Life-Cycle Costs.

The products, goods, and services designed by engineers all progress through a life cyclevery much like the human life cycle. People are conceived, go through a growth phase, reach their peak during maturity, and then gradually decline and expire. The same general pattern holds for products, goods, and services. As with humans, the duration of the dif- ferent phases, the height of the peak at maturity, and the time of the onset of decline and termination all vary depending on the individual product, good, or service. Figure 2-3 illustrates the typical phases that a product, good or service progresses through over its life cycle.

Life-cycle costing refers to the concept of designingproducts, goods, and serviceswith a full and explicit recognition of the associated costs over the various phases of their life cycles. Two key concepts in life-cycle costing are that the later design changes are made, the higher the costs, and that decisions made early in the life cycle tend to "lock in" costs that are incurred later. Figure 2-4 illustrates how costs are committed early in the product life cycle-nearly 70-90% of all costs are set during the design phases. At the same time, as the figure shows, only 10-30% of cumulative life-cycle costs have been spent.

FIGURE 2-3 Typical life cycle for products, goods and services.

 

FIGURE 2-4 Cumulativelife-cycle costs committedand dollars spent.

FIGURE 2-5 Life-cycle design change costs and ease of change.

Figure 2-5 reinforces these concepts by illustrating that downstreamproduct changes' are more costly and that upstream changes are easier (and less costly) to make. When planners try to savemoney at an early design stage, the result is often a poor design, calling for change orders during construction and prototype development. These changes, in turn, are more costly than working out a better design would have been.

FromFigures2-4 and 2-5we seethat the time to consider all life-cycleeffects, andmake design changes, is during the needs and conceptual/preliminary design phases-before a lot of dollars are committed. Some of the life-cycle effects that engineers should considerat design time include product costs for liability, production, material, testing and quality assurance, and maintenance and warranty.Other life-cycle effects include product features based on customer input and product disposal effects on the environment. The key point is that engineers who design products and the systems that produce them should consider all life-cycle costs. . ..

Cash Costs Versus Book Costs.

A cash cost requires the cash transaction of dollars "out of one person's pocket" into "the pocket of someone else." When you buy dinner for your friends or make your monthly automobile payment you are incurring a cash cost or cash flow.Cash costs and cash flows are the basis for engineering economic analysis.

Book costs do not require the transaction of dollars "from one pocket to another." Rather, book costs are cost effects from past decisions that are recorded "in the books" (accounting books) of a firm. In one common book cost, asset depreciation (which we discuss in Chapter 11), the expense paid for a particular business asset is "written off" on a company's accounting sy'stemover a number of periods. Book costs do not ordinarily represent cash flows and thus are not included in engineering economic analysis. One exception to this is the impact of asset depreciation on tax payments-which are cash flows and are included in after-tax analyses.

Recurring and Nonrecurring Costs.

Recurring costs refer to any expense that is known, anticipated, and occurs at regular intervals. Nonrecurring costs are one-of-a-kind expenses that occur at irregular intervals and thus are sometimes difficult to plan for or anticipate from a budgeting perspective.

Examples of recurring costs include those for resurfacing a highway and reshingling a roof. Annualexpenses formaintenance and operation are also recurring expenses.Examples of nonrecurring costs include the cost of installing a new machine (including any facility modifications required), the cost of augmenting equipment based on older technology to restore its usefulness, emergency maintenance expenses, and the disposal or close-down costs associatedwith ending operations.

In engineering economic analyses recurring costs aremodeled as cash flows that occur at regular intervals.(such as every year or every 5 years.) Their magnitude can be estimated, and they can be included in the overall analysis. Nonrecurring costs can be handled easily in our analysis if we are able to anticipate their timing and size. However, this is not always so easy to do.

Opportunity Costs.

An opportunity cost is associated with using a resource in one activity instead of another.

Every time we use a business resource (equipment, dollars,manpower, etc.) in one activity, we give up the opportunity to use the same resources at that time in some other activity.

Every day businesses use resources to accomplish various tasks-forklifts are used to transport materials, engineers are used to design products and processes, assembly lines are used to make a product, and parking lots are used to provide parking for employees' vehicles. Each of these resources costs the company money to maintain for those intended purposes. However, that cost is not just made up of the dollar cost, it also includes the opportunity cost. Each resource that a firmowns can feasibly be used in several alternative
ways. For instance, the assembly line could produce a different product, and the parking lot could be rented out, used as a building site, or converted into a small airstrip. Each of these alternative uses would provide some benefit to the company.

A firmthat chooses to use the resource in one way is giving up the benefits that would be derived from using it in those other ways. The benefit that would be derived by using the resource in this "other activity" is the opportunity cost for using it in the chosen activity.Opportunity cost may also be considered a forgone opportunity cost because we are forgoing the benefit that could have been realized. A formal definition of opportunity cost might be:

An opportunity cost is the benefit that is forgone by engaging a business resource in a chosen activity instead of engaging that same resource in the forgone activity.

As an example, suppose that friends invite a college student to travel through Europe over the summer break. In considering the offer, the studentmight calculate all the out-of-pocket cash costs that would be incurred.
Cost estimates might be made for items such as air travel, lodging, meals, entertainment, and train passes. Suppose this amounts to $3000 for a to-week period. After checking his bank account, the student reports that indeed he can afford the $3000 trip. However, the true cost to the student includes not only his out-
of-pocket cash costs but also his opportunity cost. By taking the trip, the student is giving up the opportunity to earn $5000 as a summer intern at a local business. The student's total cost will comprise the $3000 cash cost as well as the $5000 opportunity cost (wages forgone)-the total cost to our traveler is thus $8000.

A distributor of electric pumps must decide what to dowith a "lot" of old electric pumps purchased 3 years ago. Soon after the distributorpurchased the lot, technology advancesmade 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.

Looking at the data, the pricing manager has concluded that the price should be set at $8000.

This is the money that the firmhas "tied up" in the lot of old pumps ($7000 purchase and $1OOO storge), and it was reasoned that the company should at least recover this costs. Furthermore, the pricing manager has argtied that an $8000 price would be $1500 less than the list price from 3 years ago, and it would be $4000 less than what a lot of new pumps would cost ($12,000 - $8000).What would be your advice on price?

SOLUTION

Let's look'more closely at each of the data items.

Distributor's purchase price 3 years ago: This is a sunk cost that should not be considered in setting the price today.

Distributor's storage costs to date: The storage costs for keeping the pumps in inventoryare sunk costs; that is, they have been paid. Hence they should not influence the pricing decision.

Distributor's listprice 3 years ago: If there have been no willing buyers in the past 3 years at this price, it is unlikely that a buyer will emerge in the future. This past list price should have no influence on the current pricing decision. ~

Current listprice of newerpumps: Newer pumps now include technology and features that have made the older pumps less valuable. Directly comparing the older pumps to those with new technology is misleading.

However, the price of the new pumps and the value of the new features help determine the market value of the old pumps.

Amount offeredfrom a buyer 2 years ago: This is a forgone opportunity. At the time of the offer, the company chose to keep the lot and thus the $5000 offered became an opportunity cost for keeping the pumps. This amount should not influence the current pricing decision.

Current price the lot could bring: The price a willing buyer in the marketplace offers is called the asset's market value. The lot of old pumps in question is believed to have a current market value of $3000.

From this analysis, it. is easy to see the flaw in the' pricing manager's reasoning. In an engineering economist analysis we deal only with today's and prospectivefuture opportunities.

It is impossible to go back in time and change decisions that have been made. Thus, the pricing manager should recommend to the distributor that the price be set at the current value that a buyer assigns to the item: $3000.

Sunk Costs.

A sunk cost is money already spent as a result of a past decision. Sunk costs should be disregarded in our engineering economic analysis because current decisions cannot change the past. For example, dollars spent last year to purchase new production machinery is money that is sunk: the money allocated to purchase the production machinery has already been spent-there is nothing that can be done now to change that action.

As engineering economists we deal with present and future opportunities.

Many times it is difficult not to be influenced by sunk costs. Consider 100 shares of stock in XYZ, Inc., purchased for $15 per share last year. The share price has steadily declined over the past 12months to a price of $10 per share today. Current decisions must focus on the $10 per share that could be attained today (as well as future price potential), not the $15 per share that was paid last year.The $15 per share paid last year is a sunk cost and has no influence on present opportunities.

As anotherexample,whenReginawas a sophomore, shepurchased a newest-generation laptop from the college bookstore for $2000. By the time she graduated, the most anyone would pay her for the computer was $400 because the newest models were faster, cheaper and had more capabilities. For Regina the original purchase price was a sunk cost that has no influence on her present opportunity to sell the laptop at its current market value ($400).

Fixed, Variable, Marginal, and Average Costs: Examples.

Fixed costs are constant or unchanging regardless of the level of output or activity. In contrast, variable costs depend on the level of output or activity. A marginal cost is the variable cost for one more unit, while the average cost is the total cost divided by the number of units.

For example, in a production environment fixed costs, such as those for factory floor space and equipment, remain the same even though production quantity, number of employees, and level ofwork-in-processmay vary.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.

As another example, many universities charge full-time students a fixed cost for 12 to 18 hours and a cost per credit hour for each credit hour over 18.Thus for full-time students who are taking an overload (> 18 hours), there is a variable cost that depends on the level of activity.

This example can also be used to distinguish between marginal and average costs. A marginal cost is the cost of one more unit. This will depend on how many credit hours the student is taking. If currently enrolled for 12 to 17 hours, adding one more is free. The marginal cost of an aditional credit hour is $0.However, if the student is taking 18 or more . ours, then the marginal cost equals the variable cost of one more hour.

To illustrate average costs, the fixed and variable costs need to be specified. Suppose the cost of 12 to 18 hours is $1800 per term and overload credits are $120/hour.If a student takes 12 hours, the average cost is $1800/12 = $150 per credit hour. If the student were to take 18 hours, the average cost decreases to $1800/18 = $100 per credit hour. If the student takes 21 hours, the average cost is $102.86 per credit hour [$1800 + (3 x $120) /21].

Average cost is thus calculated by dividing the total cost for all units by the total number of units. Decision makers use average cost to attain an overall cost picture of the investment on a per unit basis.

Marginal cost is used to decidew~~therthe additional unit should bemade, purchased, or enrolledin.For the full-time'studentatourexampleuniversity,themarginalcost of another credit is $0 or $120 depending on how many credits the student has already signed up for.

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,andrefreshmentsonthe bus forhis customers.He gathereddata andcategorized the predicted expenses as either fixed or variable.

Develop an expression of DK's total fixed and total variable costs for chartering this trip.

SOLUTION
DK's fixed costs will be incurred regardless of howmany people sign up for the trip (even if only one person signs up!). These costs include bus rental, gas and fuel expense, apd the cost to hire a driver:

Total fixed costs = 80 + 75 + 20 + 50 = $225

DK's variable costs depend on how many people sign up for the charter, which is the level of activity.Thus for event tickets and refreshments, we would write

Total variable costs = 12.50 + 7.50 = $20 per person.

From Example 1 we see how it is possible to calculate total fixed and total variable costs. Furthennore, these values can be combined into a single total cost equation as follows:

Total cost =Total fixed cost + Total variable cost          (2-1)

The relationship between total cost and fixedand variable costSare shownin Figure 2-1.

The fixed-costportion of $3000 is the same across the entire range of the output variable x.

Often, the variable costs are linear (y equals a constant times x); however, the variable costs can be nonlinear. For example, employees are often paid at 150%of their hourly rate for overtime hours, so that production levels requiring overtime have higher variable costs.

FIGURE 2-1 Fixed, variable, and total costs.

Total cost in Figure2-1 is a fixed cost of $3000 plus a variable cost of $200 per unit for straight-time production of up to 10 units and $300 per unit for overtime production of up to 5 more units.

Figure 2-1 can also be used to illustrate marginal and average costs. At a volume of 5 units the marginal cost is $200 per unit, while at a volume of 12units the marginal cost is $300 per unit. The respective average costs are $800 per unit, or (3000 + 200 x 5)/5, and $467 per unit, or (3000 + 200 x 10 + 300 x 2)/12.

EXAMPLE 2

In Example 1, DK develop~dap overall total cost equation for his business expenses.Now he
wants to evaluate the potential to make money from this chartered bus trip.

SOLlJTION 

We use Equation 2-1 to findDK's total cost equation:

Using this relationship, DK can calculate the total cost for any number of people - up to the capacity of the bus. What he lacks is a revenue equatiQnto offset his costs. DK's total revenue from this trip can.be expressed as:

DK believes that he could attract 30 people at a charter ticket price of $35. Thus

So, if  30 people take the charter, DKwill net acprofit of $225. This somewhat simplastic.analysis ignores the value of DK's time-he would have to "pay himself" out of his $225 profit.

InExamples 1 and  2 DKdeveloped totalcost andtotal revenueequations to describe the charter bus proposal. These equations can be used to create what is called aprofit-loss breakeven chart (see Figure 2-2).Both the costs and revenuesassociatedwith various levels of output (activity) are placed on the same set of x-y axes. This allows one to illustrate a breakevenpoint (in terms of costs and revenue) and regions of profit and loss for some business activity.These terms can be defined as follows.

Breakeven point: The level of business activity at which the total costs to provide the product, good, or service are equal to the revenue (or savings) generated by providing the service. This is the level at which one "just breaks even."

Profit region: The output levelof the variablex greater than the breakevenpoint,where total revenue is greater than total costs.

Loss region: The output level of the variable x less than the breakeven point, where total costs are greater than total revenue. .

Notice in Figure 2-2 that the breakeven point for the number of persons on the charter trip is 15 people. For more than 15 people, DK will make a profit. If fewer than 15 sign up

FIGURE 2-2 Profit-loss breakevenchart for Examples 1 and 2.

there will be a net loss. At the breakeven level the total cost to provide the charter equals the
revenue received fromthe 15passengers.Wecan solve for the breakevenpoint by settingthe
total costs and total revenue expressions equal to each other and solving for the unknown
value of x. From Examples 2-1 and 2-2:

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, contractor and subcontractor labor, training, computer hardware and software,material handling, fixturesand tooling, datamanagement, and technical support, aswell as general support costs (overhead). In this sectionwedescribe several concepts for classifying and understanding these costs.

⇒Fixed, Variable, Marginal, and Average Costs: Examples.

⇒Sunk Costs.

⇒Opportunity Costs.

⇒Recurring and Nonrecurring Costs.

⇒Cash Costs Versus Book Costs.

⇒Life-Cycle Costs.

 

Engineering Costs and Cost Estimating: Webvan Hits the Skids.

Webvan, an on-line supermarket, aimed to revolutionize the humdrum business of selling groceries. Consumers could order their weekly provisions with a few clicks and have the goods delivered right to their door. It sounded like a great business plan, and the company had no trouble attracting capital during the dotcom boom of the late 1990s.Eager investors happily poured hundreds of millions into the company.

With that kind of money to spend, Webvan investedlavishly in building infrastructure, including large warehouses capable of filling 8000 orders a day. The firm rapidly expanded to servemultiple cities nationwide and even acquired a competing on-line company, Home Grocer.

But the hoped-for volume of customers never materialized. By early 2000, Internet grocers hadmanaged to capture only a small part of the food salesmarket-far short of the 20%they had anticipated. When the dotcom boom went bust, Webvan suddenly looked much less attractiveto investors,who quickly snapped their wallets shut.

Without newmoney coming in,Webvan suddenly had to face an uncomfortable fact: it was spending far more than it was earning. Finally, in 2001, Webvan went bankrupt. A rival on-line grocer, Peapod, narrowly escaped the same fate-but only because a Dutch retailer was willing to buy the company and continue pumping money into it. Interestingly, at the same timeWebvanwas burning through millions in dotcom cash, a bricks-and-mortar supermarket chain in Britain called Tesco also decided to get into the on-line grocery business. Tesco invested around $56 million in a computerized processing system and, instead of building warehouses, had employees in each store walk the aisles filling orders. UnlikeWebvan,Tescomade a profit.