Managerial Economics Discussion 2
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ManagerialEconomicsweek2.docx· READ Chapter 4: Extent (How Much) Decisions
· READ Chapter 5: Investment Decisions: Look Ahead and Reason Back
Chapter Introduction
In 2016, Georgetown Public Media was trying to decide how to allocate its $120,000 marketing budget across three radio stations.
· 89.3 WPGL News wanted the budget allocated by audience size. As it is larger than the other two stations, this would give it $60,000:
· (1)
to host panels on topical issues to increase the diversity of its audience and
· (2)
to advertise on buses to reach people where they are listening—in their cars.
· However, over the past three years, WPGL expenses have risen, and last year they were 40% above revenue.
· 91.9 WPGK, the independent station (blues, jazz, world music, and Americana), surveyed its listeners and found that they have a passion for live music. Consequently, WPGK wants $40,000:
· (1)
to host a backstage tent at a local music festival where it can do livestream interviews with musicians and
· (2)
to add dates to its successful Winter Wednesday concert series.
· 90.5 WPOL Classical has the smallest audience of the three, but wants $60,000 in order to collaborate with WPGK Radio on joint marketing events to attract a new and more diverse audience. A recent national study showed tremendous potential for growth because young nonwhite consumers said they love classical music, but had never heard of their local public radio station. In addition, a $10,000 marketing expenditure last year caused a 15% increase in membership.
QUESTION: Obviously, the sum of the three requests is bigger than the advertising budget (60 + 40 + 60 > 120). If you were in charge, how would you allocate the money?
The second step is to figure out where a dollar of advertising will have the biggest impact. The poll results suggest if you could somehow inform young nonwhite listeners about the classical station, they would become listeners. In addition, the effects of WPOL marketing efforts last year suggest that increases in the advertising budget would increase audience size.
Finally, if we want to fully fund the classical station, should you reduce the news advertising budget? The fact that the news station is losing money is irrelevant. We are concerned only with increasing audience size, as each new listener has the same 15% probability of becoming a member. As is common in decisions like this, there is no good evidence on whether allocating less money to news station advertising would affect its audience size.
In this case, Georgetown Public Media decided to fully fund the requests of the alternative and classical stations, and gave only $20,000 to the news station. Based on this allocation, it expects 9,280 new listeners, who are expected to contribute $194,880 to the organization.
The purpose of this chapter is to show you how to make extent decisions like this one.
4.1Fixed Costs Are Irrelevant to an Extent Decision
In 2005, Memorial Hospital’s chief executive officer (CEO) conducted performance reviews of the hospital’s departments. As part of this review process, the chief of obstetrics proposed increasing the number of babies being delivered by his department. The CEO examined the department’s financial statements and found that the average cost (AC) of deliveries ($5000) was above average revenue ($4300). He asked what seemed like a reasonable question, “Why would we want to do more of something that is losing $700 every time we do it?”
As you should now recognize, the CEO is committing the fixed-cost fallacy. As we learned in Chapter 3, the relevant costs and benefits of this extent decision (“how many babies should the hospital deliver”) are those that vary with the consequences of the decision.
Fixed costs are irrelevant to an extent decision.
If the CEO had started with a question like “Should we increase output from 500 to 501 deliveries?” he might have avoided the mistake. The answer depends only on the extra or marginal cost of another delivery, $3000. This is the relevant cost of an extent decision.
4.2Marginal Analysis
To analyze extent decisions, we break down the decision into small steps and compute the costs and benefits of taking another step. If the benefits of taking another step are greater than the costs, then take another step. Otherwise, step backward.
We call this marginal analysis. To illustrate, we use it to answer the question, “Should I sell more?” where marginal analysis applies to both costs and revenues.
Marginal cost (MC) is the additional cost incurred by producing and selling one more unit.
Marginal revenue (MR) is the additional revenue gained from selling one more unit.
If the benefit of selling another unit (MR) is bigger than the MC, then sell another unit.
Sell more if MR > MC; sell less if MR < MC. If , you are selling the right amount (maximizing profit).
Marginal analysis works for any extent decision, like whether to change the level of advertising, the quality of service, the size of your staff, or the number of parking spaces to lease. The same principle applies to each decision—do more if MR > MC, and do less if MR < MC.
Note that marginal analysis points you in the right direction, but it does not tell you how far to go. The reason for this is that MC typically rises, and MR falls, with additional steps. So after taking a step, you have to recompute MC and MR to see whether further steps are warranted.
To illustrate how to use marginal analysis, let’s return to Georgetown Public Media’s problem.
First, let’s try to estimate the MR of adding another listener. From the information in the story, the MR of adding another listener can be computed as the probability of becoming a member times the revenue expected from each member, . This is a crude estimate (some listeners may donate more), but it is the only information we have.
As is often the case, even if you have good information about MR or MC, information about the other is harder to come by. In this example, we have only a little bit of information about the MC of adding listeners, from the classical station, when last year’s $10,000 increase in advertising led to a 15% increase in listeners. If this 15% represents 2,000 new listeners, then the MC of adding a classical station listener is $5/listener, computed as $10,000/2,000, sometimes called customer acquisition cost.
Because MR > MC or $21 > $5, marginal analysis tells you to increase classical advertising, but it doesn’t tell you how far to go. Rather, you have to get there by taking steps. In this case, you might double last year’s budget and measure the effect.
|
Advertising |
MR |
MC |
Listeners |
Profit |
|
$10,000 |
$21 |
$5.00 |
2000 |
$32,000 |
|
$20,000 |
$21 |
$10.00 |
3386 |
$51,112 |
|
$40,000 |
$21 |
$20.00 |
4773 |
$60,224 |
|
$42,000 |
$21 |
$21.00 |
4870 |
$60,274 |
|
$44,000 |
$21 |
$22.00 |
4963 |
$60,227 |
From the table, you can see that the optimal level of advertising is $42,000, where the MC of acquiring a customer ($21) is equal to the MR of acquiring a customer. If you advertise more than this, the number of listeners increases, but profit falls because MC is higher than MR. Note also that as the advertising level increases, its effectiveness drops. This is reflected in the increasing MC of acquiring another customer, which is typical of many extent decisions. You pick the low-hanging fruit first (where the MC is low), and then you move to the more costly, higher-hanging fruit (where the MC is higher).
Typically, MR falls, and MC rises, the more you do.
For another application, suppose you are trying to decide when to cut down a tract of trees. As you know by now, always begin your analysis with a question, “Should I harvest the trees now or wait a year?” Because this is an extent decision, break the decision into steps, where a step is a year. Suppose further that the trees are worth $100 today and are growing at an 8% rate. Next year, they will be worth $108.
If you harvest the trees today you would earn, say $100, from selling the timber. If your investments earn 5%, after a year, you would have $105. On the other hand, if you let the trees grow, and the trees are growing at an 8% rate, after a year you would have timber worth $108. Don’t harvest.
In general, if the trees grow faster than your investments you earn more by letting them grow. As trees grow older, their growth rate will eventually fall below what you can make by investing your money. At this point, harvest the trees.
4.3Deciding between Two Alternatives
Managers often have to decide between competing strategies to achieve the same end. To see how to use marginal analysis in this setting, let’s return to the problem facing Georgetown Public Media. Imagine that the manager has $100,000 to split between the news and classical stations.
This question defines the relevant costs: the opportunity cost of spending one more dollar on advertising for the classical station is the forgone opportunity to spend that dollar on advertising for the news station. To increase profit, increase spending on whichever medium has a higher marginal impact and “pay” for the increase by reducing spending on the other. To do this, compute the marginal customer acquisition cost for both alternatives, and then shift spending toward the cheaper one. This will increase profit even if you don’t know the benefit of acquiring a customer. All you need to know is whether shifting dollars increases the total number of customers.
In the following table, we vary the amount going to the classical station. In the first row, with only $10,000 going to classical advertising, we see that the MC of adding a listener is $5. In contrast, the MC of adding a news listener is $67.50. Since it is cheaper to add customers by advertising on the classical station, increase the budget to the classical station and pay for it by reducing spending on news. In the second row, after shifting $10,000 to classical advertising, we see that the total number of listeners (last column) increases. Keep shifting dollars from news to classical, until you find the advertising split that maximizes the number of listeners.
The optimal advertising split is $60,000 going to classical and $40,000 going to news. At this split, the MC of adding consumers is the same for each medium, and the audience size is maximized (8,240). Although shifting more than this increases the number of classical listeners, the increase is not enough to offset the decline in news listeners.
|
Classical |
News |
Total |
||||
|
Advertising |
# Listeners |
MC |
Advertising |
# Listeners |
MC |
# Listeners |
|
$10,000 |
3,386 |
$5.00 |
$90,000 |
3,430 |
$67.50 |
6,816 |
|
$20,000 |
4,197 |
$10.00 |
$80,000 |
3,273 |
$60.00 |
7,470 |
|
$30,000 |
4,773 |
$15.00 |
$70,000 |
3,095 |
$52.50 |
7,867 |
|
$40,000 |
5,219 |
$20.00 |
$60,000 |
2,889 |
$45.00 |
8,108 |
|
$50,000 |
5,584 |
$25.00 |
$50,000 |
2,646 |
$37.50 |
8,229 |
|
$60,000 |
5,892 |
$30.00 |
$40,000 |
2,348 |
$30.00 |
8,240 |
|
$70,000 |
6,159 |
$35.00 |
$30,000 |
1,965 |
$22.50 |
8,124 |
|
$80,000 |
6,394 |
$40.00 |
$20,000 |
1,424 |
$15.00 |
7,819 |
|
$90,000 |
6,605 |
$45.00 |
$10,000 |
500 |
$7.50 |
7,105 |
Of course, it is very rare to have this kind of detailed information about a marginal change. Typically, you will have only the kind of information available to Georgetown Public Media. To gain more information about the effectiveness of your advertising, you might want to increase classical advertising and measure the gain in listeners. Then reduce news advertising, and measure the loss in listeners. By changing the advertising levels separately, you may be able measure the marginal effectiveness of advertising expenditures on each station.
With advertising, there may also be subtle measurement issues. For example, some psychological models of advertising suggest that for fewer than four exposures, advertising has no effect on decisions. The marginal effectiveness of that fourth exposure is thus very large, but the average effectiveness of the entire advertising budget would be much lower.
For another application of marginal analysis, let’s figure out how to reduce costs at a Fortune 50 company that produces textile products at various manufacturing plants in Latin America. The plants operate as cost centers, meaning that plant managers are rewarded for reducing costs of production. To evaluate the performance of its plants, the firm measures production using standard absorbed hours (SAH). For each garment produced, the firm computes the time required to complete each step in the manufacturing process. Complex garments like overalls require more time and thus are assigned a higher SAH (15 minutes) than simple garments like T-shirts (2 minutes). The output of a factory is thus measured in SAH, and each factory is evaluated based on how much it costs to get one hour’s worth of production in terms of cost per SAH.
Obviously, measuring output in this way allows managers to identify lower-cost factories. Suppose that a factory in the Yucatan, Mexico operates at $20/SAH, and a factory in the Dominican Republic operates at $30/SAH. As a manager, do you think you could save $10/SAH by shifting production from the Dominican Republic to the Yucatan?
Before answering this question, you might want to remember the big lesson of Chapter 3 , that costs are defined by the decision you are trying to make. Here you are trying to decide whether to shift output from one factory to another. If the costs used to compute cost per SAH include overhead that cannot be avoided, then you won’t save on overhead as you shift production—overhead is irrelevant for this extent decision. So, first you must adjust the cost per SAH to exclude fixed costs, lest you commit the fixed-cost fallacy.
Second, make sure that cost per SAH is a good proxy for MC. To check whether this is so, make sure that when you reduce output in the Dominican Republic, you really are avoiding close to $30/SAH, and make sure that you are incurring only about $20/SAH as you shift production to the Yucatan. If this is not correct, then cost per SAH is a poor proxy for MC.
If you are convinced that $10 per SAH is a reasonable proxy for difference in MCs between the two factories, you can make money by shifting production. And, as above, marginal analysis tells you what direction to go (shift production to the factory with the lower MC), but it doesn’t tell you how far to go. Decide how far to go by taking a step and then re-measuring MC to determine whether to take another step.
4.4Incentive Pay
How hard to work is an extent decision, so marginal analysis can be used to design incentives to encourage hard work. To illustrate this idea, suppose you are a landowner evaluating two different bids for harvesting a tract of timber containing 100 trees. One bid is for $150 per tree, and the other bid is for $15,000 for the right to harvest all the trees. Which bid should you accept?
Although both bids have the same face value, they have dramatically different effects on the logger’s incentives. If you charge a fixed fee of $15,000 for the right to harvest all the trees, the logger treats the price paid to the landowner as a fixed or sunk cost. He should, by the reasoning in Chapter 3, ignore that cost when deciding how many trees to cut down. In other words, under the fixed-fee contract, the marginal payment to the landowner of cutting down another tree is zero. This gives the logger an incentive to cut down trees as long as the value of each tree is greater than the cost of harvesting it. Under this contract, the logger will end up cutting down all the trees that are profitable to cut down.
On the other hand, if you charge the logger a royalty rate of $150 per tree, the logger will cut down only those trees that can generate profit greater than $150. If the forest is a mix of pine worth $200 per tree and fir worth $100 per tree, the logger will harvest only the pine and leave the fir. Consequently, the landowner will receive less money under a royalty contract. The incentive effect of a royalty rate is analogous to that of a sales tax because it deters some wealth-creating transactions, that is, the fir trees are not harvested.
The same idea can be applied to the problem of motivating salespeople. To see this, suppose you are considering two different compensation schemes. One is based on a 10% commission rate, where the salesperson earns 10% on sales she makes. The other pays a 5% commission rate plus a $50,000 per year flat salary. Each year, you expect salespeople to sell about 100 units at a price of $10,000 per unit. Which compensation scheme should you use?
As in our logging example, the two payment schemes have the same face value but dramatically different effects on incentives. If you pay a 10% commission, the marginal benefit to the salesperson of making another sale is $1,000. If you pay a 5% commission, the marginal benefit is only $500. If some sales are relatively easy to make (i.e., the salesperson gives up less than $500 worth of time and effort to make them), and some sales are relatively difficult to make (i.e., they require at least $800 worth of effort), then only the easy sales will be made under the 5% commission. Both the easy and difficult sales will be made under the 10% commission. The $50,000 salary is fixed with respect to sales effort, and so does not affect behavior.
4.5Tie Pay to Performance Measures That Reflect Effort
Measuring performance is a critical part of any organization, as the following story illustrates. In 1997, a 50-year-old chief operating officer (COO) with a bachelor’s degree in journalism and a law degree managed a consulting firm with 10 account executives. The COO was in charge of keeping clients happy and ensuring that the account executives were working in the best interests of the company. The COO earned a flat salary of $75,000.
After taking classes in human resources, economics, and accounting, the CEO recognized that the usual accounting profits were not motivating the COO to work harder. He sat down with his COO, and together they designed a new metric. All revenues counted toward the COO’s “profit” goal. But only the expenses that the COO controlled directly—like compensation and office expenses—were “charged” against his profit metric. All overhead items, like rent, were placed in another budget because the COO could not control them; that is, they were “fixed” with respect to his effort.
The CEO and the COO both agreed that, without much effort, the COO could earn $150,000 each quarter. But earning more would take extraordinary effort. To motivate the COO, they agreed on an incentive compensation scheme that paid the COO one-third of each dollar that the company earned above $150,000.
After making the change, the COO’s compensation jumped to $177,000—an increase of 136%—but the firm’s revenues also jumped from $720,000 to $1,251,000—an increase of 74%. A good economy certainly contributed to the increase, but the compensation plan also helped. Revenue increased because the COO pushed hard to make and exceed earnings goals and, for the first time, he worried about expenses. For example, he attempted to contain costs by asking why phone bills were so high.
Along with changing the COO’s compensation scheme, the CEO also moved to a system of incentive pay for the account representatives. This had equally dramatic effects on the account representatives—except for one employee who was going through a divorce. The incentive pay scheme did little to increase his marginal incentives because half of everything he earned went to his estranged wife. In other words, the marginal benefit of extra work for this employee was half as much as that of other employees, and he responded by working less hard.
Although the benefits of incentive pay seem clear, it is not a panacea—especially in cases where it is difficult to measure performance. For example, if you reward software programmers for finding and fixing “bugs” in software, you also create an incentive for the same programmers to deliberately produce bugs so they can be found later on. Research has found that incentive schemes are most effective when “effort matters, there is little intrinsic desire to do the job, and money boosts the recipient’s social status.”
On a related note, recognize that it is virtually impossible to measure and reward all the different tasks and activities you want an employee to perform. This is especially true of managers, who typically have a wide scope of responsibility. For them, do not put too much faith in monetary incentives alone. Recognize that the success of an organization often depends on managers who exert effort above and beyond the incentives set up for them. Firms should let these managers know that they are appreciated, and promote and reward them as best it can.
4.6Is Incentive Pay Unfair?
Incentive pay generates inequality simply because more productive workers or those who work harder get paid more. Some employees and managers will resist even well-designed incentive pay schemes because they consider them “unfair.” Moreover, incentive pay typically exposes workers to risk beyond their control. For example, even if they work hard, salespeople compensated on sales commission earn less if the macro economy does poorly.
However, these criticisms of incentive pay make the mistake of confusing procedural fairness (everyone has the same opportunity) with outcome fairness (everyone has the same outcome). If you adopt incentive pay, you get higher productivity (procedural fairness) but also greater inequality (outcome unfairness).
The reluctance of people to accept this trade-off can make it difficult for firms to increase productivity. For example, Spain’s policy of finiquito whereby firms have to pay fired workers 1.5 months of salary for every year worked makes it difficult to motivate long-time employees. The severance pay starts looking so good that long-term employees start trying to get fired. One employee with 17 years’ experience speculated in a blog post, “How hard should I really be working?” These kinds of policies are making it very difficult for the southern European countries to grow their way out of the recession.
But countries aren’t the only ones who resist incentive pay. Consider this reaction from a “faculty” member in the “corporate learning center” of a Fortune 50 company to a suggestion that his company adopt an incentive compensation plan:
Forfeiting our most recently espoused values of equal ownership in Firm X’s success is not the answer. I fear that we will be attempting to compete for employees interested in a class-oriented system of compensation. From where I sit, this is the last thing a corporation needing vast, systemic, team-oriented change should be trying to do to compete in the global marketplace. Many folks know I am a staunch opponent of incentive plans, and I often quote Alfie Kohn (1993), whose research shows that rewards punish. Saying “If you do this, you’ll get that” differs little from saying “Do this or this will happen to you.” Incentives are controlling.
However, another aspect of the punishment is much more evident in this change of policy: “Not receiving a reward one expects to receive is also indistinguishable from being punished.” Just ask all those who don’t receive the bonuses they were previously entitled to how they feel about it. The incentive pay policy is overt in its support of class separation over collective team participation. It ignores the premises of modern systems thinking and reverts to the mechanistic theories of Descartes and Newton for justification. A typical business school text from the 1950s would have suggested instituting such an aristocratic policy.
This company has since been acquired.
Chapter 5 Chapter Introduction
In the summer of 2007, Bert Mathews was contemplating the purchase of a 48-unit apartment building in downtown Nashville. The building was 95% occupied and generated $500,000 in annual profit. His investors were expecting a 15% return, and the bank had offered to loan him 80% of the purchase price at a rate of 5.5% interest. He computed his weighted average cost of capital or WACC as . Mr. Mathews used his cost of capital to figure out how much he could afford to pay for the property, and still earn enough to satisfy his investors. The answer was $6.75 million, computed as . In other words, if he paid $6.75 million and earned $500,000 each year, he could pay his investors 15% on their invested capital.
Even though the owner was willing to sell at this price, Mr. Mathews decided not to purchase because he was worried about the deteriorating housing market and the rising number of mortgage defaults. This turned out to be a good decision. A year later, the building’s occupancy rate fell to 90%, which reduced annual profit to $450,000. In addition, lending standards had tightened considerably. Now, the bank was willing to lend only 65% of the purchase price, and at the higher rate of 7.5%. This raised Mr. Mathews’ cost of capital to , which reduced the value that he placed on the property. If he was going to earn 10.125%, the most he could afford to pay for the property was $4.4 million, computed as , which the owners rejected as too low.
This story illustrates the effect of the financial crisis on the real estate market, but more importantly for our purposes, the relevant costs and benefits of investment decisions, the topic of this chapter.
5.1Compounding and Discounting
All investment decisions involve a trade-off between current sacrifice and future gain. Before investing, you need to know whether the future benefits are more than the current costs. Discounting is a tool that allows you to figure this out.
The easiest way to understand discounting is to first consider its opposite, compounding,
where r is the rate of return. If, for example, you invest $1 today at a 10% rate, then you would expect to have $1.10 in one year. After two years, $1 becomes ; after three years, $1.33; and so on. The general formula for compounding is
In the following table, we use the above formula to compute the time that it takes an investment to double in value, when left to grow, as in a savings account. We see that higher the interest rates cause money to double in a shorter period of time. In fact, we see that the interest rate multiplied by the time it takes to double equals about 72 (last column). This is the so-called rule of 72
If you invest at a rate of return r, divide 72 by r to get the number of years it takes to double your money.
As you can see from the entries in the “Future Value” column this is not an exact formula, but rather an approximation.
|
Current Value |
Interest Rate |
Years |
Future Value |
Rate*Time |
|
$100 |
2.00% |
36.0 |
$204 |
72 |
|
$100 |
4.00% |
18.0 |
$203 |
72 |
|
$100 |
6.00% |
12.0 |
$201 |
72 |
|
$100 |
7.20% |
10.0 |
$200 |
72 |
|
$100 |
10.00% |
7.2 |
$199 |
72 |
|
$100 |
12.00% |
6.0 |
$197 |
72 |
|
$100 |
15.00% |
5.0 |
$201 |
75 |
Discounting is the inverse of compounding and is defined by the formula,
So, for example, at a 10% discount rate, $1 next year is worth only today, $1 two years in the future is worth only today, and $1 three years in the future is worth only today.
For an example of how to use discounting, we turn to the problem of pensions. Like most U.S. cities, Nashville uses discounting to decide how much to save today to fund its future pension obligations. For a pension that pays out $100,000 in 20 years, Nashville must save today, using an 8.25% discount rate. If the city invests the $20,485 and earns 8.25%, the savings will compound and be worth $100,000 in 20 years. If, however, the investments earn less than 8.25% (in fact they have done much worse), then the city will not have saved enough when the future finally gets here.
Of course, a more realistic discount rate, say 6.5%, would mean much higher current savings, to fund the same future pension. But higher savings means less current spending, and current spending is politically popular. This explains why many politicians prefer higher discount rates, and why most public pensions are underfunded, by 25% on average.
In the following table, we compute how much more the California State Pension Fund (Calpers) must save if it were to reduce its discount rate from 7.5% to 2.56%, the risk-free rate of return.
|
Future Value |
Rate |
Years |
Present Value |
|
$100 |
7.50% |
20.0 |
$24 |
|
$100 |
6.50% |
20.0 |
$28 |
|
$100 |
5.50% |
20.0 |
$34 |
|
$100 |
4.50% |
20.0 |
$41 |
|
$100 |
3.50% |
20.0 |
$50 |
|
$100 |
2.56% |
20.0 |
$60 |
We see that as the discount rate falls from 7.5% to the risk-free rate of 2.56%, the amount that the pension fund must save increases from $24 to $60, an increase of more than 150%. But even more reasonable discount rates, like 5.5%, would require $34, an increase of 42% over what Calpers is currently saving.
5.2How to Determine Whether Investments Are Profitable
We are now in a position to use discounting to determine whether an investment is profitable. The rule is simple: discount and add up the future benefits of an investment, and compare them to the current cost of the investment. If the difference is positive (called the “net present value”), then the investment earns more than the cost of capital. This intuition can be formalized into a general decision rule, called the NPV rule .
If the net present value of the sum of all discounted cash flows is larger than zero, then the project earns more than the cost of capital.
Most projects, however, are more difficult to compare. We illustrate two such projects in Table 5.1. Both projects require an initial investment of $100. Project 1 returns $115 at the end of the first year, whereas Project 2 returns $60 at the end of the first year and $60 at the end of the second. The company’s cost of capital is 14%. To determine whether the investments are profitable, we discount all future inflows and outflows to the present so we can compare them to the initial investment.
Table 5.1
NPV Example
|
Year |
Project 1 |
Project 2 |
||
|
|
Cash Flow |
Present Value |
Cash Flow |
Present Value |
|
0 |
−100.00 |
−100.00 |
−100.00 |
−100.00 |
|
1 |
60.00 |
52.63 |
115.00 |
100.88 |
|
2 |
60.00 |
46.17 |
0.00 |
0.00 |
|
Net Value |
20.00 |
−1.20 |
15.00 |
0.88 |
To compute the present value, cash payouts after year one are divided by 1.14; and payouts after year two are divided by . Looking at the “Net Value” of the two projects in Table 5.1, it’s clear that Project 2 earns more than the cost of capital while Project 1 does not.
The NPV rule illustrates the link between “ economic profit ” introduced in Chapter 3 and investment decisions. Projects with positive NPV create economic profit because they earn more than the company’s opportunity cost of capital (i.e., the company earns profit above what is required to pay its investors and its debt service). The positive NPV of Project 2 means that Project 2’s return is higher than 14%, and the negative NPV of Project 1 means that its return is lower than 14%. We see that projects earning accounting profit (like project one) do not necessarily earn economic profit.
A close cousin of NPV analysis is the internal rate of return (IRR).
IRR is the discount rate that sets NPV equal to zero.
To see how this works, consider a project that requires an upfront payment of $2,000 (now), but pays back $500/year for the next five years.
|
|
Project |
|
|
Cost of Capital 5.00% |
||
|
Year |
Cash Flow |
Present Value |
|
0 |
−2,000.00 |
−2,000.00 |
|
1 |
500.00 |
476.19 |
|
2 |
500.00 |
453.51 |
|
3 |
500.00 |
431.92 |
|
4 |
500.00 |
411.35 |
|
5 |
500.00 |
391.76 |
|
Net Value |
|
164.74 |
To find the IRR, we increase the discount rate, until the NPV falls to zero.
|
|
Project |
|
|
|
||
|
Year |
Cash Flow |
Present Value |
|
0 |
−2,000.00 |
−2,000.00 |
|
1 |
500.00 |
463.26 |
|
2 |
500.00 |
429.23 |
|
3 |
500.00 |
397.69 |
|
4 |
500.00 |
368.47 |
|
5 |
500.00 |
341.40 |
|
Net Value |
|
0.04 |
At a discount rate of 7.93%, the NPV is only $0.04, very close to zero. We say that the IRR of this project is 7.93%. If our cost of capital is less than this, for example, 5%, we would invest in the project.
Note that the IRR and NPV give the same answer to this problem, but IRR can be harder to interpret than NPV analysis. When in doubt, use NPV.
5.3Break-Even Analysis
In your finance classes, you will learn that NPV analysis is the “correct” way to evaluate investment decisions. A positive NPV is both a necessary and a sufficient condition for an investment to be profitable. However, after doing NPV analysis in a variety of circumstances, you will begin to develop shortcuts and rules of thumb, like payback periods, that give you similar answers. This is potentially dangerous. When using shortcuts, make sure that you understand the context in which the shortcut is being used and that it gives the same answer as NPV analysis.
One of the most popular shortcuts is break-even analysis. Break-even analysis can give you the wrong answer as it ignores the time value of money. However, break-even analysis is easy to do and it generates simple, intuitive answers. To illustrate, let’s examine an entry decision. Instead of asking whether entry is profitable, break-even analysis asks an easier question, “Can I sell enough to break even?” If you can sell more than the break-even quantity , then entry is profitable; otherwise, entry is unprofitable.
To compute the break-even quantity, we have to distinguish between marginal cost (MC), which varies with quantity, and fixed cost (F), which doesn’t. Imagine that you incur a fixed cost to enter an industry and a constant per-unit MC when you begin production. You will find that most of your investment decisions can be analyzed using this very simple cost structure.
The break-even quantity is ,
where F is annual fixed cost, P is price, and MC is marginal cost.
The break-even quantity is the quantity that will lead to zero profit. The logic behind the calculation is simple. Each unit sold earns the contribution margin (P − MC), so named because this is the amount that one sale contributes to profit. You have to sell at least the break-even quantity to earn enough to cover fixed costs. If you sell more than the break-even quantity, you have earned more than enough to cover your fixed costs, or to earn a profit.
For example, consider Nissan’s 2008 redesign of its Titan pickup truck. The Titan had only two years left on its eight-year product life cycle, and Nissan had to decide whether to redesign it. Complicating the decision was a weakening demand for U.S. trucks, with sales predicted to fall from 1.3 million in 2008 to only 400,000 trucks per year by 2011.
Nissan managers used a rough break-even calculation to evaluate their investment alternatives. It would cost $400 million to design and build a new truck from the bottom up. At a 15% cost of capital, the investment would cost Nissan about $60 million per year. As it earned only $1,500 per truck, Nissan would have to sell at least 40,000 trucks each year to break even. With only a 3% share of the U.S. market, however, Nissan predicted they would sell only 12,000 Titan trucks each year, not enough to break even.
|
Platform |
Nissan |
Dodge |
|
Cost of Capital |
15% |
15% |
|
Capital |
$400,000,000 |
$80,000,000 |
|
Margin (P − MC) |
$1,500 |
$1,250 |
|
Break-Even Sales |
40,000 |
9,600 |
|
Predicted Sales |
12,000 |
12,000 |
Outsourcing the Titan to Chrysler would have made economic sense, but in early 2009, the companies issued a joint statement indefinitely postponing the project due to “declining economic conditions.”
5.4Choosing the Right Manufacturing Technology
In 1986, John Deere was building a capital-intensive factory to produce large, four-wheel-drive farm tractors when the price of wheat dropped dramatically. Demand for these tractors also fell because they’re used exclusively for harvesting wheat. In response, John Deere stopped construction of its factory and attempted to purchase Versatile, a Canadian company that assembled tractors in a big garage using off-the-shelf components.
We can characterize John Deere’s decision as abandoning their capital-intensive factory, characterized by big fixed cost but small MC, in favor of Versatile’s technology, characterized by small fixed cost but big MC. Did John Deere make the right decision?
As you should now begin to realize, the answer is “it depends.” In this case, it depends on how much John Deere expected to sell. Suppose that the capital-intensive technology had fixed costs of $100 and MCs of $10, whereas Versatile’s technology had fixed costs of $50 but MCs of $20. (Note: We’re deliberately choosing easy-to-work-with numbers so that we can illustrate the general point.) To answer the question, we compute the break-even quantity—the quantity at which John Deere is indifferent between the two technologies.
In the following table, we see that for a quantity of five units, the total costs of the two manufacturing technologies are the same.
|
|
In-House |
Versatile |
|
Quantity |
5 |
5 |
|
Fixed Costs/Year |
$100 |
$50 |
|
Marginal Cost |
$10 |
$20 |
|
Total Cost |
$150 |
$150 |
If John Deere expects to sell more than five units, it should choose the low-marginal-cost technology; and for less than five units, they should choose the low-fixed-cost technology.
In this case, John Deere decided to acquire Versatile because projected demand was low. However, the antitrust division of the U.S. Department of Justice challenged the acquisition as anticompetitive because John Deere and Versatile were two of just four firms that sold large four-wheel-drive tractors in North America.
We end this section with a warning to avoid a very common business mistake:
Do not use break-even analysis to justify higher prices or greater output.
Managers sometimes reason that they must raise price to cover fixed costs. Similarly, managers sometimes reason that since average fixed costs decline with quantity, they must sell as much as they can to reduce average cost. Both lines of reasoning are flawed because, as you know, pricing and production are extent decisions that require marginal analysis, not break-even analysis.
Remember, if you start your analysis by looking at costs you will always get confused. Instead, start your analysis by asking a question. For an extent decision, like how high to price or how much to produce, fixed or sunk costs are irrelevant because they do not vary with the consequence of the decision. For an investment decision, fixed or sunk costs are relevant because they haven’t yet been incurred.
Shut-Down Decisions and Break-Even Prices
To study shut-down decisions, we work with break-even prices rather than quantities. If you shut down, you lose your revenue, but you get back your avoidable cost. If revenue is less than avoidable cost, or equivalently, if price is less than average avoidable cost, then shut down.
The break-even price is the average avoidable cost per unit.
The only hard part in applying break-even analysis is deciding which costs are avoidable. For that, we use the Cost Taxonomy, shown in
Figure 5.1
.
Figure 5.1Cost Taxonomy
To illustrate how to use the taxonomy, consider the following problem. Fixed cost is $100/year, MC is $5/year, and you’re producing 100 units per year. How low can price go before it is profitable to shut down?
Again, the answer is “it depends.” In this case, it depends on which costs are avoidable. To make this concrete, think of the fixed cost as a one-year renewable lease and the MC as the cost of production. MC varies with how much you produce so it is avoidable. But until the lease comes up for renewal, it is unavoidable, so you ignore it when deciding whether to shut down.
In the short run, only MC is avoidable, so the shut-down price is $5. In the long run, fixed cost becomes avoidable, so it becomes relevant to the shut-down decision. In the long run, the shut-down price includes average fixed cost and rises to $6. As more costs become avoidable, the shut-down price increases to reflect this.
5.6Sunk Costs and Post-Investment Hold-Up
By 2000, Mobil Oil (now ExxonMobil) was the leading supplier of industrial lubricants in the United States. It achieved that position—and a 13% market share—by bundling engineering services with its high-quality lubricants. With twice as many field engineers as its next-largest competitor, Mobil was able to offer custom-designed lubrication programs to complement sales of its lubricants.
One of Mobil’s largest customers was TVA, a regional producer of electric power whose annual consumption of lubricants exceeded one million gallons. Early in 2000, Mobil conducted a three-month engineering audit of TVA. This audit included employee training, equipment inspections, and, for each piece of TVA equipment, repair, service, and lubricant recommendations.
TVA made the recommended repairs, but then it gave the lubricant recommendation list to a Mobil competitor that offered lubricants at lower prices. When Mobil failed to match the lower prices, they lost the contract and their three-month investment. Mobil and its managers forgot a basic business maxim.
Before investing, look ahead and reason back.
Economics is often called the “dismal science,” partly because of its dark view of human nature. However, this dark view of human nature can protect you against what economists call post-investment hold-up . sunk costs are unavoidable, even in the long run, so after you incur them, you become vulnerable to post-investment hold-up. In this case, Mobil made the investment in consulting services expecting that they could recoup the investment through their pricing. However, TVA “held them up” by buying lubricants from another vendor.
If “Cost” includes all your costs, including your opportunity cost of capital, then you are just breaking even (earning zero profit) when . If price falls below AC, then you are losing money.
To see how this affects investment decisions, imagine that you are advising a regional commercial printer, who is negotiating with a magazine, like National Geographic. For the magazine, using a regional printer reduces shipping costs. But to print a high-quality magazine, the printer must buy a $12 million rotogravure printing press. For the sake of clarity, we assume that the press has no resale value and the firm has no capital cost (it can borrow money and pay no interest). Suppose that the MC of printing a single copy is $2 and the printer expects to print one million copies per year over a two-year period.
In the following table, we compute the average cost of printing the magazine over the length of the contract.
|
Year |
Quantity |
RFP |
|
|
|
|
Sunk Cost |
Variable Cost ($2/Unit) |
|
0 |
|
$12,000,000 |
|
|
1 |
1,000,000 |
|
$2,000,000 |
|
2 |
1,000,000 |
|
$2,000,000 |
|
Total |
2,000,000 |
$12,000,000 |
$4,000,000 |
|
Average |
|
$6 |
$2 |
|
Average Cost |
$8 |
In the above table, we see that $8 is the average cost of printing magazines over the length of the contract. This is the break-even price for the printer and represents her bottom line in negotiations with the magazine. Before they are incurred, sunk costs are relevant to the negotiation.
QUESTION: Now suppose that the magazine accepts your offer of $8/unit and immediately hands you a purchase order for $8,000,000, for the first-year production. Do you accept the purchase order?
If you said “Yes,” you have just been held up. Since the $12M cost of the printer is sunk, the magazine can decide to reduce its second-year price to only $2, and you would have no option but to accept it. Instead, you should instead refuse the purchase order at that price.
If the printer anticipates hold-up, it will be reluctant to deal with the magazine. When this happens, hold-up becomes a problem not just for the potential victim but also for the potential perpetrator. The one lesson of business is to figure out how to profitably consummate the transaction between the printer and the magazine.
If possible, the printer will negotiate a contract that penalizes the magazine should it decide to hold them up. With the assurance of a contract, the printer may feel confident enough to incur sunk costs. But contracts are often difficult and costly to enforce. A better solution might be to make the magazine purchase the printing press and then lease it to the printer. In this case, the magazine no longer poses a hold-up threat to the printer because the printer has incurred no sunk costs.
Note that if the cost of the printing press is fixed, meaning that it can be recovered by selling the machine, then hold-up is not a problem. If the magazine tries to renegotiate a price less than average cost, the printer will refuse the business, sell the press, and recover its entire investment. Hold-up can occur only if costs are sunk.
In general, many investments are vulnerable to hold-up. Anytime that one party makes a specific investment —one that is sunk or lacks value outside of a trading relationship—the party can be held up by its trading partner. If one party anticipates that she is at risk of being held up, she will be reluctant to make relationship-specific investments, or demand costly safeguards, including compensation in the form of better terms from her trading partner. This gives both parties an incentive to adopt contracts or organizational forms, such as investments in reputation or merger, to reduce the risk of hold-up. The goal is to ensure that each party has both the incentive to make relationship-specific investments and to trade after these investments have been made.
Contracts should encourage both investment and trade.
For example, marriages are vulnerable to the same type of post-investment opportunism that plagues commercial relationships. Parties invest time, energy, and money in a marriage, the kinds of investments that differentiate marriages from more casual relationships, which can be thought of as spot-market transactions. These investments are valuable to the marriage parties but are largely specific, in that they have a much lower value outside the relationship. The marriage contract penalizes post-investment hold-up (i.e., divorce), and this makes couples willing to invest more in the marriage.
We close the chapter with the story of an economist and his fiancée who were receiving premarital counseling from a priest before he would marry them. The priest’s first question to the couple was “Why do you want to get married?” The economist’s fiancée answered, “Because I love him and want to spend the rest of my life with him.” As you might imagine, the economist had a different answer, “Because long-term contracts induce higher levels of relationship-specific investments .”
A year later, trying hard to find the right words to express how he felt about his wife, he wrote an anniversary e-mail—using a cursive font—declaring that his “relationship-specific investment was earning an above-average rate of return.”
Transcript
Chapter Lecture Video
>> Hi, this is Luke Froeb. I'm the author of Managerial Economics, a problem solving approach along with Brian McCann. This lecture is designed to supplement chapter four, extent, how much decisions. Imagine that you receive two bids from two different loggers for a tract of land that you own with about 100 trees on it. One bid is for 10,000 dollars for the entire tract. The second logger bids 100 dollars a tree. Since both bids have the same nominal value, does it matter which bid you accept? The answer is yes. It matters because the different incentives facing each logger. The first logger has an incentive to cut down all of the trees in the tract because the cost of cutting down an additional tree is zero. Once he pays the 10,000 dollar fixed fee, it becomes irrelevant to his decision of whether to cut down more trees. But the second logger will cut down only trees that have a value greater than 100 dollars. If the tract is a mix of low value species like fur worth only 50 dollars, and high value species like pine worth 200 dollars, the second logger will cut down only the pine and leave the fur. You will earn less than if you had accepted the first bid. In this chapter we examine extent decisions like the one facing the logger of how many trees to cut down. Let's begin with a basic rule. Fixed costs are irrelevant to an extent decision because fixed costs do not vary with how much you do. In the example above, the first logger treated the 10,000 payment is fixed, so he ignored it when deciding how many trees to cut down. Since average cost contain fixed cost, using them to analyze extent decisions can lead to mistakes. For example in 2005, Memorial Hospital's CEO conducted a performance review of all the departments in his hospital. As part of the process, the chief of obstetrics proposed increasing the number of babies being delivered by his department. The CEO examined the department's financial statements and discovered that the cost of deliveries was over three million but the revenue was two point eight. Divided by the number of babies, this amounted to an average loss of about 700 dollars. The CEO rejected that. The CEO rejected the proposal because he said each time a baby was delivered, the hospital lost 700 dollars. Now, you should recognize this statement as an example of the fixed cost fallacy from chapter three. Instead of starting with the cost, the CEO should have started with the question should we deliver more babies. If he had, he would have realized that the relevant cost of an extent decision are the marginal costs, not the average cost. If he had used marginal analysis, he would have discovered that he was making over 3,000 dollars profit on every baby he delivered. Let's look at the costs on a graph for a very simple cost function. Which has a fixed cost and a constant marginal cost. Quantity is on the horizontal axis, average and marginal cost are plotted on the vertical axis. In this case, average cost falls with output because average fixed cost fall with output. And average cost combines average fixed cost and marginal cost. Marginal cost is the extra cost required to make and sell one additional unit of output. In this case, they are below the average which causes the average to fall. To analyze extent decisions we break decisions into small steps and then compute the costs and benefits of taking an additional step. These are the marginal costs and benefits. If the marginal benefit is bigger than the marginal cost of taking a step, then take the step. Otherwise, step backwards. Marginal analysis tells you which direction to go, do more or less, but it doesn't tell you how far to go. You have to take another step and then re-measure. For example, suppose a mobile phone company increases its TV advertising budget by 50,000 dollars, and the increase in advertising spent yields a thousand new customers. To compute the marginal cost of acquiring a customer's divide 50,000 by a thousand customers to get 50 dollars per customer, which is sometimes called customer acquisition cost. Note that the experiment we are given is a big change, a thousand new customers, and from this big step we compute the marginal cost of acquiring an additional customer. If the marginal benefit of another customer is greater than 50 dollars, then increase advertising. Otherwise, reduce advertising. After you change your advertising budget, repeat the analysis to see if another step is warranted. Even if you don't know what the marginal benefit of acquiring another customer is, you can still use marginal analysis to compute the relative effectiveness of two different extent decisions, such as allocating funds between TV advertising and phone solicitation. For example, suppose that you recently reduced your phone solicitation spending by 10,000 dollars and you lost 100 customers. Divide 10,000 by 100 to compute a marginal acquisition cost of 100 dollars per customer. Since it is more costly to acquire customers with phone solicitation, shift your spending from phone solicitation to TV advertising. Remember to keep the changes separate. For example, don't reduce spending on phone solicitation at the same time that you increase spending on TV advertising. Otherwise you lose valuable information about the marginal effectiveness of each medium. The decision of how hard to work is an extent decision so we use marginal analysis to design incentives. Suppose you want to evaluate the incentive effects of two different compensation schemes. One is based on a ten percent commission rate. The other pays a five percent commission rate plus a flat 50,000 dollar per year salary. Each year you expect sales people to sell 100 units at a price of about 10,000 dollars per unit. So the contract has the same face value. However, the two contracts have very different incentive effects. If you pay a 10 percent commission the marginal benefit of another sale is a thousand dollars. But if you pay a five percent commission, it is only 500 dollars. There are, of course, easy sales and hard sales. Some might require 300 dollars' worth of time and effort from the sales person. And some might require 800 dollars. The sales person who is paid a 10 percent commission rate will make both of these sales because the marginal benefit of making a sale is bigger than the marginal cost. But the sales person who is paid only five percent will make only the easy sale, he won't make the hard sale. To summarize, the sales force responds to the smaller marginal benefit of selling with less effort, which we call shirking. To induce higher effort, use incentives that reduce marginal costs or increase marginal benefits. Fixed costs or benefits, base salary, do not change effort. Note the parallel of the sale's person's compensation schemes to the logging contracts. Just as the compensation scheme with higher marginal benefit induced higher effort. So too did the contract with the lower marginal costs induce more logging. Designing good incentives requires that you tie
[ Inaudible ]
performance measures that reflect effort. For example, in 1997, a 50 year old chief operating officer with a bachelor's degree in journalism and a law degree managed a consulting firm with 10 account executives. The COO was in charge of keeping clients happy and ensuring that the account execs were working in the best interest of the company. He earned a flat salary of 75,000. After taking some econ classes, the CEO of the company became convinced of the merits of incentive pay. So, he sat down with his COO and he came up with some profit goals for the year. They decided that all revenue accounted towards the COO's profit goal, but only the expenses that the COO controlled directly were charged against his profit. All fixed costs, like overhead, the irrelevant costs, were placed in another budget. This is an example, another example of how you have to figure out which accounting costs are relevant to the decision you are trying to make. The CEO and COO also agreed that without much effort, the COO could earn about 150,000 dollars a quarter, but earning more than that would require more effort. So to reward the CEO, COO, for putting in the extra effort, they agreed on an incentive compensation scheme that paid the COO one third of each dollar that the company earned above 150,000. As a result the COO's compensation jumped to 177,000 dollars a year, an increase of over 100 percent. The firm's revenues also increased to 1.25 million an increase of 74 percent. Revenue increased because the COO pushed hard to make and exceed earnings goals and for the first time he became concerned about expenses. For example, he attempted to contain costs by asking the account executives why their phone bills were so high. You might be wondering why if incentive pay is so good, more companies don't use it. Quite simply it is very difficult to measure performance. Later on as we develop more tools to analyze incentives, we will see that there are situations where incentive pay can be counter-productive. This is the end of chapter four. The next chapter, we'll discuss investment decisions.
Transcript
Chapter Lecture Video
>> Hi, this is Luke Froeb, I'm the author of Managerial Economics, a problem solving approach, along with Brian McCann. This lecture is designed to supplement chapter five, investment decisions. In the summer of 2007, before the credit bubble burst, Bert Matthews thought about purchasing a 48 unit apartment building in downtown Nashville. At the time, the building was 95 percent occupied and generated 550,000 in annual profit. His investors were expecting a 15 percent return on their capital and the bank had offered to loan him 80 percent of the purchase price, with an interest rate of five and a half percent. Bert had to figure out if purchasing the building would be a good idea. He did this by determining how much he could afford to pay and still give his investors a decent rate in return. So, he computed his cost of capital as the weighted average and equity of debt. With a capital cost equal to 7.4 percent, Bert could afford to pay 7.4 million for the building. In other words, the profit earned by the apartment, 550,000, equals 7.4 percent of the 7.4 million dollar purchase price. At this point, mister Matthews decided not to buy the building. In retrospect, the summer of 2007 was not a good time to invest in real estate. A year later, the buildings occupancy had fallen from 95 percent to 90 percent. And annual profit fell from 550,000 to 500,000. It was also harder to get a loan. Now the bank was willing to loan him only 65 percent of the purchase price and at a rate of seven and a half percent. This raised his cost of capital to just over 10 percent, which meant he could only offer four and a half million dollars for the apartment building. The owners rejected his offer as too small. So what does this story mean? Beyond the obviously effective rates on real estate prices, it also illustrates relevant cost and benefits of investment decisions, the topic of chapter five. Let's start by trying to figure out which investments are profitable. At the most basic level, all investments offer a trade-off between current sacrifice and future gain. In economics, we use the term discount rate, to describe the price at which you're willing to trade off current for future dollars. If you require a high rate of return to entice you to invest in a project, you have what we call a high discount rate. You've encountered this trade off before, when you put money in a savings account it grows at a compound rate of interest. If the interest rate is 10 percent, for example, then one dollar invested today will be worth a dollar ten after a year, worth a dollar 21 after two years, and worth a dollar 33 after three years. There's a useful rule of thumb here called the 10 seven rule. At a 10 percent rate of interest, your money will double after seven years, and at a seven percent rate of interest, your money will double after 10 years. Discounting is the opposite of compounding. If someone offers to pay you a dollar 10 after one year the current or present value of that promise depends on your discount rate. If it is 10 percent, then a dollar 10 next year is worth a dollar this year. Similarly the present value of a dollar 21 after two years is one dollar as is the value of a dollar 33 after three years and so on. Discounting payoffs that occur k periods in the future can be computed recursively by discounting future payoffs one period at a time until you get to the present. The formula which represents this discounting is simple. To illustrate how we use discounting to determine whether a project will earn enough money to cover the cost of capital, let's consider two projects. Both of which require an initial investment of a 100 dollars. Project one returns 115 at the end of the first year, project two returns 60 dollars at the end of the first year and 60 dollars at the end of the second year. So which project should you invest in? Looking at the total return, which is like looking at a counting providence instead of economic profit. You might be tempted to choose project two. But this would be wrong. What you want to do is compute the present discounted value of each project. To do this we discount all future inflows and outflows to the present. This is the equivalent to expressing cost, which occur in the present and benefits which occur in the future in equivalent units so we can compare them. Let's say that your cost of capital is 14 percent. We discount the future payouts at 14 percent to compare their value to the, in this initial investment. This means that the inflow after year one must be divided by 1.14 and the inflow after year two must be divided by 1.14 squared. Applying this to both projects shows that only the first project earns a positive profit. The NPV rule tells you whether an investment will earn enough to cover the cost of capital. Projects with a positive NPV create economic profit which means they earn a return higher than the company's cost of capital. The bottom line is that you should invest only in projects with a positive NPV. In your finance courses, you will learn that NPV analysis is the correct way to evaluate investment decisions. But many managers use shortcuts like break-even analysis. In fact, in a recent study, over half of CFO's use payback periods as their decision tool. To evaluate the profitability of investments, CFO's calculated how many months it would take for an investment to break-even or payback the initial investment. Break-even analysis is easier to do than NPV analysis and it produces simple, intuitive answers. So, here's how it works. When considering an investment, instead of asking whether it has a positive NPV, you ask can I sell enough to break even. If you can sell more than the break-even amount, then it's a profitable investment. And if you can't, it's not, it's that simple. How do we determine the break-even quantity? First we have to distinguish between marginal costs which vary with quantity and fixed costs which don't. The break-even quantity is the fixed cost divided by the contribution margin. If you sell the break-even quantity, your profit is exactly zero. But if you sell more, you earn money. To see how this works, consider Nissan's 2008 redesigned Titan pickup truck. The Titan had only two years left on its eight year product life cycle. And Nissan had to decide whether to redesign it. Nissan managers used a rough break-even calculation to evaluate their investment alternatives. It would cost 400 million to design and build a new truck from the bottom up. At a 12 percent cost of capital, the investment would cost Nissan about 48 million dollars a year. Since they earned only 1500 dollars on each truck, they would have to sell at least 32,000 trucks each year to break even. However, with only a three percent share of a shrinking U.S. market, Nissan predicted they would only sell 12,000 Titan trucks, not enough to break even. So instead of investing in and designing a new truck, they decided to explore other options like outsourcing a new truck from Chrysler. You can also think of stock market evaluations in break-even terms. If you purchase a stock, for say 30 dollars, and the stock earns on average, 1.50 a share, then it takes 20 years to pay back the initial investment. In the graph above, we see that the aggregate P/E ratio for the stock market was about 20 in June 2010. This is above its historical average of about 16. So some value investors would currently consider the stock market over value. Note that smaller private companies typically trade at much lower P/E ratios, around six for example. When looking at shut down decisions, we work with break-even prices rather than break-even quantities. Let's think about what happens when you shut down. You lose your revenue but you get back your avoidable cost. If revenue is less than avoidable cost, or equivalently, if price is less than average avoidable cost then shut down. The break-even price is the average avoidable cost. The challenge of break-even analysis is deciding which costs are avoidable. And for that we use the cost taxonomy from the book. You can see that in the short run, only marginal cost is avoidable. But in the long run, fixed cost become avoidable as well. So, let's say fixed costs are 100 dollars, marginal costs are five dollars and you're producing 100 units per year. In the short run, the shut-down price is equal to the marginal cots, only five dollars. But in the long run, the shut-down price includes the average fixed cost and rises to six dollars. So when does the transition between the short run and the long run occur? Think of the fixed cost as a one year renewable lease. When the lease comes up for renewal, it is relevant to the shut-down decision because it's avoidable. But until it comes up for renewal, in the short run, it's unavoidable and should not be considered when deciding to shut down. Sunk costs are relevant only before you incur them. But after you incur them, they become irrelevant and this can make you vulnerable to what economists call post-investment hold-up. Consider the case of a magazine like National Geographic trying to negotiate with a regional commercial printer to print its magazine. Using a network of regional printers, it saves the magazine shipping costs but they must convince each printer to buy a 10 million dollar printing press in order to produce a high quality magazine. If the marginal cost of printing a single copy is one dollar and the printer expects to print one million copies per year, over a two year period, the average cost of printing a magazine is six dollars, computed as the average fixed cost of the investment. 10 million dollars divided by two million copies plus the marginal cost, which is a dollar per copy. This is the break-even price for the printer and represents for bottom line in negotiations with the magazine. Before they are incurred, sunk costs are relevant to the negotiation. But once the printer purchases the press, the profit calculus changes. In this case the magazine can hold up the printer by renegotiating terms of the deal. Since the cost of the press is unavoidable, the printer's break-even price does not include it, and therefore falls to the marginal cost of printing the magazine which is only a dollar. If the commercial printer anticipates hold-up, he will be reluctant to buy the print press without some assurance. Hold-up becomes a problem not just for the printer, but for the magazine as well. There are several things the printer and magazine can do to consummate the transaction. One option is a long term contract. But contracts are often difficult and costly to enforce. A better solution is to make the magazine purchase the press and lease it back to the printer. This gets around the post investment problem because the printer has incurred no sunk costs. This leads to another maxim. Contracts should encourage both investment and trade. Any time one person makes a relationship specific investment, meaning one that is sunk or lacks value outside a trading relationship. He can be held up by his trading partner. This gives parties incentives to take actions to reduce the risk of hold-up, like signing long-term contracts or merging together, sometimes called vertical integration. We're going to close the chapter by taking a contractual view of marriage. Marriages are vulnerable to hold-up in much the same way that commercial relationships are. The stereotypical story is that a woman accuses a man of taking the best years of her life and then trading her in for a younger model. If a woman anticipates hold-up, she will be reluctant to make lone-term investments, like children. And like any commercial contract, a marriage contract is designed to restore the incentives of parties to make relationship specific investments. There is an
[ Inaudible ]
story of an economist and his fiancé who were receiving pre-marital counseling from a priest. The priest asked the economist why he wanted to get married. The economist answered long-term contracts induce higher levels of relationship-specific investment. The priest looked as if he didn't understand so the economist added, you know the kinds of investments that differentiate a marriage from a series of meaningless stock market transactions. On their first anniversary, the economists wife gave him a card declaring that her relationship specific investment was earning an above-average rate of return.
