4.4 Advanced Financial Evaluation: Annual Worth, SIR, Depreciation, and Interest Formulas

AEE Certified Energy Manager CEM

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1 Chapter 1: Energy and Sustainability Policies, Codes, and Standards

1.1 Federal and State Energy Policies, Decarbonization Targets, and ESG Reporting 1.2 Building Energy Codes: ASHRAE Standard 90.1, IECC, and Compliance Paths 1.3 Energy Management Systems: ISO 50001, ENERGY STAR Benchmarking, and Portfolio Manager

2 Chapter 2: Energy Rates, Tariffs, and Supply Options

2.1 Utility Rate Structures: Volumetric vs. Demand Charges, Time-of-Use (TOU), and Real-Time Pricing 2.2 Demand Charges, Ratchets, Peak Shaving, and Power Factor Penalties 2.3 Energy Procurement, Deregulated Markets, Supply Contracts, and Green Tariffs 2.4 Demand-Side Management, Load Curtailment, and Transportation Energy Efficiency

3 Chapter 3: Energy Audits and Instrumentation

3.1 Energy Audit Methodologies: ASHRAE Level I, II, and III Audit Scopes 3.2 Audit Instrumentation, Data Loggers, Metering Accuracy, and Safety (PPE) 3.3 Baseline Energy Data, Utility Bill Disaggregation, and ECM Identification 3.4 Energy Modeling, Simulation, Digital Tools, and Performance Indicators

4 Chapter 4: Energy Accounting and Economics

4.1 Energy & Power Units (kWh, kW, Therms, MMBtu, Joules) and Conversion Calculations 4.2 Financial Metrics: Simple Payback Period, Return on Investment (ROI), and LCCA 4.3 Time Value of Money: Net Present Value (NPV), Internal Rate of Return (IRR), and Escalation 4.4 Advanced Financial Evaluation: Annual Worth, SIR, Depreciation, and Interest Formulas

5 Chapter 5: Electrical Power Systems and Motors

5.1 Electrical Fundamentals: Single/Three-Phase Power, Apparent/Real/Reactive Power, and Power Factor 5.2 Electric Motors: Efficiency Classes, Loading Calculations, NEMA Premium, and Losses 5.3 Variable Frequency Drives (VFDs), Affinity Laws, and Electrical Harmonics

6 Chapter 6: Lighting Systems

6.1 Lighting Fundamentals: Photometric Quantities (Lumens, Lux, Foot-Candles, CRI, CCT) and Efficacy 6.2 Lighting Technologies & Retrofits: LED Systems, Fluorescent/HID Replacement, and LPD 6.3 Lighting Controls: Occupancy/Vacancy Sensors, Daylight Harvesting, Dimming, and Task Tuning

7 Chapter 7: HVAC Systems and Building Envelope

7.1 HVAC Fundamentals & Psychrometrics: Dry-Bulb, Wet-Bulb, Dew Point, Relative Humidity, and Enthalpy 7.2 Cooling and Heating Equipment: Chillers (COP, kW/ton, EER, SEER), Heat Pumps, and Boilers 7.3 Air and Water Distribution: AHUs, VAV vs. CAV, Pumping Systems, Fans, and Economizers 7.4 Building Envelope: Heat Transfer (U-factor, R-value, SHGC), Infiltration, and Thermal Insulation 7.5 Building Envelope Calculations: Degree-Days, Solar Heat Gain, and Passive Design 7.6 Refrigerants, Cooling Towers, and Specialized HVAC Technologies (Absorption, VRF, Chilled Beams)

8 Chapter 8: Building Automation, Controls, and Artificial Intelligence Systems

8.1 Building Automation Systems (BAS) Architecture, BACnet, Modbus, and DDC Loops 8.2 Energy Control Strategies: Temperature/Pressure Resets, Night Setback, and Deadbands 8.3 Fault Detection & Diagnostics (FDD), Energy Analytics, and AI Optimization 8.4 IoT, Cloud-Based BAS, Expert Systems, and Cyber-Security

9 Chapter 9: Energy Storage Systems

9.1 Battery Energy Storage Systems (BESS): Technologies, Capacity, Efficiency, and Safety 9.2 Thermal Energy Storage (TES): Chilled Water, Ice Storage, and Phase Change Materials 9.3 Storage Dispatch Strategies, Tariff Integration, Peak Shaving, and Microgrid Integration

10 Chapter 10: Boiler and Steam Systems

10.1 Boiler Fundamentals & Efficiency: Combustion Efficiency, Excess Air, and Stack Losses 10.2 Steam Distribution & Traps: Steam Trap Types, Failure Modes, Testing, and Insulation 10.3 Condensate Recovery, Boiler Blowdown Control, and Waste Heat Recovery

11 Chapter 11: Distributed Generation and Renewable Energy Systems

11.1 Solar Photovoltaic (PV) and Wind Energy Systems: Design, Inverters, and Capacity Factor 11.2 Combined Heat and Power (CHP) / Cogeneration: Thermal Efficiency and System Sizing 11.3 Grid Interconnection, Net Metering, Islanding, and Microgrid Resilience 11.4 Biomass, Geothermal, Hydropower, Solar Thermal, and Waste-to-Energy Systems

12 Chapter 12: Industrial Systems

12.1 Compressed Air Systems: Efficiency, Pressure Drop, Leak Management, and Receiver Storage 12.2 Industrial Process Heating, Cooling Towers, and Industrial Refrigeration 12.3 Production-Normalized Energy Metrics, Pumping System Optimization, and Process Integration

13 Chapter 13: Operations, Maintenance, and Commissioning

13.1 Preventive, Predictive, and Reliability-Centered Maintenance Strategies 13.2 Building Commissioning: Existing Building Commissioning (EBCx) & Retro-Commissioning (RCx) 13.3 Savings Persistence, Continuous Commissioning, Sensor Calibration, and Alarms 13.4 Quantifying O&M Losses: Compressed Air Leaks, Steam Traps, Boiler Scale, and Group Relamping 13.5 CMMS, Water Treatment, and Human Behavior in Energy Management

14 Chapter 14: Energy Savings Performance Contracting and Measurement & Verification

14.1 Energy Savings Performance Contracting (ESPC), ESCO Roles, and Financing Models 14.2 Measurement and Verification (M&V): IPMVP Options A, B, C, and D 14.3 Baselines, Weather Normalization, Non-Routine Adjustments, and M&V Reporting

4.4 Advanced Financial Evaluation: Annual Worth, SIR, Depreciation, and Interest Formulas

Key Takeaways Explain This Topic AI

The six core interest factors—(F/P), (P/F), (F/A), (A/F), (P/A), and (A/P)—are the algebraic foundation of every energy-finance calculation; the capital-recovery factor (A/P,i,n) converts a present cost into an equal annual series.

Annual Worth (AW), also called Equivalent Uniform Annual Cost (EUAC), restates a project's life-cycle cost as a level yearly amount, enabling comparison of alternatives with different service lives.

The Savings-to-Investment Ratio (SIR) = PV(savings) ÷ PV(incremental investment); an SIR > 1.0 is cost-effective, and federal agencies rank projects by SIR to allocate limited capital.

Depreciation (straight-line, declining-balance, sum-of-years-digits, and MACRS) is a non-cash tax deduction that lowers taxable income; MACRS accelerates deductions, improving after-tax project economics through a larger early-year tax shield.

Interest factor tables (and their formulas) let the CEM solve payback, NPV, EUAC, and SIR by hand in the open-book exam without relying on a spreadsheet.

Last updated: July 2026

Advanced Financial Evaluation: Annual Worth, SIR, Depreciation, and Interest Formulas

Simple payback (Section 4.2) and NPV/IRR (Section 4.3) answer "is this project worth it?" But when a CEM must rank competing projects with different lives, different scales, or different tax treatments, those two tools are not enough. The CEM Body of Knowledge adds Interest Formulas and Tables , Annual Worth , the Savings-to-Investment Ratio , and Depreciation Methods to complete the financial toolkit.

Interest Formulas and Factors

All time-value-of-money math reduces to six factors relating a present sum (P), a future sum (F), and a uniform annual series (A) at interest rate i over n periods. With the factor notation (X/Y, i, n) = "find X given Y":

• Factor Symbol Formula Use
• Future given Present (F/P,i,n) (1+i)^n Project a cost forward
• Present given Future (P/F,i,n) 1/(1+i)^n Discount a future sum
• Future given Annual (F/A,i,n) [(1+i)^n − 1]/i Accumulate annual savings
• Annual given Future (A/F,i,n) i/[(1+i)^n − 1] Sinking fund
• Present given Annual (P/A,i,n) [(1+i)^n − 1]/[i(1+i)^n] Capitalize an annual stream
• Annual given Present (A/P,i,n) [i(1+i)^n]/[(1+i)^n − 1] Capital recovery

The capital recovery factor (A/P,i,n) is the workhorse: it converts a first cost into the equal annual payment that recovers it with interest. The CEM exam provides interest tables; the candidate must pick the correct factor and apply it.

Annual Worth (Equivalent Uniform Annual Cost)

Annual Worth (AW) , or Equivalent Uniform Annual Cost (EUAC) when costs-only, restates a project's entire life-cycle cash flow as a single level yearly amount. Because it is expressed per year, it lets the CEM compare alternatives with different service lives on equal footing—something NPV cannot do directly without repeated cycles.

For an asset with first cost P , salvage value S , life n , and discount rate i :

EUAC = (P − S)(A/P,i,n) + S·i

The capital-recovery portion (P−S)(A/P) recovers the depreciable base; the S·i term accounts for the opportunity cost of the salvage tied up over the life. Savings-side Annual Worth (AW) is computed similarly for the annual savings stream and compared against EUAC: a project is economic when AW(savings) ≥ EUAC .

Worked Example: EUAC of a Chiller Replacement

A chiller costs $80,000, has a salvage value of $8,000 after 15 years, and the discount rate is 8%.

• (A/P, 8%, 15) = [0.08(1.08)^15]/[(1.08)^15 − 1] = 0.1168
• EUAC = (80,000 − 8,000)(0.1168) + 8,000(0.08) = 72,000 × 0.1168 + 640 = $8,410 + $640 = $9,050/yr

The chiller's owning cost is ~$9,050 per year before any energy is consumed. Comparing this EUAC against the annual energy savings of a competing high-efficiency unit tells the CEM which wins on a level-year basis.

Savings-to-Investment Ratio (SIR)

SIR = PV(operating savings) ÷ PV(incremental investment cost) . It is a dimensionless ratio, so it scales across project sizes. Rules:

SIR > 1.0 → cost-effective (savings exceed the investment).

Higher SIR = better return per dollar invested → federal agencies and ESCOs rank projects by SIR to ration limited capital.

SIR complements NPV: NPV picks the project with the largest absolute net gain; SIR picks the one that squeezes the most savings from each dollar. For a constrained budget, ranking by SIR maximizes total savings achieved.

Depreciation Methods

Depreciation is a non-cash deduction that spreads an asset's first cost over its useful life for tax purposes. It does not change cash flow directly, but the tax shield (depreciation × tax rate) lowers taxable income and improves after-tax project economics. The CEM should know four methods:

• Method Pattern Notes
• Straight-line Equal deduction each year (P − S)/n; simplest, lowest early shield
• Declining balance Fixed % of remaining book Accelerated; larger early deductions
• Sum-of-years-digits Fraction n, n−1, … of depreciable base Accelerated, moderate
• MACRS IRS statutory percentages Most accelerated; U.S. tax standard for equipment

Modified Accelerated Cost Recovery System (MACRS) is the U.S. federal depreciation system: it assigns each asset class a recovery period and a statutory percentage table that front-loads deductions. Bonus depreciation (e.g., 100%/80% first-year under the IRA trajectory) and Section 179 expensing further accelerate the shield. Because a dollar of deduction today is worth more than one in year 10, accelerated depreciation raises a project's after-tax IRR and is a real lever in the investment decision (the CEM exam treats an investment tax credit as effectively reducing first cost, not as a tax-rate cut).

How the Four Tools Fit Together

A complete financial case stacks the tools: interest factors fund the math, NPV/IRR flag viability, Annual Worth equalizes lives for comparison, SIR ranks the portfolio, and depreciation adjusts for taxes. A CEM who stops at simple payback leaves both money and rank-order accuracy on the table.