positive NPV suggests the project could be profitable.
Step-by-step explanation:
To calculate the net present value (NPV) of a 5-year capital budgeting project with an initial outlay of $180,300 and expected cash flows of [40,000, 45,000, 50,000, 60,000, 68,000] over five years at required rates of return [0.025, 0.027, 0.028, 0.029, 0.031], we need to discount each expected cash flow back to its present value and sum them, then subtract the initial outlay.
- Year 1: $40,000 / (1 + 0.025)
- Year 2: $45,000 / (1 + 0.027)^2
- Year 3: $50,000 / (1 + 0.028)^3
- Year 4: $60,000 / (1 + 0.029)^4
- Year 5: $68,000 / (1 + 0.031)^5
Let's do the math for each year and then sum the present values:
- Year 1 PV = $39,024.39
- Year 2 PV = $42,616.98
- Year 3 PV = $45,212.02
- Year 4 PV = $52,125.94
- Year 5 PV = $58,155.98
The total present value of the cash flows is the sum of these amounts, which equals $237,135.31. Subtracting the initial outlay from this total gives us the NPV:
NPV = $237,135.31 - $180,300 = $56,835.31
The project's NPV is therefore $56,835.31, which suggests that the project is likely a profitable one because the NPV is positive.