Question

The Third Street Eatery is considering a 4 year expansion project that will require an initial fixed asset investment of $2.19 million. The fixed asset will be depreciated straight-line to zero over its 4 year tax life, after which time it will have a market value of $430,000 . The project requires an initial investment in net working capital of $245,000 , which will be fully recovered when the project is terminated. Estimated sales are $2,305,000 per year, with costs of $956,000 .The tax rate is 19.0% and the required return for the project is 20.70%. Find the project's NPV.

Answer 1

To calculate the project's NPV, we need to calculate the cash flows for each year of the project and discount them to present value. The NPV is the sum of the present values of all cash flows.

Step-by-step explanation:

To calculate the project's NPV, we need to calculate the cash flows for each year of the project and discount them to present value. The initial fixed asset investment of $2.19 million will be depreciated straight-line to zero over its 4-year tax life, so the annual depreciation expense will be $2.19 million / 4 = $547,500. The net operating cash flow for each year will be the estimated sales of $2,305,000 minus the costs of $956,000 and the depreciation expense. The tax rate is 19%, so the after-tax cash flow will be the net operating cash flow multiplied by (1 - tax rate).

Here is the calculation for each year:

1. Year 1:
   Net operating cash flow = ($2,305,000 - $956,000 - $547,500) x (1 - 0.19) = $629,105
   Year 2:
   Net operating cash flow = ($2,305,000 - $956,000 - $547,500) x (1 - 0.19) = $629,105
   Year 3:
   Net operating cash flow = ($2,305,000 - $956,000 - $547,500) x (1 - 0.19) = $629,105
   Year 4:
   Net operating cash flow = ($2,305,000 - $956,000 - $547,500) x (1 - 0.19) = $629,105

To calculate the terminal cash flow in year 4, we need to add back the salvage value of the fixed asset and recover the net working capital:

Terminal cash flow = salvage value + net working capital = $430,000 + $245,000 = $675,000

Now we can calculate the NPV using the required return of 20.70%. We discount each cash flow to present value using the formula:

NPV = cash flow / (1 + required return)^year

Finally, we sum up the present values of all cash flows:

NPV = $629,105 / (1 + 0.207)^1 + $629,105 / (1 + 0.207)^2 + $629,105 / (1 + 0.207)^3 + ($629,105 + $675,000) / (1 + 0.207)^4 - $2,190,000

Calculating this equation gives us the project's NPV.