Question

a project requires an initial outlay of -$810,000. expected cash flows in each of the next three years are $333,000; $178,000; and $168,000. the firm must also incur a $99,000 cash outflow in year 4 to clean up project waste. if the cost of capital is 12%, what is the project's npv? round your answer to the nearest penny. be sure you enter a negative sign (-) if your answer is a negative number.

Answer 1

The project's Net Present Value (NPV) at a cost of capital of 12% is calculated by discounting the cash inflows and outflows to their present values. The calculated NPV is -$317,136.80, indicating that the project would not be a profitable investment.

The question involves calculating the Net Present Value (NPV) of a project with initial and future cash flows discounted at the firm's cost of capital.

The NPV measures the profitability of a project and informs whether it should be undertaken.

To calculate it, we need to discount the future cash inflows and outflows to their present values using the cost of capital, which is given as 12%.

The formula for calculating the present value of a future cash flow is
`CF/(1+r)^t`, where CF is the cash flow, r is the rate, and t is the time period.

Here is the step-by-step calculation:

Initial outlay (already in present terms): -$810,000

Year 1 cash flow: $333,000 /
`(1 + 0.12)^1` = $297,321.43

Year 2 cash flow: $178,000 /
`(1 + 0.12)^2` = $142,077.29

Year 3 cash flow: $168,000 /
`(1 + 0.12)^3` = $119,563.96

Year 4 cash outflow for clean-up:
`-$99,000 / (1 + 0.12)^4 = -$66,099.48`

Now, we add up these present values to find the NPV:

NPV = -$810,000 + $297,321.43 + $142,077.29 + $119,563.96 - $66,099.48

NPV = -$317,136.80 (Rounded to the nearest penny)

The project's NPV is negative, which suggests that it is not a profitable investment given the cost of capital at 12%.