A Five-Year Project Has An Initial Fixed Asset Investment ✓ Solved

A Five Year Project Has An Initial Fixed Asset Investment Of 355000

A five-year project has an initial fixed asset investment of $355,000, an initial net working capital (NWC) investment of $39,000, and an annual operating cash flow (OCF) of −$38,000. The fixed asset is fully depreciated over the life of the project and has no salvage value. If the required return is 11 percent, what is this project's equivalent annual cost (EAC)? Negative amounts should be indicated by a minus sign. Do not round intermediate calculations and round your final answer to 2 decimal places.

Sample Paper For Above instruction

Introduction

The concept of Equivalent Annual Cost (EAC) is a vital financial metric used to evaluate the annualized cost of a project or investment over its lifespan. It enables comparison between projects of different durations by translating the total net present value (NPV) into an equivalent annual figure. In this analysis, we calculate the EAC for a five-year project with specific initial investments, operational cash flows, and depreciation parameters.

Understanding the Project Parameters

The project involves an initial fixed asset investment of $355,000 and an initial net working capital (NWC) investment of $39,000. The fixed asset is fully depreciated over five years with no salvage value, implying straight-line depreciation. The project generates a negative annual operating cash flow of −$38,000, indicating an annual net outflow during operation. The required rate of return is 11%, which is essential in discounting future cash flows to their present values.

Step 1: Calculating Net Initial Investment

The total initial investment includes both fixed asset investment and NWC:

  • Fixed Asset Investment: $355,000
  • NWC Investment: $39,000

Total initial outlay at year zero:

Total Initial Investment = $355,000 + $39,000 = $394,000

Step 2: Adjusting for the Operating Cash Flows and Depreciation

Since the fixed asset is fully depreciated over five years without salvage value, straight-line depreciation per year is:

Depreciation per year = $355,000 / 5 = $71,000

The annual operating cash flow (OCF) already accounts for operating expenses, taxes, and depreciation, so it's used directly in NPV calculations. Since the OCF is negative (−$38,000), it represents an annual outflow, which impacts the project's cash flow analysis.

Step 3: Calculating the Net Present Value (NPV) of Cash Flows

The key cash flows to consider are:

- Initial investment (outflow at year 0): $394,000

- Operating cash flows (perpetual or over 5 years):−$38,000 annually

- NWC recovery at project end: NWC of $39,000 recovered at year 5

The NPV of operating cash flows over five years:

NPV_OCF = ∑ (OCF / (1 + r)^t) for t = 1 to 5


where OCF = -$38,000, r = 11%

Calculating the present value of an annuity:

PV of OCF = OCF × [1 - (1 + r)^-n] / r


= -$38,000 × [1 - (1 + 0.11)^-5] / 0.11


= -$38,000 × [1 - 1 / (1 + 0.11)^5] / 0.11

Calculate denominator:

(1 + 0.11)^5 ≈ 1.68506

PV:

PV of OCF = -$38,000 × [1 - 1 / 1.68506] / 0.11


= -$38,000 × [1 - 0.593] / 0.11


= -$38,000 × 0.407 / 0.11


≈ -$38,000 × 3.7027


≈ -$140,505.86

The recovered NWC at year 5 is discounted:

NPV of NWC recovery = $39,000 / (1 + 0.11)^5 ≈ $39,000 / 1.68506 ≈ $23,140.33

Total NPV:

Total NPV = Initial outlay + PV of OCF + PV of NWC recovery


= -$394,000 + (-$140,505.86) + $23,140.33


≈ -$511,365.53

Step 4: Calculating the Equivalent Annual Cost (EAC)

EAC converts the NPV into a uniform annual amount over five years, using the capital recovery factor:

EAC = NPV × [r / (1 - (1 + r)^-n)]


where:


r = 0.11,


n = 5

Calculate the capital recovery factor:

Factor = 0.11 / (1 - (1 + 0.11)^-5) = 0.11 / (1 - 1 / 1.68506) ≈ 0.11 / 0.407 ≈ 0.27

Thus:

EAC ≈ -$511,365.53 × 0.27 ≈ -$138,174.00

The negative sign indicates this is an annual cost.

Final Answer

The project's equivalent annual cost (EAC) is approximately −$138,174.00, meaning the project costs this amount annually over the five-year horizon.

Conclusion

Calculating the EAC provides a clear picture of the project's annualized cost, enabling decision-makers to compare it with alternative investments or operational plans. In this case, with a significant initial investment and negative operational cash flows, the project’s high EAC reflects substantial ongoing costs, which must be weighed against expected benefits or strategic considerations.

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