To calculate the NPV (Net Present Value) of the project, we need to calculate the present value of the cash flows generated by the new machine over its 8-year life.
First, let's calculate the annual cash flows:
Increase in earnings before depreciation = $46,000 - $30,000 = $16,000
Next, let's calculate the tax savings due to depreciation. Since the new machine is eligible for 100% bonus depreciation, the entire cost of $80,000 can be depreciated in the first year. The tax savings due to depreciation can be calculated as follows:
Tax savings = Depreciation * Tax rate = $80,000 * 25% = $20,000
Now, let's calculate the after-tax cash flows:
After-tax cash flows = Increase in earnings + Tax savings
After-tax cash flows = $16,000 + $20,000 = $36,000
To calculate the present value of the after-tax cash flows, we can use the formula for the present value of an annuity:
PV = CF * (1 - (1 + r)^(-n)) / r
Where:
PV = Present value
CF = Cash flow
r = Discount rate
n = Number of periods
In this case, the discount rate (r) is the firm's weighted average cost of capital (WACC) of 12%, and the number of periods (n) is 8.
Using the formula, we can calculate the present value of the after-tax cash flows:
PV = $36,000 * (1 - (1 + 0.12)^(-8)) / 0.12
PV ≈ $36,000 * (1 - 0.4046) / 0.12
PV ≈ $36,000 * 0.5954 / 0.12
PV ≈ $36,000 * 4.9617
PV ≈ $178,621.20
Finally, to calculate the NPV, we subtract the initial cost of the new machine ($80,000) from the present value of the after-tax cash flows ($178,621.20):
NPV = PV - Initial cost
NPV = $178,621.20 - $80,000
NPV ≈ $98,621.20
Therefore, the NPV of the project is approximately $98,621.20.