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Engineering Economics

Engineering Costs and Cost Estimating

William Loendorf, P.E.

Engineering Costs

• Evaluating a set of feasible alternatives requires that many costs be analyzed.

• Examples include costs for: initial investment, new construction, facility modification, general labor, parts and materials, inspection and quality, training, material handling, fixtures and tooling, data management, technical support, as well as general support costs (overhead).

Engineering Costs

Classifications of costs– Fixed - constant, unchanging

• Rent is constant (single, married, children)• Typically includes building leases, insurance,

salaries, heating, and lighting costs.

– Variable - depend on activity level• Food depends on the number of occupants• Typically vary with the level of production.

– Marginal - variable cost for the next unit• Depends on the next unit (adult, child, baby)

– Average - total cost/number of units• Rent+ food+…+n/number of units

Engineering Costs• For example, in a production environment a

fixed cost, such as costs for factory floor space and equipment, remains the same even though the production quantity, number of employees, or level of work-in-process are varying.

• Labor costs are classified as a variable cost because they depend on the number of employees in the factory.

• Thus fixed costs are level or constant regardless of output or activity, and variable costs are changing and related to the level of output or activity.

Fixed, Variable and Total Costs

Example 1

• An entrepreneur named DK was considering the money making potential of chartering a bus to take people from his hometown to an event in a larger city.

• DK planned to provide transportation, tickets to the event, and refreshments on the bus for those who signed up.

• He gathered data and categorized these expenses as either fixed or variable:

Fixed, Variable and Total CostsExample 1

Bus Rental 80.00$ Event Tickets 12.50$ Gas Expense 75.00$ Refreshments 7.50$ Other Fuels 20.00$ Bus Driver 50.00$ Total FC 225.00$ Total VC 20.00$

People Fixed cost Variable cost Total cost0 225.00$ -$ 225.00$ 5 225.00$ 100.00$ 325.00$

10 225.00$ 200.00$ 425.00$ 15 225.00$ 300.00$ 525.00$ 20 225.00$ 400.00$ 625.00$

Fixed Costs Variable Costs

Total costs

$-

$200.00

$400.00

$600.00

$800.00

0 5 10 15 20

Volume

Cost

($)

Total cost

Fixed cost

Profit and Loss Terms

• In terms of costs and revenues there are three possible profit and loss points for a business activity.

• Breakeven: total revenue = total costs– Just getting along

• Profit region: total revenue > total costs– Putting money in the bank

• Loss region: total revenue < total costs– Going into debt

Profit and Loss

Breakeven ChartsExample 2

• DK developed an overall total cost equation for his business expenses.

• Now DK wants to evaluate the potential to make money from this chartered bus trip.

Total Cost = Total Fixed Cost + Total Variable Cost

= $225 + ($20)(the number of people on the trip) • Let x = number of people on the trip• Thus,

Total Cost = 225 + 20x

• Using this relationship, DK can calculate the total cost for any number of people - up to the capacity of the bus.

Breakeven Charts• What he lacks is a revenue equation to offset his costs. • DK's total revenue from this trip can be expressed as:

Total Revenue =

= (Charter ticket price)(number of people on the trip)

= (ticket price)(x)

• Profit or loss can now be calculated as:

Total Profit =

= [Total Revenue] - [Total Costs]

= [ticket price]x – [225 + 20x]

If he charged a charter ticket price of $35, then

= [35x] - [225 + 20x]

= 15x - 225

Breakeven ChartsExample 2

Ticket priceBus Rental 80.00$ Event Tickets 12.50$ 35.00$ Gas Expense 75.00$ Refreshments 7.50$ Other Fuels 20.00$ Bus Driver 50.00$ Total FC 225.00$ Total VC 20.00$

People Fixed cost Variable cost Total cost Revenue Profit Region0 225.00$ -$ 225.00$ -$ (225.00)$ Loss5 225.00$ 100.00$ 325.00$ 175.00$ (150.00)$ Loss

10 225.00$ 200.00$ 425.00$ 350.00$ (75.00)$ Loss15 225.00$ 300.00$ 525.00$ 525.00$ -$ Breakeven20 225.00$ 400.00$ 625.00$ 700.00$ 75.00$ Profit25 225.00$ 500.00$ 725.00$ 875.00$ 150.00$ Profit30 225.00$ 600.00$ 825.00$ 1,050.00$ 225.00$ Profit35 225.00$ 700.00$ 925.00$ 1,225.00$ 300.00$ Profit40 225.00$ 800.00$ 1,025.00$ 1,400.00$ 375.00$ Profit

Fixed Costs Variable Costs

Profit-loss breakeven chart

$-

$500.00

$1,000.00

$1,500.00

0 5 10 15 20 25 30 35 40

Volume

Co

st

($)

Total cost

Fixed cost

Revenue

Past (Sunk) Costs and Future (Opportunity) Costs

• Sunk cost - money spent due to a past decision. We cannot do anything about these costs.– Purchase price paid for a car two years ago.

• Opportunity cost - a benefit that is foregone by engaging a resource in a chosen activity instead of engaging that same resource in some other activity. We make a choice or decision.– Buying lunch instead of gas.

Which amount is the value at present?Example 3

• A distributor of electric pumps must decide what to do with a "lot" of old electric pumps that was purchased 3 years ago.

• Soon after the distributor purchased the lot, technology advances were made.

• These advances made the old pumps less desirable to customers.

• The pumps are becoming more obsolescent as they sit in inventory.

• The pricing manager has the following information.

Which amount is the value at present?Example 3

Price when purchased 7,000.00$ Sunk cost Past decisionsStorage costs 1,000.00$ Sunk cost Past decisionsList price when purchased 9,500.00$ Old list Past decisionsCurrent list price of new pumps 12,000.00$ New list different features Past decisionsAmount offered for pumps 2 years ago 5,000.00$ Foregone opportunity Past decisionsCurrent price that the pumps could be sold for 3,000.00$ Market value Present opportunity

Expense Types

• Recurring costs – known, anticipated and occurs at regular intervals.– Purchasing food, paying rent.

• Non-recurring costs - one-of-a-kind event that occurs at an irregular interval.– Emergency maintenance expenses.

Sometimes we attempt to plan for large non-recurring costs by buying insurance. Paying the periodic insurance premium turns this expense into a recurring cost.

Incremental Costs• An incremental cost is the difference between the

costs of two alternatives.

Example 4• Choose between alternative models A and B. What

incremental costs occur with model B?

Cost Items A BPurchase price 10,000.00$ 17,500.00$ 7,500.00$ Installation costs 3,500.00$ 5,000.00$ 1,500.00$ Annual maintenance costs 2,500.00$ 750.00$ (1,750.00)$ Annual utility expenses 1,200.00$ 2,000.00$ 800.00$ Disposal costs after useful life 700.00$ 500.00$ (200.00)$

Model Costs

Incremental

Cash Costs vs. Book Costs

• Cash costs - movement of money from one owner to another - also known as a cash flow.– Payment this month on an auto loan.

• Book cost - cost of a past transaction that is recorded in an accounting book.– Down payment recorded in your

checkbook from last years automobile purchase.

Life-cycle Costs

• Life-cycle - all the time from the initial conception of an idea to the death of a product (process).

• Life-cycle costs - sum total of all the costs incurred during the life cycle.

• Life-cycle costing - designing a product with an understanding of all the costs associated with a product during it’s life-cycle.

Product Life-cycle

Cumulative Life-cycle Costs Committed and Dollars Spent

Life-cycle Design Change Costs and Ease of Change

Cost Estimating

• Economic analysis is future based.

• Costs and benefits in the future require estimating.

• Estimated costs are not known with certainty.

• The more accurate the estimate, the more reliable the decision.

• Estimating is the foundation of economic analysis.

Types of Estimates

• There are three general types of estimates:

1. Rough – order of magnitude, used for high level planning, inaccurate, range from -30% to +60% of actual values.

2. Semi-detailed - based on historical records, reasonably sophisticated and accurate, -15% to +20% of actual values.

3. Detailed - based on detailed specifications and cost models, very accurate, within -3% to +5% of actual.

Accuracy vs. Cost Tradeoff in Estimating

Estimating Models

Microsoft Excel

Worksheet

Microsoft Excel

Worksheet

Tracking cost improvements.Learning Curve

Looking at costs from several perspectives.

Triangulation

Scaling previous known costs up or down (economies of scale).

Power Sizing

Index number based on historical changes in cost.

Cost Indexes

Divide problem into items, estimate each & sum.

Segmenting

Uses a “per unit” factor.

$/sq ft, Benefits/employee

Per Unit

ExplanationModel Examples

US CPI

Estimating Benefits

• So far we have focused on cost terms and cost estimating.

• However, engineering economists must often also estimate benefits.

• Example benefits include sales of products, revenues from bridge tolls and electric power sales, cost reductions from reduced material or labor costs, reduced time spent in traffic jams, and reduced risk of flooding.

• These benefits are the reasons that many engineering projects are undertaken.

• The cost concepts and cost estimating models can also be applied to economic benefits.

Cash Flow Diagrams• The costs and benefits of engineering projects occur

over time and are summarized on a Cash Flow Diagram (CFD).

• Specifically, a CFD illustrates the size, sign, and timing of individual cash flows. In this way the CFD is the basis for engineering economic analysis.

• A Cash Flow Diagram is created by first drawing a segmented time-based horizontal line, divided into appropriate time units.

• The time units on the CFD can be years, months, quarters or any other consistent time unit.

• Then at each time when there is a cash flow, a vertical arrow is added - pointing down for costs and up for revenues or benefits.

• These cash flows are drawn to relative scale.

Cash Flow Diagrams

Cash Flow Diagrams

• Summarizes the flow of money over time• Can be represented using a spreadsheet

Year Capital costs O&M Overhaul Total0 (80,000.00)$ (80,000.00)$ 1 (12,000.00)$ (12,000.00)$ 2 (12,000.00)$ (12,000.00)$ 3 (12,000.00)$ (25,000.00)$ (37,000.00)$ 4 (12,000.00)$ (12,000.00)$ 5 (12,000.00)$ (12,000.00)$ 6 10,000.00$ (12,000.00)$ (2,000.00)$

Cash flow

$(100,000.00)

$(80,000.00)

$(60,000.00)

$(40,000.00)

$(20,000.00)

$-

$20,000.00

0 1 2 3 4 5 6

Year

Ca

sh

flo

w

Overhaul

O&M

Capital costs

Summary• This chapter introduced the cost concepts: fixed and

variable, marginal and average, sunk, opportunity, recurring and nonrecurring, incremental, cash and book, and life cycle.

• Fixed costs are constant and unchanging as volumes change, while variable costs change as output changes.

• Fixed and variable costs are used to find the breakeven value between costs and revenues, as well as the regions of net profit and loss.

• A marginal cost is for one more unit, while the average cost is the total cost divided by the number of units.