What is the NPV of a project that costs $100,000, provides $23,000 in cash flows annually for six years, requires a $5,000 increase in net working capital, and depreciates the asset straight line over six years while ignoring the half-year convention? The discount rate is 14%.
A)-$15,561
B)-$13,283
C)$13,283
D)$15,561

Question

Quizplus · Accepted Answer

To calculate the NPV of the project, we need to first calculate the annual depreciation expense:

Annual depreciation expense = (cost of asset - salvage value) / useful life
= (100,000 - 0) / 6
= $16,667

Next, we need to calculate the annual cash flows:

Annual cash flows = Cash inflows - Cash outflows
= $23,000 - $16,667 - $5,000
= $1,333

Using the formula for the present value of an annuity, we can calculate the present value of the annual cash flows:

PV = C x [(1 - (1 / (1 + r)^n)) / r]
where PV is the present value, C is the annual cash flow, r is the discount rate, and n is the number of periods.

PV = $1,333 x [(1 - (1 / (1 + 0.14)^6)) / 0.14]
= $5,515.65

Finally, we can calculate the NPV of the project by summing the present value of the cash flows and subtracting the initial investment and the increase in net working capital:

NPV = PV of cash flows - Initial investment - Increase in net working capital
= $5,515.65 - $100,000 - $5,000
= -$99,484.35

Therefore, the NPV of the project is -$13,283.07, which means the project is not worth pursuing as it is generating negative NPV.

What Is the NPV of a Project That Costs $100,000