Chapter 2 - Cost Terminology and DesignEconomics

SEEM2440A/B 1

Cost terminology

Fixed, variable, and incremental costsFixed costs that remain constant over a specific range ofoperating conditions. It is subject to change when largerchanges in the operating conditions involved such as plantexpansion or shutdown.Variable costs that vary in total with the output units, e.g.,material cost.Incremental costs are the additional costs that result fromincreasing the output level by one or more units.

Recurring and nonrecurring costsRecurring Costs are those that are repetitive and occurwhen an organization produces similar goods or serviceson a continuing basis, e.g., variable cost and also a periodicfixed cost like office rent.Nonrecurring Costs are those that are not repetitive, e.g.,construction cost of the manufacturing plant.

SEEM2440A/B 2

Example 2.1

Fixed Variable Recurring NonrecurringRaw mtl.s

Direct labor

Rent

Admin. salaries

Utilities

Property tax

Property set up

SEEM2440A/B 3

Cost terminology

Direct, indirect (overhead), and standard costsDirect costs that can be attributed to a specific activity oroutput, e.g., labor and material costs directly associatedwith the a product.Indirect costs that cannot be attributed to a specific activityor output. Normally, they are allocated through a selectedformula, such as by proportion, to the outputs or workactivities. Cost of common tools is an example of theindirect costs.Standard costs are planned costs per unit of output that areestablished in advance of actual production. The standardcosts play an important role in cost control and othermanagement functions. One typical use is to measureoperating performance by comparing actual cost per unitwith the standard unit cost.

SEEM2440A/B 4

Cost terminology

Cash and book costsCash Costs that involve payment of cash and would resultin a cash flow.Book Costs that do not involve cash transaction and isreflected in the accounting system as a noncash cost, e.g.,depreciation.

Sunk costsSunk Costs are those that have occurred in the past andirretrievable.Sunk costs are not relevant in the engineering economicanalysis because they cannot be changed regardless ofwhat decisions is made now or in the future.The original cost of an equipment is considered to be thesunk cost for a firm in deciding to replace it or not.

SEEM2440A/B 5

Cost terminology

Opportunity costThe opportunity cost is incurred because there are onlylimited resources available.The opportunity cost of the selected alternative is the valueof the next best alternative opportunity that is forgone(given up).The value of the next best alternative opportunity that isforgone can be obtained as the answer of the followingquestion:

"What would you gain if you selected the best alternativeopportunity instead of the choice you are considering ?"

The opportunity cost is forward looking in that it measuresthe value that the decision maker sacrifices at the time thedecision is made and beyond.

SEEM2440A/B 6

Cost terminology

Opportunity cost - Example 1

Suppose you have $2,000 in your bank account, you can eitherkeep it in the bank or invest it in stock market.What is the opportunity cost of investing in stock market?

You will earn the accured interest of $2,000 if you choose tokeep it in the bank instead of investing it in stock market.Therefore, The opportunity cost of investing in stock market isthe accured interest of $2,000.

Remark:By the forward looking nature of the opportunity cost, $2,000 isnot counted into the opportunity cost since it has already beenexisted before the time of making decision.

SEEM2440A/B 7

Opportunity cost - Example 2

Option 1: Continue your own business with the annual expenseof $180,000;Option 2: Stop the business and go out to earn $75,000 peryear.What is the opportunity cost of continuing in business over thenext year ?

If you choose option 2, the amount of benefit you gain= earn $75,000 (the income you earn for choosing Option 2) +$180,000 (the amount you save for choosing Option 2)= $255,000.Therefore, the opportunity cost of continuing in business overthe next year is $255,000.

SEEM2440A/B 8

Cost terminology

Life-cycle cost is the sum of all costs related to a productor service during its life span.

Acquisition phase: Investment cost, capital investment,working capital.Operation phase: operation and maintenance cost,disposal cost.

SEEM2440A/B 9

Questions

If the capacity of an operation is significantly changed(e.g., a manufacturing plant), the fixed costs will alsochange. (T/F)A nonrefundable cash outlay (e.g., money spent on apassport) is an example of a sunk cost. (T/F)Stock you own from a bankrupt and out-of-businesscompany is an example of a ... cost. (Choose one:opportunity/sunk/direct/variable)

SEEM2440A/B 10

Answers

If the capacity of an operation is significantly changed (e.g.,a manufacturing plant), the fixed costs will also change. (T)A nonrefundable cash outlay (e.g., money spent on apassport) is an example of a sunk cost. (T)Stock you own from a bankrupt and out-of-businesscompany is an example of a ... cost. (sunk)

SEEM2440A/B 11

General economics concepts

Price-demand relationships1 Model 1: Selling price per unit (p) is a linear function of

demand (D)p = a bD for 0 D ab , and a > 0, b > 0

2 Model 2: Selling price per unit is independent of demandMaximizing total revenue (TR): (Use Model 1)TR = p.D = (a bD)D = aD bD2TR is a concave function. (Check the second derivative:d2TRdD2 = 2b < 0)

Find the maximizer D from the first derivative:dTRdD = a 2bD = 0 D = a2bMaximizing profit: (Use Model 1)Profit = TR TC, what is Total Cost (TC)?Assumption: TC = CF + cvDwhere CF is the fixed cost and cv is the variable cost perunit.Thus, Profit = aD bD2 (CF + cvD)

SEEM2440A/B 12

Maximizing profit contd

Maximizing profit:Profit = aD bD2 (CF + cvD) = bD2 + (a cv)D CFIn order for a positive profit to occur and to avoid negativedemand, a cv > 0 or a > cv.From the first derivative, we havedProfit

dD = a cv 2bD = 0 D = acv2b .Since d

2ProfitdD2 = 2b < 0 for all D, D = acv2b is the

maximizer of the Profit.

Remark: Companies may also gain insights fromBreakeven points other than the profit-maximizing points.At a breakeven point, total revenue is equal to total cost.

SEEM2440A/B 13

Breakeven analysis

Finding the breakeven points: (Model 1)Solve bD2 + (a cv)D CF = 0. We obtain two roots:D = (acv)[(acv)

24bCF]1/22b

Finding the breakeven points: (Model 2)p is independent of D.TR = p.DTC = CF + cvDTR = TC D = CFpcv (unique!)

SEEM2440A/B 14

SEEM2440A/B 15

SEEM2440A/B 16

Example 2.2

A company produces circuit boards used to update outdatedcomputer equipment. The fixed cost is $42,000 per month, andthe variable cost is $53 per circuit board. The selling price perunit is p = 150 0.02D. Maximum output of the plant is 4,000units per month.

Determine the optimum demand that maximizes profit?What is the maximum profit per month?What is the breakeven point?What is the companys range of profitable demand?

SEEM2440A/B 17

Solution:p = 150 0.02D, where a = 150 and b = 0.02; CF = 42, 000;cv = 53.a) D = acv2b = 2, 425.b) Profit = aD bD2 (CF + cvD) =150(2, 425) 0.02(2, 425)2 (42, 000+ 53(2, 425)) = $75, 612.50.c) D = (15053)[(15053)

24(0.02)(42,000)]1/22(0.02)

D1 = 481; D2 = 4, 369.

d) D is profitable in the range 481 4, 369.

SEEM2440A/B 18

Cost driven design optimization

The cost driven design optimization refers to how to designthe product in order to minimize the cost.General approach:

1 Identify the design variable that is the primary cost driver(e.g., the thickness of the material).

2 Write an expression for the cost model in terms of thedesign variable.

3 Find the optimum value of the design variable to have theminimum cost value.

SEEM2440A/B 19

Example 2.3

The cost of operating a large ship (CO) varies as the square ofits velocity (v); specifically, CO = knv2, where n is the trip lengthin miles and k is a constant of proportionality. It is known that at12 miles/hour the average cost of operation is $100 per mile.The owner of the ship wants to minimize the cost of operation,but it must be balanced against the cost of perishable cargo(CC), which the customer has set at $1,500 per hour. At whatvelocity should the trip be planned to minimize the total cost(CT ), which is the sum of the cost of operating the ship and thecost of perishable cargo?

SEEM2440A/B 20

Example 2.3

Solution:We need to find k. Cost per mile is COn = kv

2. At v = 12, cost permile is given as $100. Hence, k = 100

(12)2 = 0.694.We want to minimize CT where CT = CO + CC = knv2 + 1, 500nvdCTdv = 0 2knv 1, 500 nv2 = 0 v = (1,5002k )1/3 v = 10.25

miles per hour.(Note: Check the second derivative to verify CT is convex, i.e.,d2CTdv2 > 0.)

SEEM2440A/B 21

Present economy studies

When the time horizon over which projects and alternatives arecompared and evaluated is one year or less, and the influenceof the time on money can be ignored, these analyses are calledpresent economy studies.

SEEM2440A/B 22

Example 2.4

Ocean water contains 0.8 ounce of gold per ton.Method A:costs $210 per ton of water processed and will recover80% of the metal.Method B:costs $150 per ton of water processed and will recover60% of the metal.

The two methods require the same investment and are capableof producing the same amount of gold every day. If theextracted gold can be sold for $380 per ounce. Assume that thesupply of ocean water is unlimited.

On the basis of profit per ounce of gold extracted, whichmethod of extraction should be used?

SEEM2440A/B 23

Example 2.4

Solution:

Method A:Profit per ounce =$380 per ounce ($210 per ton of water)/(0.8 80%) =$51.88.Method B:Profit per ounce =$380 per ounce ($150 per ton of water)/(0.8 60%) =$67.50.

Select Method BAlternatively, since both methods have the same revenue, wecould also choose the method with the minimal cost.

SEEM2440A/B 24

Example 2.5

Machine A and Machine B are being considered for theproduction of a part of a product. The capital investmentassociated with the machines are about the same and can beignored. The important differences between the machines are

their production capacities (product rate availableproduction hours);their reject rates (% of parts produced that cannot be sold).

Machine A Machine BProduction rate 100 parts/hr 130 parts/hr

Hours available for production 7 hrs/day 6 hrs/dayReject rate 3 % 10 %

SEEM2440A/B 25

Example 2.5

The material cost is $6.00 per part, and all defect-free partsproduced can be sold for $12 each. The rejected parts have novalue. For either machine, the operator cost is $15.00 per hourand the variable overhead rate for traceable costs is $5.00 perhour.

Assume that the daily demand for this part is large enoughthat all defect-free parts can be sold. Which machineshould be selected?What would be the reject rate have to be for Machine B tobe as profitable as Machine A?

SEEM2440A/B 26

Example 2.5

Solution:Since both machines have different total daily revenue and totaldaily cost, we should base on the daily profit to select themachine.

Profit per day= Revenue per day Cost per day= (Production rate)(Production hrs)($12/part)

(1 reject rate)(Production rate)(Production hrs)($6/part)(Production hrs)($15/hr + $5/hr)

Machine A: Profit per day = $3,808 per day.Machine B: Profit per day = $3,624 per day.

Therefore, select Machine A.SEEM2440A/B 27

Example 2.5

The breakeven reject rate, X, for Machine B, can be obtained byequating the profits from Machine A and Machine B.

3808 = (130)(6)(12)(1 X) (130)(6)(6) (6)(15+ 5)X = 0.08.

So, the reject rate for Machine B can be no higher than 8% for itto be as profitable as Machine A.

SEEM2440A/B 28