1. Chapter 2 Engineering Costs and Cost Estimating1

2. Learning Objectives Understand various cost concepts Breakeven charts
Understand various cost estimation models
Be able to estimate engineering costs with various models
Cash Flow Diagrams

3. Engineering Costs
Fixed costs
The costs that do not change during the time horizon of the study. They may relate to the constant costs of equipment, utilities, rent, etc.
Constant, independent of the output or activity level.
Examples:
Property taxes, insurance
Management and administrative salaries
License fees, and interest costs on borrowed capital
Rental or lease

4. Example
A manufacturing plant that assembles television sets has variable output volume from 200 sets to 350 sets a day. The building for both manufacturing and warehousing has an area of 80, 000 square feet. It employs about 250 people. It produces all of the components that go into the assembly.
An example for fixed cost in this plant is
Equipment Cost
Power cost
Labor Cost
Material Cost
Equipment cost stays the same regardless the level of output once the plant has been designed to produce at a certain level.

5. Engineering Costs Variable costs
Costs that vary during the time horizon of the study. Over the long-term all costs are variable.
Depends on the level of output or activity.
Proportional to the output or activity level.
Example:
Direct labor cost
Direct materials

6. Example
A manufacturing plant that assembles television sets has variable output volume from 200 sets to 350 sets a day. The building for both manufacturing and warehousing has an area of 80, 000 square feet. It employs about 250 people. It produces all of the components that go into the assembly. An example for variable cost in the plant is A) Building cost B) Equipment Cost C) Labor Cost D) Property Taxes
Labor cost depends on the output level

7. Relevant Formulae Total Variable Cost = Unit Variable Cost * Quantity
TVC = VC * Q
Total Cost = Total Fixed Cost + Total Variable Cost
TC = FC + VC * Q
Total Revenue = Unit Selling Price * Quantity
TR = SP * Q
where TVC = Total variable cost
VC = Variable cost per unit
Q = Production/Selling quantity
FC = Total Fixed costs
TR = Total revenue
SP = Selling price per unit

8. Example
A company produces a single, high-volume product. One year its production volume was 780,000 units, its fixed costs were $3.2 million and its variable costs were $16 per unit. What was the company's total cost for the year? A) $3,200,000 B) $3,200,016 C) $12,480,000 D) $15,680,000
TVC = 780,000 x 16 = $12,480,000
FC = $3.2M
TC = FC+TVC = $15,680,000

9. Breakeven Analysis
Breakeven point: The level of business activity at which the total costs to provide the products (goods), or services are equal to the revenue generated. That is:
Total costs = Total revenue
Total costs = Total fixed costs + Total variable costs
Applications of Breakeven analysis:
Determining minimum production quantity
Forecast production profit / loss

10. Breakeven Analysis $ Production Quantity Total Revenue Total Costs
Profit
Variable Costs
Fixed Costs
Loss
Break-even Point
Production Quantity

11. Example 2-1 X # of Customers Total Revenue = 35X $1000 $800 $600 $400
$200 $0
Total Costs
= $ X
Profit
Variable Costs
= 20X
Fixed Costs
= $225
Loss X
# of Customers 5 10 15 20 25

12. Example
A manufacturing firm’s specialty circuit board division has annual fixed costs of $100,000 and variable costs of $20.00 per board. If they charge $100 per circuit board, how many circuit boards must they produce and sell in order to break even?
To break even, total costs = total revenue,
where total costs = total fixed costs + total variable costs.
$100,000 + $20X = $100X
X = $100,000/$80 = 1250 circuit boards.

13. Example
In breakeven analysis, the profit at the breakeven point is equal to A) The total cost B) Zero C) The total revenue D) The variable cost multiplied by the number of items sold
The total revenue is equal to the total cost. Therefore…

14. Marginal Costs and Average Costs
Used to decide whether an additional unit should be made, purchased, or enrolled in.
the variable cost for one more unit of output
Capacity Planning: excess capacity
Basis for last-minute pricing
Average Costs:
total cost divided by the total number of units produced.
Basis for normal pricing

15. Example What is marginal cost? Explain with an example.
the cost of producing one additional unit.
used for making a decision of whether or not it is economical to produce another unit of the same item.
Example: Taking the fifth person in a taxicab that can take only four passengers.
For the fifth person, a second cab has to be hired.
The cab fare for the second cab is the marginal cost.

16. 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, engineers and other specialists to obtain such information

17. Albert’s Charter Bus Venture (example)
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 $ Ticket $12.50
Gas Expense $ Refreshments $ 7.50
Other Fuel Costs $20
Bus Driver $50
Total Costs $ 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?

18. Albert’s Charter Bus Venture (example)
Answer: Total Cost = $225 + $20 n. 
Graph of Total Cost Equation:  
Total cost n

19. marginal cost
-The cost to take one more person
average cost
- Average cost: the cost per person
Avg. Cost = TC/n
Avg. Cost = ($225+$20n)/n = $20 + $225/n
For n = 30, TC = $885
Avg. Cost = $885/30 = $29.50

20. How many people does Albert need to break even?
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 – ( n) = 15n – 225
Question:
How many people does Albert need to break even?
(not lose money on his venture)

21. How many people does Albert need to break even?
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 21

22. Albert’s Charter Bus Venture (example)
Where is the Loss Region?
Where is the Profit Region? 
Where is the Breakeven point?

23. Exercise 2.3
A new machine comes with 100 free service hours over the first year. Additional time costs $75 per hour. What are the average and marginal costs per hour for the following quantities?
a) 75 hours

24. Exercise 2.3
A new machine comes with 100 free service hours over the first year. Additional time costs $75 per hour. What are the average and marginal costs per hour for the following quantities?
b) 125 hours

25. Exercise 2.3
A new machine comes with 100 free service hours over the first year. Additional time costs $75 per hour. What are the average and marginal costs per hour for the following quantities?
c) 250 hours

26. Exercise 2.7
A privately owned summer camp for youngsters has the following data for a 12-week session:
Charge per camper $120 per week
Fixed costs $48,000 per session
Variable cost per camper $80 per week
Capacity campers
a) Develop the mathematical relationships for total cost and total revenue.

27. Exercise 2.7
A privately owned summer camp for youngsters has the following data for a 12-week session:
Charge per camper $120 per week
Fixed costs $48,000 per session
Variable cost per camper $80 per week
Capacity campers
b) What is the total number of campers that will allow the camp to just break even?
$48,000 = $480 x

28. Exercise 2.7
A privately owned summer camp for youngsters has the following data for a 12-week session:
Charge per camper $120 per week
Fixed costs $48,000 per session
Variable cost per camper $80 per week
Capacity campers
c) What is the profit or loss for the 12-week session if the camp operates at 80% capacity

29. Exercise 2.7
A privately owned summer camp for youngsters has the following data for a 12-week session:
Charge per camper $120 per week
Fixed costs $48,000 per session
Variable cost per camper $80 per week
Capacity campers
d) What are marginal and average costs per camper at 80% capacity?
x = 160
Marginal cost is the slope of the equation which is equal to $960
Average cost is Total Cost/x = ($48,000 + $960 * 160)/160 = $1260

30. Sunk Costs Costs associated with decisions already made.
Money already spent as a result of a past decision.
Cost that has occurred in the past and has no relevance to estimates of future costs and revenues related to an alternative
Must be ignored because current decisions can not change the past

31. 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

32. Sunk Costs
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 now costs $20 but you bought for $80) 32

33. Example
All of the following are usually included in an engineering economic analysis except
A) Fixed costs 
B) Variable costs 
C) Sunk costs 
D) Total revenue 

34. Opportunity Costs Using a resource in one activity instead of another
Cost of the foregone opportunity and is hidden or implied
Going for $3000 trip and miss the opportunity of earning $5000 in summer internship

35. Sunk and Opportunity Cost-1
Example 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

36. Sunk and Opportunity Cost-2
Example (cont.)
Item Amount Type of Costs
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 36

37. Recurring Costs and Non-recurring Costs
Recurring Costs: Repetitive, and occur when a firm produces similar goods and services on a continuing basis
Office space rental
Non-recurring Costs: Not repetitive, even though the total expenditure may be cumulative over a period of time
Typically involves developing or establishing a capability or capacity to operate
Examples are purchase cost for real estate and the construction costs of the plant

38. Incremental Costs
Incremental Costs: Difference in costs between two alternatives.
Suppose that A and B are mutually exclusive alternatives. If A has an initial cost of $10,000 while B has an initial cost of $14,000, the incremental initial cost of (B - A) is $4,000.

39. Example 2-3 Choosing between Model A & B
Cost Items
Model A
Model B
Incremental Cost
Purchase Price
$10,000
$17,500
Installation Costs
$3,500
$5,000
Annual Maintenance *
$2,500
$750
Annual Utility *
$1,200
$2,000
Disposal Cost
$700
$500
$7,500
$1,500
$ -1,750/yr
$800/yr
$ -200
* Must be multiplied by the number of years of service.

40. Cash Costs versus Book Costs
You must know this.
Cash Costs versus Book Costs
Book Costs:
Costs that do not involve money/cash transaction
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.
Depreciation Example:
Depreciation is charged for the use of assets, such as plant and equipment—This is used to determine the value of the company and in computing taxes.

41. Cash Costs versus Book Costs
You must know this.
Cash Costs versus Book Costs
Cash Costs:
Costs that involve money/cash transaction
Require the cash transaction of dollars from “one pocket to another”.
Example:
Interest payments, taxes, etc.
You might use Kelley Blue Book 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.

42. You must know this.
Life-Cycle Costs
Life-Cycle Costs: Summation of all costs, both recurring and nonrecurring, related to a product, structure, system, or service during its life span.
Life cycle begins with the identification of the economic needs or wants (the requirements) and ends with the retirement and disposal activities.

43. Phases of Life Cycle You must know this. 1. Need Assessment
2.Conceptual Design
3. Detailed Design
4. Production /Construction
5.Operational Use
6. Decline/ Retirement
Requirements
Analysis
Impact Analysis
Allocation of Resources
Production of Goods/ Services
Distribution of Goods/ Services
Phase Out
Overall Feasibility Study
Proof of Concept
Detailed Specifications
Building of Supporting Facilities
Maintenance/ Support
Disposal
Conceptual Design Planning
Prototype/ Breadboard
Component/ Supplier Selection
Quality Control/ Assurance
Retirement Planning
Retirement
Development/ Testing
Production Planning
Operational Planning
Detailed Design Planning

44. Cumulative Life-Cycle Costs Committed and Spent
You must know this.
Cumulative Life-Cycle Costs Committed and Spent
100%
90%
80%
70%
Life-Cycle Costs Committed
60%
50%
Life-Cycle Costs Spent
40%
30%
20%
10% 0%
Need
Conceptual
Detailed
Production
Operational
Decline/
Assessment
Design
Design
/Construction
/Use
Retirement

45. Cost/Ease of Design Changes in Product Life Cycle
You must know this.
Cost/Ease of Design Changes in Product Life Cycle 0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Need
Assessment
Conceptual
Design
Detailed
Production
/Construction
Operational
/Use
Decline/
Retirement
Ease of Design Changes
Cost of Design Changes

46. Think – Pair – Share
Tech Engineering Inc. makes a consumer product for which the following cost data are available.
Fixed cost/ year = $120,000
Variable costs/ unit = $15
i. Determine the breakeven volume if each unit can be sold for $40.
ii. If a net profit of $100,000 is required, determine the number of units that needed to be sold.

47. Think – Pair – Share
Tech Engineering Inc. makes a consumer product for which the following cost data are available.
Fixed cost/ year = $120,000
Variable costs/ unit = $15
i. Determine the breakeven volume if each unit can be sold for $40.

48. Think – Pair – Share
Tech Engineering Inc. makes a consumer product for which the following cost data are available.
Fixed cost/ year = $120,000
Variable costs/ unit = $15
ii. If a net profit of $100,000 is required, determine the number of units that needed to be sold.

49. Cost Estimating and Estimating Models
You must know this.
Needs for Cost Estimating
Importance of Cost Estimating
Types of Cost Estimating
Rough Estimates -30% to +60%
Used for general feasibility activities
Semi-detailed Estimates -15% to +20%
Budgeting and preliminary design decisions
Detailed Estimates -3% to +5%
Establishing design details and contracts

50. Trade-off between Accuracy and Cost
You must know this.
Trade-off between Accuracy and Cost
High
Cost of Estimate
Low
Low
Medium
High
Accuracy of Estimate
Figure 2-6. Accuracy versus cost trade-off in estimation

51. Difficulties in Estimation
You must know this.
One-of-a-Kind or first-run projects Estimates
Ex: First NASA mission
Time and Effort Available
Constraint on time and person-power can make the overall estimating task more difficult.
Estimator Expertise

52. Categories of Cost Estimating
You must know this.
Categories of Cost Estimating
Capital Investment (S&H, Installation, Training)
Labor Costs (Direct and Indirect)
Material Costs (Direct & Indirect)
Maintenance Costs (Regular & Overhaul)
Property Taxes and Insurance
Operating Costs (Rental, Gas, Electricity)
Quality Costs (Scrap, Rework, Inspection)
Overhead Costs (Administration, Sales)
Disposal Costs
Revenues
Market Values

53. Sources of Cost Estimating Data
You must know this.
Sources of Cost Estimating Data
Accounting records
Other sources within the firm:
Engineering, Production, Quality
Sales, Purchasing, Personnel
Published information:
Statistical Abstract of US – Cost indexes
Monthly Labor Review – Labor costs
Building Construction Cost Data
Other sources outside the firm:
Vendor, Salespeople
Research & Development
Pilot plant, Test market

54. We will look at each of these.
Estimating models
You must know this.
Per-Unit Model (Unit Technique)
Segmenting Model
Cost Indexes
Power-Sizing Model
Triangulation
Improvement and the Learning Curve
We will look at each of these.

55. Per-Unit Model (Unit Technique)
You must know this.
Per-Unit Model (Unit Technique)
Per-Unit Model (Unit Technique)
Construction cost per square foot (building)
Capital cost of power plant per kW of capacity
Revenue / Maintenance Cost per mile (hwy)
Utility cost per square foot of floor space
Fuel cost per kWh generated
Revenue per customer served

56. Example 2-4: Cost Estimating using Per-Unit Model
Cost estimation of camping on an island for 24 students over 10 days.
Planned Activities:
2 days of canoeing
3-day hikes
3 days at the beach
Nightly entertainment

57. Example 2-4: Cost Estimating using Per-Unit Model
Cost Data:
Van (capacity 15) rental: $50 one way
Camp is 50 miles away, van gets 10 miles/gallon, and gas is $1/gallon
Each cabin holds 4 campers, rent is $10/day-cabin
Meals are $10/day-camper
Boat transportation is $2/camper (one way)
Insurance/grounds fees/overhead is $1/day-camper
Canoe (capacity 3) rentals are $5/day-canoe
Day hikes are $2.50/camper-day
Beach rental is $25/group-(half-day)
Nightly entertainment is free

58. Example 2-4: Cost Estimating using Per-Unit Model`
Solution:
Assumption: 100% participation in all activities
Transportation Costs:
Van: $50/van-trip * 2 vans * 2 trips = $200
Gas: $1/gallon * (50 miles / 10 miles/gallon) *2 *2 = 20
Boat: $2/camper-trip * 24 campers * 2 = 96
Subtotal $316

59. Example 2-4: Cost Estimating using Per-Unit Model`
Solution:
Living Costs:
Meals: $10/day-camper * 24 campers * 10 days = $2400
Cabin rental: $10/day-cabin * (24/4) cabins *10 days = 600
Insurance: $1/day-camper * 24 campers * 10 days = 240
Subtotal $3240 59 59

60. Example 2-4: Cost Estimating using Per-Unit Model
Solution (Continued):
Entertainment Costs:
Canoe rental: $5/day-canoe * 2 days * (24/3) canoes = $80
Beach rental: $25/group-(half-day) * (3*2) half-days = 150
Day hike: $2.50/camper-day* 24 campers * 3 days = 180
Nightly entertainment 0
Subtotal $410
Total Costs: $3966
Thus, the total cost per student would be $3966/24 = $165.25

61. Segmenting Model (example)
Estimate is decomposed into individual components
Estimates are made at component level
Individual estimates are aggregated back together
Consider a lawnmower
A. Chassis
B. Drive Train
C. Controls
D. Cutting/Collection system

62. Segmenting Model (example)
A. Chassis
B. Drive Train
Cost Item
Estimate
A.1 Deck
$7.00
A.2 Wheels
10.00
A.3 Axles
5.85
Subtotal
$22.85
Cost Item
Estimate
B.1 Engine
$38.50
B.2 Starter assembly
6.90
B.3 Transmission
4.45
B.4 Drive disc assembly
10.00
B.5 Clutch linkage
6.15
B.6 Belt assemblies
8.70
Subtotal
$72.70

63. Segmenting Model (example)
C. Controls
D. Cutting/Collection system
Cost Item
Estimate
C.1 Handle assembly
$2.85
C.2 Engine linkage
9.55
C.3 Blade linkage
5.70
C.4 Speed control linkage
20.50
C.5 Drive control assembly
7.70
C.6 Cutting height adjuster
6.40
Subtotal
$52.70
Cost Item
Estimate
D.1 Blade assembly
$11.80
D.2 Side chute
6.05
D.3 Grass bag & adapter
7.75
Subtotal
$25.60
Total material cost = $ $ $ $25.60 = $173.85

64. Costs indexes Reflect historical change in cost
Cost index could be individual cost items (labor, material, utilities), or group of costs (consumer prices, producer prices)
Indexes can be used to update historical costs
(Eq. 2-2)

65. Example 2.6
Miriam is interested in estimating the annual labor and material costs for a new production facility.
She was able to obtain the following labor and material cost data:
Labor cost index value was at 124 ten years ago and is 188 today.
Annual labor costs for a similar facility were $575,500 ten years ago.
188
$575,500
871,800
124

66. Example 2.6 (Continued)
Miriam is interested in estimating the annual labor and material costs for a new production facility.
She was able to obtain the following labor and material cost data:
Material cost index value was at 544 three years ago and is 715 today.
Annual material costs for a similar facility were $2,455,000 three years ago.

67. Power-Sizing Model X = Power-sizing exponent
(Eq. 2-3)
X = Power-sizing exponent
Example Power Sizing Exponent Values
Equipment/Facility X
Blower, centrifugal
0.59
Compressor
0.32
Crystallizer, vacuum
0.37
Dryer, drum
0.40
Fan, centrifugal
1.17
Equipment/Facility X
Filter, vacuum
0.48
Lagoon, aerated
1.13
Motor
0.69
Reactor
0.56
Tank, horizontal
0.57

68. Example 2.7
Miriam has been asked to estimate the cost today of a 2500 ft2
heat exchange system for the new plant being analyzed. She has the following data.
Her company paid $ for a 1000 ft2 heat exchanger 5 years ago.
Heat exchangers within this range of capacity have a power sizing exponent (x) of 0.55
A. Considering Power-Sizing Index Change

69. Example 2.7 (Continued)
Miriam has been asked to estimate the cost today of a 2500 ft2
heat exchange system for the new plant being analyzed. She has the following data.
Five years ago the Heat Exchanger Cost Index (HECI) was 1306; it is 1487 today.
B. Considering Cost Index Change

70. Triangulation
Techniques Used in Surveying: To map points of interest by using three fixed points and horizontal angular distance
Application in Economic Analysis: To approach economic estimate from different perspectives, such as different source of data, or different quantitative models.

71. Improvement and Learning Curve
Learning Phenomenon: As the number of repetitions increase, performance of people becomes faster and more accurate.
Learning curve captures the relationship between task performance and task repetition.
In general, as output doubles the unit production time will be reduced to some fixed percentage, the learning curve percentage or learning curve rate

72. Learning Curve Let T1 = Time to perform the 1st unit
TN = Time to perform the Nth unit
b = Constant based on learning curve LC%
N = Number of completed units
(Eq. 2-4)
(Eq. 2-5)

73. Example 2.8
Calculate the time required to produce the hundredth unit of a production run if the first unit took
32.0 minutes to produce and the learning curve rate for production is 80%.

74. Example 2.9
Estimate the overall labor cost portion due to a task that has a learning-curve rate of 85% and reaches a steady state value of 5.0 minutes per unit after 16 units.
Labor and benefits are $22 per hour, and the task requires two skilled workers.
The overall production run is 20 units.

75. Cost Estimating Using Learning Curve
Example 2-9:
Cost Estimating Using Learning Curve
Example 2-9 Cost Estimating using
Learning Curve N TN 1
9.60 2
8.16 3
7.42 4
6.94 5
6.58 6
6.31 7
6.08 8
5.90 9
5.73 10
5.59 N TN 11
5.47 12
5.36 13
5.26 14
5.17 15
5.09 16
5.00 17 18 19 20

76. Estimating Benefits-1 Sample Benefits Sales of products
Revenues from bridge tolls & electric power sale
Cost reduction from reduced material or labor costs
Less time spent in traffic jams
Reduced risk of flooding

77. Estimating Benefits-2
Cost concepts and cost estimating models can also be applied to economic benefits
Uncertainty in benefit estimating is typically asymmetric, with a broader limit for negative outcomes, e.g. -50% to +20%
Benefits are more difficult to estimate than costs 77 77

78. Cash Flow Diagrams (CFD)
CFD summarize costs & benefits occur over time
CFD illustrates the size, sign, and timing of individual cash flows
Components of CFD
A segmented time-based horizontal line, divided into time units
A vertical arrow representing a cash flow is added at the time it occurs
Arrow pointing down for costs and up for benefits

79. Cash Flow Diagrams (CFD) Example
Timing of Cash Flow
Size of Cash Flow
At time zero (now)
Positive $100
1 time period from today
Negative $100
2 time periods from today
3 time periods from today
Negative $150
4 time periods from today
5 time periods from today
Positive $50 4 1 2 3 5

80. Categories of Cash Flows
First cost: expenses to build or to buy and install
Operations and maintenance (O&M): annual expense, such as electricity, labor, and minor repairs
Salvage value: receipt at project termination for sale or transfer of the equipment
Revenues: annual receipts due to sale of products or services
Overhaul: major capital expenditure that occurs during the asset’s life

81. Drawing a Cash Flow Diagram
CFD shows when all cash flows occur
In a CFD, the end of period t is the same time as the beginning of period t+1
Rent, lease, and insurance payments are usually treated as beginning-of-period cash flows
O&M, salvage, revenues, and overhauls are assumed to be end-of-period cash flows
The choice of time 0 is arbitrary

82. Drawing Cash Flow Diagrams with Spreadsheet
Year
Capital Costs
O&M
Overhaul
-$80,000 1
$(12,000) 2 3
$(25,000) 4 5 6
$ 10,000

83. End of Chapter 2