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### Engineering Costs and Cost Estimating

Cost Indices

Estimating Benefits

Cash Flow Diagrams

Costs:

Fixed and Variable

Direct and Indirect

Marginal and Average

Sunk and Opportunity

Recurring and Non-Recurring

Incremental

Cash and Book

Life-Cycle

Engineering Costs and Cost Estimating

Fixed Costs:

are constant and unchanging regardless of the level of the activity over a feasible range of operations for the capacity or capability available.

Variable costs:

operating costs that vary in total with the quantity of output or other measures of activity level.

Direct Costs:

cost that can be reasonably measured and allocated to a specific output or work activity.

Indirect/Overhead Cost:

cost that it is difficult to attribute or allocate to a specific output or work activity.

Engineering Costs and Cost Estimating

- Key Question: Where do the numbers come from that we use in engineering economic analysis?
- Cost estimating is necessary in an economic analysis
- When working in industry, you may need to consult with professional accountants to obtain such information

Engineering Costs and Cost Estimating

Example 2-1. Albert’s Charter Bus Venture

Albert plans to charter a bus to take people to see a wrestling match show in Jacksonville. His wealthy uncle will reimburse him for his personal time, so his time cost can be ignored.

Item Cost Item Cost

Bus Rental $80 Ticket $12.50

Gas Expense $75 Refreshments $ 7.50

Other Fuel Costs $20

Bus Driver $50

Total Costs $225.00 Total Costs $20.00

- Which of the above are fixed and which are variable costs?
- How do we compute Albert’s total cost if he takes n people to Jacksonville?

Albert’s Charter Bus Venture (example)

- Answer:Total Cost = $225 + $20 n.

Graph of Total Cost Equation:

Total cost

n

Albert’s Charter Bus Venture (example)

marginal cost(marginal tax)

-The cost to take one more person

average cost

- Average cost: the cost per person

Avg. Cost = TC/n

Avg. Cost = ($225+$20n)/n

- For n = 30, TC = $885

Avg. Cost = $885/30 = $29.50

Total cost cannot be calculated

from an average cost value

For n =35, TC 35*($29.50) = $ 1,032.50

Suppose Albert’s ticket cost drops to $10 per person if he brings 20 or more people. What is the total cost equation? What is the total cost if number of people exceeds capacity of 1 bus (bus capacity= 40)? What is the marginal cost in this case?

Albert’s Charter Bus Venture (example)

Question: Do we have enough information yet to decide how much money Albert will make on his venture? What else must we know?

- Albert needs to know his total revenue
- Albert knows that similar ventures in the past have charged $35 per person, so that is what he decides to charge
- Total Revenue = 35n (for n people)

Total profit =

Total Revenue – Total Cost:

35n – (225 + 20n) = 15n – 225

Question:

How many people does

Albert need to break even?

(not lose money on his venture)

Solve 15 n – 225 = 0 => n=15

more than 15, he makes money

Albert’s Charter Bus Venture (example)

Where is the Loss Region?

Where is the Profit Region?

Where is the Breakeven point?

Can you make this chart in Excel?

Sunk Costs

A sunk cost is money already spent due to a past decision.

- As engineering economists we deal with present and future opportunities
- We must be careful not to be influenced by the past
- Disregard sunk costs in engineering economic analysis

Example:

Suppose that three years ago your parents bought you a laptop PC for $2000.

- How likely is it that you can sell it today for what it cost?
- Suppose you can sell the laptop today for $400. Does the $2000 purchase cost have any effect on the selling price today?

The $2000 is a sunk cost. It has no influence on the present opportunity to sell the laptop for $400. ( stock costs now $20 you bought for $80)

Opportunity Cost

- An opportunity cost is the benefit that is foregone by engaging a business resource in a chosen activity instead of engaging that same resource in the foregone activity.
- Example: Suppose your wealthy uncle gives you $75,000 when you graduate from high school. It is enough to put you through college

(5 years at $15,000 per year). It is also enough for you to open a business making web pages for small companies instead of going to college. You estimate you would make $20,000 per year with this business.

- If you decide to go to college you give up the opportunity to make $20,000 per year
- Your opportunity cost is $20,000
- Your total cost per year is $35,000

Sunk and Opportunity Cost

Example 2-3. A distributor has a case of electric pumps. The pumps are unused, but are three years old. They are becoming obsolete. Some pricing information is available as follows.

Item Amount Type of Costs

Price for case 3 years ago $7,000

Sunk cost

Storage costs to date $1,000

Sunk cost

List price today for a case of

new and up to date pumps $12,000

Can be used to help determine what the lot is worth today.

Amount buyer offered for case

2 years ago $5,000

A foregone opportunity

Case can currently be sold for $3,000

Actual market value today

Recurring and Non-Recurring Costs

- Recurring costs are those expenses that are known, anticipated, and occur at regular intervals. These costs can be modeled as cash flows.
- Non-recurring costs are one-of-a-kind and occur at irregular intervals. They are difficult to plan for or anticipate.
- Example. You decide to landscape a lot of ground and then care for it. Which are recurring and which are non-recurring costs you incur?
- Remove existing trees, vegetation
- Have land graded with bulldozer
- Have yard planted with grass
- Plant shrubs, trees
- Mow grass
- Fertilize grass, shrubs
- Water grass, shrubs

Incremental Cost

- Incremental Cost is the additional cost that results from:
- Increasing the output of a system by one (or more) units
- Selecting one alternative over another

Example 2-4. Philip can choose between model A or model B. The following information is available.

Cost ItemsModel AModel BIncremental Cost of B

Purchase price$10,000 $17,500

$7,500

Installation cost$3,500$5,000

$1,500

Annual maintenance cost $2,500$750

$-1,750/yr

$800/yr

Annual utility expense$1,200$2,000

Disposal cost after useful life$700$500

$-200

- Can we conclude that model B is more expensive than model A?

Cash Costs vs. Book Costs

Cash costs

require the cash transaction of dollars from “one pocket to another”.

Book costs

are cost effects from past decisions that are recorded in the books (accounting books) of a firm

- Do not represent cash flows
- Not included in engineering economic analysis
- One exception is for asset depreciation (used for tax purposes).

Example: You might use Edmond’s Used Car Guide to conclude the book value of your car is $6,000. The book value can be thought of as the book cost. If you actually sell the car to a friend for $5,500, then the cash cost to your friend is $5,500.

Life-Cycle Costs

Life-cycle costs are the summation of all costs, both recurring and nonrecurring, related to a product, structure, system, or service during its life span

Products go through a life cycle, just like people

- Assessment & Justification Phase
- Conceptual or Preliminary Design Phase
- Detailed Design Phase
- Production or Construction Phase
- Operational Use Phase
- Decline and Retirement Phase

Life-Cycle Costs

Comments:

- The later design changes are made in the life-cycle, the higher the costs.
- Decisions made early in the life-cycle tend to “lock in” costs incurred later in the life cycle:

Nearly 70 to 90% of all costs are set during the design phases, while only 10 to 30% of the cumulative life-cycle costs have been spent.

- Question. When is the best time to consider all life-cycle effects, and make design changes?
- Bottom Line. Engineers should consider all life-cycle costs when designing products and the systems that produce them.

Cost Indices

- The U.S. federal government publishes cost index data through the Department of Commerce Bureau of Statistics.
- The Statistical Abstract of the United States publishes cost indexes for labor, construction, and materials.
- The best-known example is the consumer price index (CPI), a measure of inflation.
- The measure is scaled, so it is only the relative values of any two measures that are meaningful.
- For example, in 1920, the measure was about 20; in 1997 it was about 160. The conclusion is that one would have to spend 160/20, or 8 times as much in 1997 as in 1920 for the same consumables.
- Cost indices work in the same way asprice indices.
- Cost indices are dimensionless.

Estimating Benefits

For the most part, we can use exactly the same approach to estimate benefits as to estimate costs:

- Fixed and variable benefits
- Recurring and non-recurring benefits
- Incremental benefits
- Life-cycle benefits
- Rough, semi-detailed, and detailed benefit estimates
- Difficulties in estimation
- Segmentation and index models

Major differences between benefit and costestimation:

- Costs are more likely to be underestimated
- Benefits are most likely to be overestimated
- Benefits tend to occur further in the future than costs

Example

Two summer Camps have the following data for a 12-week session:

a. Develop the mathematical relationships for total cost and total revenue for camp A

b. What is the total number of campers that will allow camp B to break even?

c. What is the profit or loss for the 12-week session if camp A operates at 80% capacity?

d. Determine the breakeven number of campers for the two camps to have equal total costs for a 12-week session.

Camp A

Charge per camper $120 per week

Fixed costs $48,000 per session

Variable cost per camper $80 per week

Capacity 200 campers

Camp B

Charge per camper $100 per week

Fixed costs $60,600 per session

Variable cost per camper $50 per week

Capacity 150 campers

100

100

50

0

1

2

3

4

5

100

Today

150

150

Cash Flow DiagramsExample:

Time Period Size of Cash Flow

0 (today) Receive $100 (positive CF)

1 Pay $100 (negative CF)

2 Positive CF of $100

3 Negative CF of $150

4 Negative CF of $150

5 Positive CF of $50

- Cash flow diagrams (CFD) summarize the costs and benefits of projects
- A CFD illustrates the size, sign,

and timing of individual cash flows

- Periods may be months, quarters, years, etc.

- COMMENTS:
- The end of one period is the beginning of the next one
- Arrows point up for revenues or benefits, down for costs
- One person’s payment (cash outflow w. neg. sign) is another person’s receipt (cash inflow w. pos. sign)
- It is essential to use only one perspective in any CFD

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