Production Cost Analysis and Estimation Applied Problems

Production Cost Analysis and Estimation Applied Problems

Please complete the following two applied problems:

Problem 1:

William is the owner of a small pizza shop and is thinking of increasing products and lowering costs. William’s pizza shop owns four ovens and the cost of the four ovens is $1,000. Each worker is paid $500 per week.

Save your time - order a paper!

Get your paper written from scratch within the tight deadline. Our service is a reliable solution to all your troubles. Place an order on any task and we will take care of it. You won’t have to worry about the quality and deadlines

Order Paper Now

Workers employed

Qty of pizzas produced per week

0
1
2
3
4
5
6
7
8

0
75
180
360
600
900
1140
1260
1360

Show all of your calculations and processes. Describe your answer for each question in complete sentences, whenever it is necessary.

  1. Which inputs are fixed and which are variable in the production function of William’s pizza shop? Over what ranges do there appear to be increasing, constant, and/or diminishing returns to the number of workers employed?
  2. What number of workers appears to be most efficient in terms of pizza product per worker?
  3. What number of workers appears to minimize the marginal cost of pizza production assuming that each pizza worker is paid $500 per week?
  4. Why would marginal productivity decline when you hire more workers in the short run after a certain level?
  5. How would expanding the business affect the economies of scale? When would you have constant returns to scale or diseconomies of scale? Describe your answer.

Problem 2:

The Paradise Shoes Company has estimated its weekly TVC function from data collected over the past several months, as TVC = 3450 + 20Q + 0.008Q2 where TVC represents the total variable cost and Q represents pairs of shoes produced per week. And its demand equation is Q = 4100 – 25P. The company is currently producing 1,000 pairs of shoes weekly and is considering expanding its output to 1,200 pairs of shoes weekly. To do this, it will have to lease another shoe-making machine ($2,000 per week fixed payment until the lease period ends).

Show all of your calculations and processes. Describe your answer for each item below in complete sentences, whenever it is necessary.

  1. Describe and derive an expression for the marginal cost (MC) curve.
  2. Describe and estimate the incremental costs of the extra 200 pairs per week (from 1,000 pairs to 1,200 pairs of shoes).
  3. What are the profit-maximizing price and output levels for Paradise Shoes? Describe and calculate the profit-maximizing price and output.
  4. Discuss whether or not Paradise Shoes should expand its output further beyond 1,200 pairs per week. State all assumptions and qualifications that underlie your recommendation.

Carefully review the Grading Rubric (Links to an external site.)Links to an external site. for the criteria that will be used to evaluate your assignment.

10

Competitive Bids and Price Quotes

Learning Objectives

After reading this chapter, you should be able to:

• Discuss the nature of price setting where a buyer calls for competitive bids or tenders to supply goods and/or services that are not available “off-the-shelf.”

• Distinguish between three different modes of competitive bidding: fixed-price, cost-plus- fee, and incentive (risk-sharing) bid pricing.

• Apply the logic of incremental costs and revenues, and thus contribution analysis, to the competitive bid pricing problem, incorporating into the analysis any opportunity and future costs and revenues.

• Demonstrate that high search costs induce firms to set competitive bid prices using a standard markup over a standard cost base, with variations for nonmonetary consider- ations including aesthetics, politics, and risk attitudes of the buyer and seller.

• Explain how the firm can adjust its standard cost base and/or its standard markup rate to raise its success probability, capacity utilization rate, or profit rate, when these are below the levels that best serve the firm’s objectives.

©Apostrophe Productions/Getty Images

dou70192_10_c10_297-324.indd 297 11/1/12 4:29 PM

 

 

CHAPTER 10Introduction

Introduction

This is the fourth chapter concerned with the pricing decision of the business firm or other organization. In this chapter, we will look into competitive bidding, a differ-ent type of pricing decision problem that is quite commonly found in business-to- consumer (B2C), business-to-business (B2B), and business-to-government (B2G) transac- tions. Competitive bidding occurs in any market where a single buyer calls for a price quote (or tender) from one or more sellers. It is a single buyer situation in the sense that the buyer wants a special package of goods and services that is not stock standard and, thus, cannot simply or easily be purchased “off-the-shelf” from a supplier. Instead, the buyer calls for competitive bids from one or more potential suppliers and then compares the value proposition offered by each responding bidder. Consumers effectively call for com- petitive bids every time they want their car fixed, their teeth braced, their house painted, or any other kind of repair work or service that is specific to their particular preferences or requirements. Firms call for competitive tenders for stationery supplies, new vehicles or machines, component parts, consulting advice, new buildings, and so on, both to econo- mize on their time and to induce lower prices from suppliers who are most keen to get their business. Governments wanting roads and dams built, military hardware, fleets of cars supplied, and so on, similarly call for competitive bids from potential suppliers. In many cases, some, or even all, of the products required by the buyer are indeed available off-the-shelf, but when the buyer wants a complex combination of products and services it is more efficient if the supplier quotes on the whole package rather than have the buyer separately go around finding out prices and buying them individually (thus avoiding search costs and transactions costs). Quoting on the whole package also allows the sup- plier to reduce its profit margin on individual items in favor of winning a relatively large contract with an acceptable profit margin.

Each seller should expect that the buyer will ask for a competitive bid from other sup- pliers as well; although, in practice, buyers often ask for a single quote and if that seems fair they will accept that price without seeking additional quotes. Seller will realize that if their price quote is too high the business will go elsewhere. Conversely, if their price is too low they will get the job but may end up losing money on the job—this latter situ- ation is known as the winner’s curse.1 The pricing problem in competitive bid markets is that the seller must select a price that is high enough to provide a sufficient contribution to overheads and profit, yet low enough to ensure that it wins enough jobs to maintain a sufficient volume of work to ensure its survival. Sellers cannot expect to win every job they tender for. Since there is only one buyer and several potential sellers, sellers must operate on the basis of “win some and lose some,” but win enough to survive and hope- fully prosper.

1. The winner’s curse applies to a range of situations where the costs of completing the contract are uncertain. If potential suppliers each make estimates of their costs to complete, and one buyer inadvertently underestimates these costs and subsequently bids at a lower level, it is likely to win the contract, but later find out that its actual costs exceed the price tendered and it is forced to take a loss on the contract.

dou70192_10_c10_297-324.indd 298 11/1/12 4:29 PM

 

 

CHAPTER 10Section 10.1 Types of Competitive Bids and Price Quotes

In addition to the uncertainty the seller faces concerning the bids of other potential sellers, there is uncertainty surround- ing the cost of completing the job as specified. Unless the job is completely specified down to the last nut and bolt, and is oth- erwise straightforward, there will be uncertainty about exactly what repairs, services, parts, and labor will be required. Also, since the price is specified ini- tially and the work is done later, weather and other uncontrolla- ble disturbances may add unex- pected costs to the project. Thus, competitive bidding is a complex pricing practice faced by many firms in the economy and is espe- cially applicable to business-to- business (B2B) transactions.

10.1 Types of Competitive Bids and Price Quotes

There are two main types of competitive bids plus an intermediate (or combination) type. First, there is the fixed-price bid where the seller quotes a price and under-takes to complete the job for exactly that price regardless of unexpected variations in the costs of completing the project. In this case, the seller faces the entire risk of cost vari- ability. That is, if actual costs are higher than expected costs, the seller will make reduced profit (or even take a loss) on the project. The second main type is the cost-plus-fee bid, where the parties agree that the ultimate price will be the actual costs plus a predeter- mined profit margin for the seller, and in this case the buyer bears the entire risk of cost variability. In this case, the buyer may end up paying more than it initially expected the final price to be. In most B2B and B2G situations the buyer retains the right to an audit of the seller’s costs, but in B2C situations it is more commonly a “take it or leave it” tender, or the price is subject to renegotiation if the buyer thinks all the bids are too high. In this case, the buyer might receive the bids and then go back to one or more bidders and ask for variations, inclusions, or exclusions before choosing the winning tender.

©Hemera/Thinkstock

When quoting a price, sellers take a gamble. They must operate on the mentality of “win some and lose some” but sellers must win often enough to cover overhead costs and realize a profit.

dou70192_10_c10_297-324.indd 299 11/1/12 4:29 PM

 

 

CHAPTER 10Section 10.1 Types of Competitive Bids and Price Quotes

Fixed-price bids are more common where the items to be purchased can be priced sepa- rately, such as building materials, and where labor costs are more predictable. Alterna- tively, cost-plus bids are more common where the degree of uncertainty regarding costs is high. Repair work to automobiles, houses, and industrial plant and equipment typically proceeds on the latter basis because the actual labor time and parts required only become known as the repair work progresses and after the item to be repaired has been at least partially disassembled. The buyer’s problem with cost-plus bids is that the seller has little incentive to work fast and efficiently and thus minimize costs. Given that an audit of the seller’s costs will be time consuming and imperfect, due to the asymmetry of information, the final price to the buyer most likely will be higher than if the seller had a strong incen- tive to keep costs to the minimum.

In Table 10.1, we show the circumstances under which one of these bid types is likely to be preferred over the other. If costs are relatively easy to control, then the buyer will probably demand fixed-price bids and the sellers will need to bid in this mode to be considered by the buyer. Conversely, if costs are harder to control or are subject to unexpected increases, sellers will strongly prefer the cost-plus-fee mode and buyers will generally have to bid in this mode. Of course the bidding mode also depends on the relative bargaining power of the buyer. In some B2B and B2G situations a large and important customer might simply announce that it will only accept fixed-price bids.

Next, we consider the degree of risk aversion of the buyer and seller. If the seller is highly risk-averse, it will prefer not to bid in the fixed-price mode; and oppositely, if the buyer is highly risk-averse it will prefer not to receive cost-plus-fee bids. As we noted in Chapter 2, however, even risk-averse people can afford to be risk-neutral with regard to the next decision if they have a portfolio of risky assets. So, if the seller bids on many tenders over the year, it can afford to be risk-neutral with respect to any one tender, expecting that cost over-runs on one project tender might be offset by cost under-runs on other projects. The same applies from the buyer’s perspective: If the buyer routinely calls for tenders for simi- lar jobs, such as a taxi cab company repairing its cabs, it can afford to be risk-neutral with respect to any one cab repair. This is because some repairs will cost more and others will cost less, and on balance the jobs that cost less than expected will tend to offset the jobs that cost more than expected.

dou70192_10_c10_297-324.indd 300 11/1/12 4:29 PM

 

 

CHAPTER 10Section 10.1 Types of Competitive Bids and Price Quotes

Table 10.1: Factors influencing choice of fixed-price versus cost-plus bids

Factor Fixed-price bids Cost-plus-fee bids

Degree of cost uncertainty (and/or uncontrollability)

If costs are relatively easy to control, buyers will insist on this mode, and seller must tolerate the risk of cost variability.

If cost uncertainty is high, sellers will strongly prefer this mode, and buyers must tolerate the risk of cost variability.

Seller’s attitude to risk If highly risk-averse, the seller will not want to bid in this mode, unless required to (unless the seller can be risk-neutral due to many concurrent bids, in which case, the seller will tolerate these).

Whatever the degree of risk aversion (unless the seller is risk- neutral) the seller will prefer cost- plus bids since these push all the cost variability risk to the buyer.

Buyer’s attitude to risk If highly risk-averse, the buyer will strongly prefer this mode.

If highly risk-tolerant, the buyer will accept these, and indeed sellers will only want to bid in this mode if cost uncertainty is high.

Many trials of the same risk

If the seller routinely and repetitively bids on similar contracts, it can act as if it is risk- neutral (and submit fixed-price bids), since high-cost jobs will tend to be balanced by low-cost jobs.

If the buyer routinely and repetitively calls for similar tenders, it can act as if it is risk-neutral (and submit cost-plus-fee bids), since high-cost jobs will tend to be balanced by low-cost jobs.

Any request for tender (RFT) by a buyer will have an implicit or explicit quality expecta- tion built into the specifications of the work to be done. For example, if you ask for a quote for new tires on your car, or to fix your transmission, you expect the job to be completed to a particular level of quality. You want new tires that comply with road safety regulations, or you want your transmission to work properly again. The buyer will typically be happy enough to bear a legitimate cost over-run that is necessary to achieve that expected level of quality, even if the extra cost is unexpected. The problem is the asymmetry of infor- mation between the buyer and the seller: The buyer may not be sure that the extra costs charged by the seller are, in fact, necessary to achieve the desired level of quality. Where observation and monitoring of the project by the buyer is unsafe (as in the workshop) or would be expensive (in terms of incurred costs and opportunity costs) there needs to be a mechanism to ensure that the seller does indeed deliver the specified quality without leveraging the asymmetry of information to raise its profit at the expense of the buyer.2

2. By seeking multiple quotes, and more detail from each potential seller, the buyer is likely to reduce the information asymmetry by gaining more information about the production side of the job, including what the job is most likely to involve and what is likely to be the costs of labor, materials, parts, and so on.

dou70192_10_c10_297-324.indd 301 11/1/12 4:29 PM

 

 

CHAPTER 10Section 10.1 Types of Competitive Bids and Price Quotes

The third type of competitive bid provides one such mechanism. It is known as incentive bid pricing, and involves the buyer and seller agreeing on the bid price initially, but also agreeing to share any deviation from the expected cost in an agreed proportion. The vari- ance of actual costs from the expected costs is a cost over-run (if positive) or a cost under- run (if negative). For example, the share of the cost variance might be agreed to be 50% to each party, or in another case 70:30, with one party taking the larger proportion. In these situations, the seller has a substantial incentive to control costs, since it will have to pay a proportion of any cost over-run and this will reduce its profit from the job. Conversely, any cost under-run will also add to its profit because the seller will receive an agreed portion of that cost saving. The buyer’s incentive to pay more, to cover unexpected cost increases, is to achieve the desired level of quality associated with the job. On the other hand, if the repair is not as extensive as anticipated, or if weather and other uncontrollable factors play nicely, both the buyer and the seller benefit from the unexpected cost savings.

Apart from price and quality, the third major issue with competitive tenders is time to completion. Project management of a competitive bid transaction involves the efficient management of costs, quality, and the time it takes to complete the project. The buyer will typically want to set a deadline by which time the job is to be completed, and this deadline will usually be part of the tender specifications. Especially when the project is consid- ered to be urgent, such as completing major road works, bridges, and other public infra- structure (for B2G contracts); completing the manufacture and installation of new capital equipment to allow a business to get back in business (for B2B contracts); or completing a car repair or house renovation (for B2C contracts), the tender specifications might include a clause relating to penalties for late completion, and, conversely, for bonuses if the project is completed before the deadline. Note that such agreements are effectively risk sharing agreements as well, since production delays might be caused by both controllable factors (such as poor management by the seller) and uncontrollable factors such as bad weather and unavoidable delays in receiving materials. If the seller beats the deadline it receives a bonus for early completion, and indeed it may have put in place an incentive contract

with its own managers and employees to share this bonus with them if the contract is com- pleted prior to the deadline. The buyer will be happy to pay this bonus because it will allow early access to the completed project and the bonus will be less than the opportunity cost associated with waiting for the job to be completed. On the other hand, if completion of the project is delayed beyond the planned delivery date, the seller’s profit will be reduced to the extent of the penalties imposed and the buyer’s opportunity costs will be offset to some degree.

©iStockphoto/Thinkstock

Project management of a competitive bid transaction involves the efficient management of costs, quality, and the time it takes to complete the project.

dou70192_10_c10_297-324.indd 302 11/1/12 4:29 PM

 

 

CHAPTER 10Section 10.2 Incremental Costs and Revenues and the Optimal Bid Price

10.2 Incremental Costs and Revenues and the Optimal Bid Price

From the information above, we can deduce that it is very important that the prospec-tive seller carefully calculates the incremental costs that are expected to be associated with completing any contract that it wins through a competitive tender process. We saw in Chapter 6 that there are three main categories of incremental costs and revenues, namely present-period explicit costs and revenues, opportunity costs and revenues, and future-period costs and revenues. Let us now consider these in the competitive bid pricing problem.

The Incremental Costs of the Contract The incremental costs of the contract are all those costs, expressed in present value terms, that are incurred as a result of winning and completing the contract. Costs that have been incurred already (sunk costs) and costs that will be incurred whether this contract is won or lost (unavoidable costs) are not incremental costs for the purposes of the pricing deci- sion to be made.

Present-Period Explicit Costs

These include the direct and explicit costs associated with undertaking and completing the project. Included are such cost categories as direct materials, direct labor, and variable overheads that are due to the project under consideration. These may be estimated on the basis of the firm’s experience with completing similar contracts previously, modified to reflect present materials and labor prices, plus a trend factor if completion of the project will take several months or years. In addition, the contract may require the firm to pur- chase and deliver to the buyer capital equipment that needs to be purchased by the seller at current prices.

In some cases, the completion of the contract will necessitate the seller purchasing special machines, tools, or other items of capital equipment that are needed to complete the job but which remain the property of the seller after the contract is completed. If these items have a useful life remaining, it seems unfair to the buyer to charge the entire cost against the current contract. The appropriate way to deal with this is indeed to charge the entire cost of the item as an incremental cost to the buyer, but to also take account of possible future income or cost savings that are likely to be obtained subsequently. These should be counted as incremental revenues to reduce the incremental cost by an amount represent- ing the net present value of the future revenues and the future costs avoided (which we call “opportunity revenues”).

Another consideration is the capacity utilization rate of the firm. When the firm is at or near to its full capacity rate of output, it must consider the additional incremental costs that will be incurred if it wins the contract, such as overtime labor rates, outside contract- ing expenses, penalty charges associated with delays on other existing contracts, and new capital equipment that must be purchased to enable the contract to be undertaken and completed.

dou70192_10_c10_297-324.indd 303 11/1/12 4:29 PM

 

 

CHAPTER 10Section 10.2 Incremental Costs and Revenues and the Optimal Bid Price

Opportunity Costs

As we know, opportunity costs are the value of resources in their next-most-valuable use. Hence, if plant and equipment are lying idle, they have zero opportunity cost if they are used in the contract under consideration.3 On the other hand, if they are currently employed in a project that must be set aside, delayed, or cancelled to accommodate the contract under consideration, then the contribution to overheads and profits that these resources could have made must be counted as an opportunity cost for the project under consideration. For example, a firm producing relatively low-value items to build up its inventories for supply to wholesale and retail customers may decide to bid on a tender and if successful would stop producing these items, utilizing its resources more profitably on the contract under consideration. The contribution foregone is an opportunity cost of the contract under consideration. If the alternative production is simply delayed and this simply causes revenues from the sale of those items to be delayed, the opportunity cost is simply the interest income foregone on the revenues involved.

Future Costs

Future incremental costs may include the effects of customer ill will, deteriorating labor relations or supplier relations, and legal recourse by dissatisfied buyers or government prosecutors. Ill will (or ill feeling) toward the seller may manifest itself in the expected present value of contribution (EPVC) of future contracts that are lost if this current con- tract is undertaken. For example, undertaking a difficult or politically contentious contract today might come back to haunt the firm if it upsets employees, suppliers, or government regulators. To the extent that such future costs are envisioned, the firm should allow for them in the current calculation of incremental costs. For example, a trucking company that wins a contract to move the city’s garbage during a garbage-workers’ strike may well expect to lose business in the future from people and organizations who are sympathetic to labor unions.

In practice, it is not likely to be worth the search costs required to carefully estimate every single opportunity and future incremental costs associated with a particular competi- tive tender, nor is the bidding firm likely to have the time required for this information search activity, since RFTs are typically issued with only a short time for potential sellers to respond. More realistically the bidding firm will simply add a “cushion” (or safety mar- gin) to its explicit incremental costs to reflect its recognition that there are opportunity and future incremental costs involved.