To determine the simple payback period for the energy-saving project, we need to apply the standard formula used in energy management as per the Association of Energy Engineers (AEE) Certified Energy Manager (CEM) guidelines. The simple payback period is a widely used metric in energy efficiency projects to evaluate how long it takes for the initial investment to be recovered through net savings. Let’s break this down step-by-step using the provided data and CEM-aligned methodology.
Step 1: Understand the Simple Payback Formula
Formula: Simple Payback Period (years)=Initial Investment CostNet Annual Savings\text{Simple Payback Period (years)} = \frac{\text{Initial Investment Cost}}{\text{Net Annual Savings}}Simple Payback Period (years)=Net Annual SavingsInitial Investment Cost
Definition: The simple payback period represents the time (in years) required for the cumulative savings to equal the initial investment, without considering the time value of money (e.g., discount rates or inflation).
CEM Reference: AEE CEM training materials emphasize this formula in the "Energy Economics" section, where simple payback is a fundamental tool for assessing project feasibility.
Step 2: Identify Given Data
Initial Investment Cost: $540,000 (one-time cost of the project).
Annual Energy Savings: $160,000 per year (benefit from the project).
Annual Maintenance Costs: $25,000 per year (additional cost incurred due to the project).
Net Annual Savings: This must account for both the savings and the costs incurred annually.
Step 3: Calculate Net Annual Savings
Definition: Net annual savings is the difference between the annual energy savings and any additional annual costs (e.g., maintenance).
Verification: The problem specifies maintenance costs as an ongoing expense tied to the project, which reduces the effective savings. CEM guidelines require including such costs in payback calculations unless explicitly stated otherwise.
Step 4: Compute the Simple Payback Period
Apply the Formula: Simple Payback Period=Initial Investment CostNet Annual Savings\text{Simple Payback Period} = \frac{\text{Initial Investment Cost}}{\text{Net Annual Savings}}Simple Payback Period=Net Annual SavingsInitial Investment Cost Simple Payback Period=540,000135,000=4.0 years\text{Simple Payback Period} = \frac{540,000}{135,000} = 4.0 \, \text{years}Simple Payback Period=135,000540,000=4.0years
Result: The payback period is exactly 4.0 years, meaning it takes 4 years for the net savings to recover the initial investment.
Step 5: Validate Against Options
Options:A. 2.0 yearsB. 3.0 yearsC. 4.0 yearsD. 5.0 years
Check:
If we ignored maintenance costs (incorrectly), payback would be 540,000160,000=3.375 \frac{540,000}{160,000} = 3.375 160,000540,000=3.375 years, which rounds to 3.4—not an exact match for any option.
With maintenance costs included, 540,000135,000=4.0 \frac{540,000}{135,000} = 4.0 135,000540,000=4.0, which matches option C precisely.
Conclusion: Option C (4.0 years) is correct based on the net savings approach.
