Final answer:
To calculate the Net Present Value (NPV), each future cash flow is discounted to its current value using the cost of capital. After summing these present values and subtracting the initial investment, the NPV for the project is found to be negative, indicating that the project should not be undertaken. Option 6 none of the above is the correct answer.
Step-by-step explanation:
The question requires a calculation of the Net Present Value (NPV) for cash flows from a project, taking into account the cost of capital, which is essentially the discount rate. To determine the NPV, we discount each future cash flow back to its present value using the cost of capital and then subtract the initial investment.
Net Present Value Calculation
To calculate NPV, we use the formula:
NPV = ∑ (Cash Flow in Year t / (1 + r)^t) - Initial Investment,
where:
∑ = sum of the values
t = year of the cash flow
r = discount rate (cost of capital)
Cash Flow in Year t = cash inflows from the project in year t
Here is the calculation for each year:
Year 1: $52,000 / (1 + 0.08)^1 = $48,148.15
Year 2: $58,000 / (1 + 0.08)^2 = $49,690.80
Year 3: $64,000 / (1 + 0.08)^3 = $50,641.69
Year 4: $59,000 / (1 + 0.08)^4 = $43,682.84
Year 5: $55,000 / (1 + 0.08)^5 = $37,775.34
Adding up these present values, we get the total present value of the cash flows:
Total Present Value of Cash Flows = $48,148.15 + $49,690.80 + $50,641.69 + $43,682.84 + $37,775.34 = $229,938.82
Now, we subtract the initial investment from the total present value of cash flows to get the NPV:
NPV = $229,938.82 - $238,000 = -$8,061.18
Since the NPV is negative, the project would decrease the value of the company by $8,061.18, so it should not be undertaken.
The final answer is that the project should not be undertaken, as the NPV is negative.