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Chapter 2

Cost Concepts and the Economic Environment

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� Fixed cost� unaffected by changes in activity level, e.g. insurance and

taxes on facilities, license fees, interest costs on borrowing capital etc.

� Variable cost� vary in total with the quantity of output (or similar measure

of activity)

� Incremental cost� additional cost, or revenue resulting from increasing output

of a system by one (or more) units

� Direct� can be measured and allocated to a specific work activity.

� e.g. material cost.

� Indirect� difficult to attribute or allocate to a specific output or work

activity (also overhead or burden). � e.g. cost of equipment maintenance etc.

� Standard cost� cost per unit of output, established in advance of

production or service delivery. � e.g. direct labor hours.

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� Cash cost� a cost that involves a payment of cash.

� Book cost� a cost that does not involve a cash transaction but is

reflected in the accounting system.

� Sunk cost� a cost that has occurred in the past and has no relevance to

estimates of future costs and revenues related to an alternative course of action.� e.g. R&D cost, cost of buying a machine few years ago and now the

machine has worn off

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� Opportunity cost� the monetary advantage foregone due to limited resources.

The cost of the best rejected opportunity.

� Life-cycle cost� the summation of all costs related to a product, structure,

system, or service during its life span.

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� Why analysing Life Cycle Cost (LCC)

� What do I need now and how much will it cost me for a project?

� What will I need to do in the future and how much will that cost me?

� How long is the ‘future’?� How do I evaluate future costs vs current costs?

� Divided into 2 phases: � Acquisition phase� Operating phase

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� 6 stages involve: � 3 stages in acquisition phase� 3 stages in operation phase

1. Analysis � planning a project/propose an idea in produce a new

product/design etc.� Analysis include the economy needs for the product, system,

structure of service

2. Research and development

� Conceptual ideas turn to preliminary design

� Development on feasible alternatives

� With engineering analysis, preferred alternative will be selected

� Prototype testing to support preliminary design

3. Design and planning

� Detail design or planning for production or construction

� Prepare operational facilities and other resources

4. Production or Construction� production, delivery, or construction of the end item or

service

5. Customer service or maintenance

6. Retirement and disposal� Retirement from active operation or use

� Disposal of physical assets

Phases of the Life Cycle and Their Relative Cost

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� demand for a product or service is directly related to its price

p = a - bD Where,

p = priceD = demanda = intercept on the price axis b = constants that depend on the particular product or service.

o Price high, demand will decrease

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Total revenue (TR) is the product of the selling price per unit ( p) and the number of units sold (D).

TR = price x demand = p (D)

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TR = aD – bD2

Solving the derivation, the optimal demand is

To guarantee that D maximizes total revenue, check the second derivative to be sure it is negative:

d2TR/-dD2 = - 2b

� Profit is achieve when total revenue (TR) > total cost (CT)

Profit (loss) = Total Revenue – Total Cost

Where,

TR = aD – bD2

CT = Fixed cost (CF) + Variable cost (CV)

CV = variable cost per unit (cv) x demand (D)

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Profit (loss) = Total Revenue – Total Cost

= (aD - bD2) - (CF + cvD)

= -bD2 + (a - cv)D – CF

Where,

and a > 0 , b > 0

� For profit to occur:1. (a - cv) > 02. TR > CT

ba≤≤ D0

� Number of demand (D) needed to achieve maximum profit:

� To verify the maximum profit, second derivative must achieve negative value:

02)profit( =−−= bDca

dDd

v

bdDprofitd

2)(

2

2

−=

bca

D v

2*

−=

• Breakeven point, D1’• Total revenue = total cost• Increase in demand result in profit

• Optimum demand, D*• Profit is maximised

• Breakeven point, D2’• Total revenue = total cost• Additional volume result in loss

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Breakeven is found when,

total revenue = total cost

aD – bD2 = CF + cvD

-bD2 + (a - cv )D - CF = 0

Solving the breakeven point D1’ and D2’ (the root of the equation), demand (D) to achieve breakeven can be obtained

)(2))((4)()(

'2

b

CbcacaD Fvv

−−−−−±−−

=

• Single breakeven point can be achieved when:

1. price (p) is independent from demand (D)

2. Price is greater than cost per unit (cv)

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� A company produces an electronic timing switch that is used in consumer and commercial products made by several other manufacturing firms. The fixed cost (CF) is $73,000 per month, and the variable cost (cv) is $83 per unit. The selling price per unit is p = $180 – 0.02 (D), based on the optimal value of D that maximizes profit. For this situation

a) Determine the optimal volume for this product and confirm that a profit occurs (instead of a loss) at this demand; and

b) Find the volumes at which breakeven occurs; that is, what is therange of profitable demand?

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� An engineering consulting firm measures its output in a standardservice hour unit, which is a function of the personnel grade levels in the professional staff. The variable cost (cv) is $62 per standard service hour. The charge-out rate [i.e., selling price (p)] is $85.56 per hour. The maximum output of the firm is 160,000 hours per year, and its fixed cost (CF) is $2,024,000 per year. For this firm,

a) What is the breakeven point in standard service hours and in percentage of total capacity, and

b) What is the percentage reduction in the breakeven point (sensitivity) i. if fixed costs are reduced 10%ii. if variable cost per hour is reduced 10%iii. if both costs are reduced 10%iv. if the selling price per unit is increased by 10%?