Lecture 2: Estimating Engineering Costs and Benefits

Engineering Economic Analysis

Introduction: Where Do the Numbers Come From?

Understanding engineering costs and benefits is fundamental to the engineering economic analysis.

Categories of Cash Flows

The primary categories of expense and receipts typically represented on a CFD are:

  • First Cost: The initial expense to build, buy, or install the asset (occurs at time 0).
  • Operating and Maintenance (O&M): Annual expenses like electricity, labor, and minor repairs.
  • Salvage Value: The receipt (or cost) at the project’s termination for the sale or transfer of the equipment (occurs at the end of the project life).
  • Revenues: Annual receipts from the sale of products or services.
  • Overhaul: A major capital expenditure that occurs mid-life to extend the asset’s usefulness.

Drawing Convention

When evaluating a set of feasible alternatives, various costs must be analyzed, including initial investment, construction costs, labor, materials, maintenance, and support costs. This chapter defines the fundamental concepts and models used to develop reliable estimates for these economic factors.

A cash flow diagram (CFD) visually represents the timing and magnitude of cash flows over the project life. It shows:

  • Time 0 (Start): First Cost (initial investment)
  • Years 1-N: Operating & Maintenance costs (outflows), Revenues (inflows)
  • Mid-life: Overhaul costs (major expenditures)
  • End of life: Salvage value (inflow or disposal cost)

Arrows indicate direction: downward for costs, upward for revenues.

Fundamental Engineering Cost Concepts

Engineering costs can be classified in many ways to aid in decision making.

Fixed, Variable, Marginal, and Average Costs

Cost Type Definition
Fixed Costs Costs that are constant or unchanging, regardless of the level of output (activity volume). Examples include rent, property taxes, and insurance.
Variable Costs Costs that change in proportion to the level of output or activity. Examples include material costs, direct labor, and sales commissions.

The Total Cost for producing a product or service is the sum of the total fixed cost and the total variable cost.

\[ \text{Total Cost} = \text{Total Fixed Cost} + \text{Total Variable Cost} \]

Fixed costs are only fixed over a certain range of activity; if production falls to zero or exceeds capacity limits, the fixed costs may change (e.g., some fixed costs might be avoidable if a course is canceled, or increased if a larger facility is needed).

Breakeven Analysis

The relationship between costs and revenues is often analyzed using a profit–loss breakeven chart:

  • Breakeven Point: The activity level (volume of output) at which total costs are exactly equal to the revenue or savings generated. This is the point where the business “just breaks even.”
  • Profit Region: The volume is greater than the breakeven point, and total revenue exceeds total costs.
  • Loss Region: The volume is less than the breakeven point, and total revenue is less than total costs.

📊 Excel Example: Breakeven Analysis

Scenario: A manufacturing company wants to produce a new product. They need to determine the breakeven volume.

Excel Spreadsheet Setup:

Cell Description Formula/Value
B2 Fixed Costs (Annual) $50,000
B3 Variable Cost per Unit $25
B4 Selling Price per Unit $45
B5 Contribution Margin =B4-B3 → $20
B6 Breakeven Volume =B2/B5 → 2,500 units
B7 Breakeven Revenue =B6*B4 → $112,500

Data Table for Sensitivity Analysis:

Create a table to see profit at different volumes:

Volume Fixed Cost Variable Cost Total Cost Revenue Profit
0 $50,000 $0 $50,000 $0 -$50,000
500 $50,000 $12,500 $62,500 $22,500 -$40,000
1,000 $50,000 $25,000 $75,000 $45,000 -$30,000
1,500 $50,000 $37,500 $87,500 $67,500 -$20,000
2,000 $50,000 $50,000 $100,000 $90,000 -$10,000
2,500 $50,000 $62,500 $112,500 $112,500 $0 ← Breakeven
3,000 $50,000 $75,000 $125,000 $135,000 $10,000
3,500 $50,000 $87,500 $137,500 $157,500 $20,000
4,000 $50,000 $100,000 $150,000 $180,000 $30,000

Excel Formulas to Use:

// Cell C11 (Variable Cost)
=A11*$B$3

// Cell D11 (Total Cost)
=B11+C11

// Cell E11 (Revenue)
=A11*$B$4

// Cell F11 (Profit)
=E11-D11

Create a Chart: 1. Select columns A, D, and E (Volume, Total Cost, Revenue) 2. Insert → Line Chart 3. The intersection point is your breakeven volume

What-If Analysis (Goal Seek): - Go to: Data → What-If Analysis → Goal Seek - Set Cell: F11 (Profit) - To Value: 0 - By Changing Cell: A11 (Volume) - Result: Volume = 2,500 units

Marginal and Average Costs

  • Marginal Cost: The cost associated with producing one additional unit of output.
  • Average Cost: The total cost divided by the total number of units produced.

Sunk Costs

A sunk cost is money already spent as a result of a past decision.

Principle: Sunk costs must be ignored in engineering economic analysis because current decisions cannot change the past.

For example, the original purchase price of an asset purchased last year is a sunk cost and has no influence on the asset’s current market value or future profitability.

  • Exception: Sunk costs become relevant only when calculating depreciation and income taxes. The original cost basis is needed to figure out how much is owed in taxes when an asset is sold or disposed of.

Opportunity Costs

An opportunity cost is associated with using a resource in one activity instead of another. Every time a business resource (e.g., equipment, money, or manpower) is used in a chosen activity, the firm gives up the opportunity to use that resource in other beneficial activities.

  • Definition: An opportunity cost is the benefit that is forgone by engaging a business resource in a chosen activity instead of engaging that same resource in the forgone activity.
  • True Cost: The true cost of an endeavor includes not only the out-of-pocket cash costs but also the opportunity cost (the value of the best alternative foregone).

For existing assets (e.g., inventory or machinery), the relevant value for decision making is the current market value (or salvage value), as this represents the opportunity cost of keeping the asset rather than selling it.

Recurring, Nonrecurring, and Incremental Costs

  • Recurring Costs: Expenses that are anticipated and occur at regular intervals (e.g., annual maintenance, yearly labor costs). These are modeled as cash flows in economic analysis.
  • Nonrecurring Costs: One-of-a-kind or sudden expenditures that are often difficult to anticipate, such as initial investments, emergency maintenance, or facility disposal costs.

Incremental Costs

A fundamental principle of economic analysis states that in choosing between alternatives, the focus should be only on the differences between those alternatives. These differences are the incremental costs (or incremental benefits). Costs that are the same between two choices should be disregarded.

Cash Costs Versus Book Costs

  • Cash Costs: Also known as out-of-pocket costs, these represent actual cash flows (exchange of money) between or among parties. Engineering economic analysis is primarily concerned with cash costs.
  • Book Costs: Costs that do not involve the direct exchange of money but are recorded in a firm’s accounting books, such as depreciation charges. Book costs are primarily important in after-tax analysis.

Considering All Costs: Life-Cycle Costing

Life-Cycle Costs (LCC)

The life-cycle cost concept involves designing products, goods, and services with a full and explicit recognition of all associated costs and benefits over the various phases of their life cycles, from conception to retirement.

The typical phases in a product life cycle include:

  1. Needs Assessment and Justification
  2. Conceptual or Preliminary Design Phase
  3. Detailed Design Phase
  4. Production or Construction Phase
  5. Operational Use Phase
  6. Decline and Retirement Phase (including responsible disposal)

Cost Commitment vs. Cost Spending

A critical insight of life-cycle costing is that decisions made early in the life cycle tend to “lock in” future costs.

  • Nearly 70% to 90% of all life-cycle costs are committed during the initial design phases (Phases 1-3).
  • However, during this same period, only 10% to 30% of the cumulative life-cycle costs have actually been spent.

Therefore, the most cost-effective time to consider all life-cycle effects (liability, maintenance, warranty, and disposal) and make design changes is during the needs and conceptual design phases. Later changes are significantly more costly and difficult to implement.

Internal and External Costs

Green engineering extends life-cycle costing to differentiate between internal and external costs:

  • Internal Costs: Costs incurred and paid directly by the firm (e.g., production cost, labor, materials). These are used to determine profitability.
  • External Costs: Costs that are outside the firm’s normal cost accounting system and do not directly affect the price of goods or services. These costs are often borne by the public or the environment (e.g., costs of pollution, degradation of air/water quality, or long-term waste management).

Sustainable engineering strives to internalize external costs into the economic analysis to promote environmentally and socially ethical decision making.

Cost and Benefit Estimating

Cost estimating is the process of developing the numerical values (the “numbers”) to be used in engineering economic analysis. Because these consequences occur in the future, they must be estimated, not known with certainty.

Types of Estimates

The purpose, required resources, and accuracy vary significantly across different types of estimates:

Type Purpose & Timing Typical Accuracy Range
Rough Estimates (Order-of-Magnitude) High-level planning, feasibility, initial evaluation. Generally −30% to +60%
Semidetailed Estimates Budgeting, conceptual or preliminary design stages. Generally −15% to +20%
Detailed Estimates Detailed design, contract bidding, final purchasing. Generally −3% to +5%

Increased accuracy requires added time and resources. Estimates must be detailed enough to serve their specific purpose but should not require unwarranted effort, especially for projects that may be quickly eliminated.

Difficulties in Estimation

  1. One-of-a-Kind Estimates: Projects that are entirely new (e.g., first-run products or processes) lack local or global historical cost data, making estimates difficult. This is often addressed through estimation by analogy, drawing on knowledge from “close cousins” or similar past projects.
  2. Lack of Time and Effort: This requires planning and matching the estimate’s detail level to its necessity (e.g., not developing a detailed estimate for a feasibility study).
  3. Estimator Expertise: Experience and knowledge of products and processes are crucial for realistic estimates. Firms often use mentors or historical databases to build expertise.

Estimating Models

Several mathematical models and techniques are used to formulate cost and benefit estimates:

  • Per-Unit Model: Uses a simple unit factor (e.g., cost per mile, cost per square foot) to develop an estimate, typically for rough, order-of-magnitude estimates.
  • Segmenting Model: Decomposes the project’s design specifications into major subsystems and components (using a work breakdown structure), estimating the costs for each component, and then summing them up for the overall estimate.
  • Cost Indexes: Numerical values that reflect the historical change in costs. They are used to update past costs to the present time.

\[ \frac{\text{Cost at time A}}{\text{Cost at time B}} = \frac{\text{Index value at time A}}{\text{Index value at time B}} \]

📊 Excel Example: Cost Index Calculations

Scenario: A piece of equipment cost $120,000 in 2018. Estimate the cost in 2025 using a cost index.

Excel Spreadsheet Setup:

Cell Description Value/Formula
B2 Equipment Cost in 2018 $120,000
B3 Cost Index in 2018 585.7
B4 Cost Index in 2025 687.3
B5 Estimated Cost in 2025 =B2*(B4/B3) → $140,826
B6 Percentage Increase =(B5/B2-1)*100 → 17.4%

Multiple Equipment Tracking:

Equipment 2018 Cost Index 2018 Index 2025 2025 Estimate Formula
Pump $120,000 585.7 687.3 =B8*(D8/C8) $140,826
Compressor $85,000 585.7 687.3 =B9*(D9/C9) $99,743
Heat Exchanger $45,000 585.7 687.3 =B10*(D10/C10) $52,809
Total $250,000 =SUM(E8:E10) $293,378

Inflation Adjustment Formula:

// Cell E8 (Estimated Cost)
=B8*(D8/C8)

// Alternative: Using named ranges
=Cost_2018*(Index_2025/Index_2018)

Quick Tip: Use Excel’s INDEX/MATCH to pull cost index values from a historical data table automatically.

  • Power-Sizing Model: Used to estimate the cost of industrial plants or equipment of a different size or capacity than one previously purchased, accounting for economies of scale.

📊 Excel Example: Power-Sizing Model

Formula: \(\text{Cost}_B = \text{Cost}_A \times \left(\frac{\text{Size}_B}{\text{Size}_A}\right)^X\)

Where \(X\) is the power-sizing exponent (typically 0.6 for many industrial facilities - the “six-tenths rule”).

Scenario: A 50,000-gallon storage tank cost $180,000. Estimate the cost of a 100,000-gallon tank.

Excel Spreadsheet Setup:

Cell Description Value/Formula
B2 Known Cost (Cost_A) $180,000
B3 Known Size (Size_A) 50,000 gallons
B4 Desired Size (Size_B) 100,000 gallons
B5 Power-Sizing Exponent (X) 0.6
B6 Estimated Cost (Cost_B) =B2*(B4/B3)^B5 → $273,901
B7 Size Ratio =B4/B3 → 2.0
B8 Cost Ratio =B6/B2 → 1.52

Sensitivity Analysis for Different Exponents:

Exponent (X) Estimated Cost Cost per Gallon Formula
0.4 =B\$2*(B\$4/B\$3)^A12 $232,263 =B12/B\$4
0.5 $254,558 $2.55
0.6 $273,901 $2.74 (Six-tenths rule)
0.7 $291,341 $2.91
0.8 $307,239 $3.07
1.0 $360,000 $3.60 (Linear scaling)

Multiple Equipment Comparison:

Equipment Type Base Cost Base Size New Size Exponent New Cost
Storage Tank $180,000 50,000 gal 100,000 gal 0.6 =B20*(D20/C20)^E20
Reactor Vessel $450,000 1,000 L 2,500 L 0.68 $831,447
Distillation Column $320,000 10 trays 18 trays 0.55 $479,847

Excel Formula Template:

// Cell F20 (New Cost)
=B20*(D20/C20)^E20

// With cell references
=Base_Cost*(New_Size/Base_Size)^Exponent
  • Triangulation: Seeking varying perspectives, information sources, and analytical models to develop an estimate.
  • Improvement and the Learning Curve: As the number of task repetitions increases, the time required to complete the task decreases due to learning. The learning curve rate indicates the percentage reduction in time achieved when the cumulative production volume doubles. This effect is especially important for short production runs.

📊 Excel Example: Learning Curve Analysis

Formula: \(T_N = T_1 \times N^b\) where \(b = \frac{\log(\text{Learning Rate})}{\log(2)}\)

Scenario: The first unit takes 100 hours. With an 80% learning curve, estimate time for subsequent units.

Excel Spreadsheet Setup:

Cell Description Value/Formula
B2 Time for First Unit (T₁) 100 hours
B3 Learning Curve Rate 80% (or 0.8)
B4 Learning Exponent (b) =LOG(B3)/LOG(2) → -0.3219

Production Schedule Table:

Unit (N) Time per Unit (hrs) Cumulative Time Avg Time per Unit Formula
A B C D
1 =\$B\$2*A7^\$B\$4 =B7 =C7/A7 100.0 hrs
2 80.0 180.0 90.0 (80% of 100)
4 64.0 314.2 78.5 (80% of 80)
8 51.2 534.6 66.8 (80% of 64)
16 41.0 910.8 56.9
32 32.8 1,553.4 48.5
50 27.6 2,186.2 43.7
100 21.0 3,950.2 39.5

Excel Formulas:

// Cell B4 (Learning Exponent)
=LOG(B3)/LOG(2)

// Cell B7 (Time for Unit N)
=$B$2*A7^$B$4

// Cell C7 (Cumulative Time)
=SUM($B$7:B7)

// Cell D7 (Average Time)
=C7/A7

Total Cost Calculation:

Cell Description Formula
B15 Labor Rate ($/hr) $75
B16 Total Units to Produce 50
B17 Total Labor Hours =SUMPRODUCT(A7:A56,\$B\$2*A7:A56^\$B\$4)
B18 Total Labor Cost =B17*B15 → $164,465
B19 Avg Cost per Unit =B18/B16 → $3,289

Comparison: With vs Without Learning:

Scenario Total Hours Total Cost Savings
No Learning (100 hrs/unit) 5,000 $375,000 —
80% Learning Curve 2,186 $164,465 $210,535
Savings -56.3% -56.1%

Create a Learning Curve Chart: 1. Select columns A and B (Unit Number and Time per Unit) 2. Insert → Scatter Plot with Smooth Lines 3. Add a trendline with equation displayed

Estimating Benefits

The concepts applied to cost estimating (fixed/variable, categories of estimates, mathematical models, difficulties) apply directly to estimating economic benefits.

Benefits include revenues, cost reductions (savings), and public gains (e.g., less traffic congestion, reduced flood risk). Benefits are generally prone to more uncertainty and may be overestimated (the “optimist’s bias”) compared to costs, which often occur earlier in the project life.

Cash Flow Diagrams

The economic consequences of a project are costs and benefits that occur over time. A cash flow diagram (CFD) is the necessary tool for summarizing the size, sign, and timing of individual cash flows, forming the basis for subsequent economic analysis.

A CFD is constructed using a segmented horizontal line representing time periods (usually years, but can be months or quarters).

Categories of Cash Flows

The primary categories of expense and receipts typically represented on a CFD are:

  • First Cost: The initial expense to build, buy, or install the asset (occurs at time 0).
  • Operating and Maintenance (O&M): Annual expenses like electricity, labor, and minor repairs.
  • Salvage Value: The receipt (or cost) at the project’s termination for the sale or transfer of the equipment (occurs at the end of the project life).
  • Revenues: Annual receipts from the sale of products or services.
  • Overhaul: A major capital expenditure that occurs mid-life to extend the asset’s usefulness.

Drawing Convention

  • Timing: Cash flows are typically assumed to occur at the end of the period. The end of period t is considered the same time as the beginning of period t+1. Beginning-of-period cash flows (e.g., rent, leases) are placed on the diagram at the start of that period.
  • Direction: Costs/Disbursements are typically shown as downward arrows. Revenues/Receipts/Benefits are typically shown as upward arrows. The length of the arrow usually reflects the magnitude of the flow.

📊 Excel Example: Complete Cash Flow Analysis

Scenario: A company is evaluating a new production machine with a 5-year life.

Project Data: - First Cost (Initial Investment): $150,000 - Annual Revenue: $75,000 - Annual O&M Costs: $20,000 - Mid-life Overhaul (Year 3): $30,000 - Salvage Value (Year 5): $25,000 - Discount Rate: 10%

Excel Spreadsheet Setup:

Year First Cost Revenue O&M Cost Overhaul Salvage Net Cash Flow PV Factor Present Value
A B C D E F G H I
0 -$150,000 =B5+C5-D5-E5+F5 =1/(1+\$B\$2)^A5 =G5*H5
1 $75,000 -$20,000 $55,000 0.9091 $50,000
2 $75,000 -$20,000 $55,000 0.8264 $45,455
3 $75,000 -$20,000 -$30,000 $25,000 0.7513 $18,783
4 $75,000 -$20,000 $55,000 0.6830 $37,566
5 $75,000 -$20,000 $25,000 $80,000 0.6209 $49,672
NPV = =SUM(G5:G10) $51,476
IRR = =IRR(G5:G10) 21.8%

Key Parameters:

Cell Description Formula/Value
B2 Discount Rate 10% (or 0.10)
B3 Project Life 5 years

Excel Formulas:

// Cell G5 (Net Cash Flow for Year 0)
=B5+C5-D5-E5+F5
// Result: -$150,000

// Cell G6 (Net Cash Flow for Year 1)
=B6+C6-D6-E6+F6
// Result: $55,000

// Cell H5 (PV Factor for Year 0)
=1/(1+$B$2)^A5
// Result: 1.0000

// Cell H6 (PV Factor for Year 1)
=1/(1+$B$2)^A6
// Result: 0.9091

// Cell I5 (Present Value for Year 0)
=G5*H5
// Result: -$150,000

// Cell I6 (Present Value for Year 1)
=G6*H6
// Result: $50,000

// Cell I11 (Net Present Value)
=SUM(I5:I10)
// Or use: =NPV($B$2,G6:G10)+G5
// Result: $51,476

// Cell I12 (Internal Rate of Return)
=IRR(G5:G10)
// Result: 21.8%

Alternative: Using Excel’s Built-in Financial Functions:

Cell Description Formula Result
B15 NPV (Method 1) =SUM(I5:I10) $51,476
B16 NPV (Method 2) =NPV(B2,G6:G10)+G5 $51,476
B17 IRR =IRR(G5:G10) 21.8%
B18 Payback Period Manual calculation ~3.3 years

Cumulative Cash Flow Analysis:

Year Net Cash Flow Cumulative CF Formula
0 -$150,000 -$150,000 =B22
1 $55,000 -$95,000 =C22+B23
2 $55,000 -$40,000 =C23+B24
3 $25,000 -$15,000 =C24+B25
4 $55,000 $40,000 ← Positive =C25+B26
5 $80,000 $120,000 =C26+B27

Payback Period Calculation:

// Payback occurs between Year 3 and Year 4
// Remaining to recover after Year 3: $15,000
// Cash flow in Year 4: $55,000
// Payback Period = 3 + (15,000/55,000) = 3.27 years

Sensitivity Analysis - Varying Discount Rate:

Discount Rate NPV Decision Formula
5% =NPV(A32,G\$6:G\$10)+G\$5 $81,234 Accept
10% $51,476 Accept ✓ Base Case
15% $27,945 Accept
20% $9,403 Accept
22% -$403 Reject ← IRR threshold
25% -$6,428 Reject

Create Charts:

  1. Cash Flow Timeline Chart:
    • Select columns A and G (Year and Net Cash Flow)
    • Insert → Column Chart
  2. NPV Sensitivity Chart:
    • Select discount rates and NPV values
    • Insert → Line Chart with Markers
  3. Cumulative Cash Flow:
    • Select Year and Cumulative CF
    • Insert → Line Chart
    • Shows payback period visually

Decision Criteria Summary:

Metric Value Interpretation
NPV @ 10% $51,476 Positive → ACCEPT
IRR 21.8% > 10% hurdle rate → ACCEPT
Payback Period 3.27 years < 5-year life → ACCEPT
Recommendation ACCEPT PROJECT ✓

Advanced Excel Tips:

  1. Data Validation: Create dropdown lists for scenario analysis
  2. Conditional Formatting: Highlight positive/negative cash flows
  3. Named Ranges: Use names like DiscountRate, CashFlows for clarity
  4. Goal Seek: Find the discount rate where NPV = 0 (to verify IRR)
  5. Scenario Manager: Compare optimistic/base/pessimistic cases
  6. Sparklines: Add mini-charts in cells to show trends

Summary: Excel Skills for Engineering Economics

Throughout this chapter, you’ve learned to use Excel for:

  1. ✅ Breakeven Analysis - Calculate and visualize profit/loss regions
  2. ✅ Cost Indexing - Adjust historical costs to present values
  3. ✅ Power-Sizing - Estimate equipment costs at different capacities
  4. ✅ Learning Curves - Project labor hours and costs for repetitive tasks
  5. ✅ Cash Flow Analysis - Evaluate projects using NPV, IRR, and payback

Key Excel Functions Used: - SUM(), SUMPRODUCT() - Totals and weighted sums - NPV(), IRR() - Financial analysis - LOG() - Learning curve calculations - POWER() or ^ - Exponential calculations - Cell references ($B$2) - Absolute and relative - Data tables and charts - Visualization

Practice Exercise: Create a complete Excel workbook with all five examples and customize them with your own project data!