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.)
To calculate the Equivalent Annual Cost (EAC), we need to determine the annual cash flows for the project and then discount them back to their present value.
The annual cash flows consist of the OCF (Operating Cash Flow) and the changes in NWC (Net Working Capital).
The OCF is given as $34,000 per year.
The change in NWC is the initial NWC investment minus the NWC recovery at the end of the project. Since there is no salvage value for the fixed asset, the NWC recovery is $0. Therefore, the change in NWC is -$35,000.
The annual cash flow for each year can be calculated as:
Annual Cash Flow = OCF + Change in NWC
Annual Cash Flow = $34,000 + (-$35,000)
Annual Cash Flow = -$1,000
To calculate the Equivalent Annual Cost (EAC), we need to discount the annual cash flows back to their present value using the required return of 10%.
The present value factor for a perpetuity (infinite cash flows) can be calculated as:
Present Value Factor = 1 / (Required Return - Growth Rate)
- Since there is no growth rate in this problem, the present value factor is equal to 1 / Required Return.
Present Value Factor = 1 / 10% = 1 / 0.1 = 10
Finally, the Equivalent Annual Cost (EAC) can be calculated as:
EAC = Annual Cash Flow * Present Value Factor
EAC = -$1,000 * 10
EAC = -$10,000
Therefore, this project's equivalent annual cost (EAC) is -$10,000.
The Equivalent Annual Cost (EAC) is a measure used to compare the costs of different projects with varying durations. It represents the equal annual cash flow required to recover the initial investment and operating costs of a project over its entire life.
To calculate the EAC, we need to determine the annual cash flows for the project. Here are the steps to calculate the EAC:
1. Calculate the annual cash flow (ACF) excluding depreciation.
ACF = OCF - Depreciation
ACF = $34,000 - Depreciation
2. Calculate the annual depreciation expense.
Depreciation = Initial Fixed Asset Investment / Project Life
Depreciation = $335,000 / 5
3. Calculate the net cash flow (NCF) for each year, which includes the annual cash flow and the depreciation expense.
NCF = ACF + Depreciation
4. Calculate the present value (PV) of each year's net cash flow.
PV = NCF / (1 + Required Return)^Year
5. Sum up the present values of all years to find the net present value (NPV).
NPV = ∑PV
6. Now, calculate the equivalent annual cost (EAC) using the NPV.
EAC = NPV / (1 - (1 / (1 + Required Return)^Project Life))
Let's calculate it step by step:
Step 1: Calculate ACF
ACF = $34,000 - Depreciation
Step 2: Calculate Depreciation
Depreciation = $335,000 / 5
Step 3: Calculate NCF for each year
NCF = ACF + Depreciation
Step 4: Calculate PV for each year
PV = NCF / (1 + Required Return)^Year
Step 5: Calculate NPV
NPV = ∑PV
Step 6: Calculate EAC
EAC = NPV / (1 - (1 / (1 + Required Return)^Project Life))
Let me calculate it for you.