A five-year project has an initial fixed asset investment of $335,000, an initial NWC investment of $35,000, and an annual OCF of −$34,000. The fixed asset is fully depreciated over the life of the project and has no salvage value. If the required return is 10 percent, what is this project’s equivalent annual cost, or EAC? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.
-131605.07
To calculate the equivalent annual cost (EAC) of a project, you need to determine the present value (PV) of all the cash flows associated with the project and then convert it into an annual cost.
In this case, the project has a five-year duration, and the initial investment consists of a fixed asset investment of $335,000 and a net working capital (NWC) investment of $35,000. The annual operating cash flow (OCF) is -$34,000.
Step 1: Calculate the annual depreciation expense.
Since the fixed asset is fully depreciated over the life of the project and has no salvage value, the annual depreciation expense is simply the initial fixed asset investment divided by the project's duration:
Annual Depreciation = Initial Fixed Asset Investment / Project Duration
Annual Depreciation = $335,000 / 5 years
Annual Depreciation = $67,000
Step 2: Calculate the net annual cash flow (NCF) for each year.
Net Annual Cash Flow = OCF + Depreciation
Net Annual Cash Flow = -$34,000 + $67,000
Net Annual Cash Flow = $33,000
Step 3: Calculate the present value (PV) of the net annual cash flows.
To calculate the present value, you need to discount each net annual cash flow back to the present using the required return of 10%.
PV of Net Annual Cash Flow = Net Annual Cash Flow / (1 + Required Return)^Year
PV of Net Annual Cash Flow Year 1 = $33,000 / (1 + 0.10)^1 = $30,000
PV of Net Annual Cash Flow Year 2 = $33,000 / (1 + 0.10)^2 = $27,272.73
PV of Net Annual Cash Flow Year 3 = $33,000 / (1 + 0.10)^3 = $24,793.39
PV of Net Annual Cash Flow Year 4 = $33,000 / (1 + 0.10)^4 = $22,539.45
PV of Net Annual Cash Flow Year 5 = $33,000 / (1 + 0.10)^5 = $20,490.41
Step 4: Calculate the present value of the initial investment.
Since there is no salvage value and the initial NWC investment is not considered in EAC calculation, the present value of the initial investment is simply the initial fixed asset investment:
PV of Initial Investment = Initial Fixed Asset Investment
PV of Initial Investment = $335,000
Step 5: Calculate the sum of the present values.
Sum of PVs = PV of Net Annual Cash Flows + PV of Initial Investment
Sum of PVs = $30,000 + $27,272.73 + $24,793.39 + $22,539.45 + $20,490.41 + $335,000
Sum of PVs = $459,095.98
Step 6: Calculate the equivalent annual cost (EAC).
To find the EAC, you divide the sum of PVs by the present value annuity factor, which is calculated as follows:
PV Annuity Factor = (1 - (1 / (1 + Required Return)^Number of Present Value Periods)) / Required Return
PV Annuity Factor = (1 - (1 / (1 + 0.10)^5)) / 0.10
PV Annuity Factor = 3.790787
EAC = Sum of PVs / PV Annuity Factor
EAC = $459,095.98 / 3.790787
EAC ≈ $121,049.77
Therefore, the equivalent annual cost (EAC) of this project is approximately $121,049.77.
To calculate the equivalent annual cost (EAC) of the project, we need to calculate the annual cash flows and then discount them to the present value.
Step 1: Calculate the annual cash flows (OCF):
The annual cash flows (OCF) can be calculated by subtracting the annual depreciation expense from the annual operating cash flow.
Annual OCF = Annual Operating Cash Flow - Annual Depreciation Expense
Given:
Initial fixed asset investment = $335,000
Initial NWC investment = $35,000
Annual OCF = -$34,000
Since the fixed asset is fully depreciated over the life of the project with no salvage value, the annual depreciation expense will be:
Annual Depreciation Expense = Initial Fixed Asset Investment / Number of Years
Number of years = 5 (as given in the question)
Annual Depreciation Expense = $335,000 / 5 = $67,000
Now, we can calculate the annual OCF:
Annual OCF = -$34,000 - $67,000 = -$101,000
Step 2: Discount the annual cash flows to their present value:
The present value of each annual cash flow can be calculated using the required return rate:
Present Value (PV) = Cash Flow / (1 + Required Return Rate)^Year
Given:
Required return rate = 10% (0.10)
First, calculate the present value of the initial fixed asset investment and the initial NWC investment:
PV of Fixed Asset Investment = -$335,000 (as it's an outflow)
PV of NWC Investment = -$35,000 (as it's an outflow)
Next, calculate the present value of the annual OCF for each year using the required return rate:
PV of OCF = Annual OCF / (1 + Required Return Rate)^Year
PV of OCF = -$101,000 / (1 + 0.10)^1
= -$101,000 / 1.10
= -$91,818.18
Finally, calculate the EAC:
EAC = PV of Fixed Asset Investment + PV of NWC Investment + PV of OCF
EAC = -$335,000 + -$35,000 + -$91,818.18
= -$461,818.18
Therefore, the project's equivalent annual cost (EAC) is -$461,818.18.