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hedging bets and monitoring uncertain situations aggressively) are recom- mended for describing and evaluating potential outcomes regarding real investments (e.g., buildings, equipment, and training), financial investments (e.g., stocks, bonds, and insurance), and clinical decisions (e.g., testing and therapy).

4.2 Describing Potential Outcomes

The first step in any decision is to describe what could happen, including the probabilities and value of possible outcomes, and calculate descriptive statis- tics about the possible outcomes.

Description begins with an assessment of the probabilities of the pos- sible outcomes. Ideally, the assessment should generate an objective prob- ability—an estimate based on evidence about the frequencies of different outcomes. For example, if 250 of 1,000 patients reported nausea after taking a medication, a good estimate of the probability of nausea would be 0.25 (250 divided by 1,000). More often, though, description assesses the subjec- tive probability—the decision maker’s perception of how likely an outcome is to occur.

In some cases, decision makers have incomplete data. In other cases, the data do not fit the situation. For example, if a careful study of a drug in a population of men older than 18 years finds that the probability of nausea is 0.25, what value should we use for a sample of women older than 65 years? In still other cases, individuals may feel that population frequencies do not apply to them. Someone who claims to have a cast-iron stomach may believe that his probability of nausea is much less than 0.25. The decision maker with a cast-iron stomach may be correct in thinking that the population frequency does not apply to him, or he may just be overly optimistic.

In practice, decision makers predominantly use subjective probabili- ties. Unfortunately, these subjective probabilities are often inaccurate, even when the estimates are made by highly trained clinicians or experienced managers. Studies have found that physicians overestimate the probability of skull fractures, cancer, pneumonia, and streptococcal infections, and manag- ers are notorious for being overenthusiastic in their forecasts of how well new projects will be run and how well they will be received. For a variety of reasons, humans generally are poor probability calculators. Examining data about population frequencies can significantly improve decision makers’ choices. For example, even if you believe that your hospital is less likely than average to lose money on the primary care practices it has just purchased, knowing that the majority of hospitals have lost money tells you that your hospital is still prone to loss. Moreover, in many cases, an honest assessment

Objective probability An estimate of probability based on observed frequencies

Subjective probability An individual’s judgment about how likely a particular event is to occur

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of the probabilities results in broad generalizations, not a point estimate of probabilities. A manager may be able to say only that he or she thinks one scenario is more likely than another. This information is still useful; general impressions can often clarify the situation and help managers make the best decision.

Betting on Medicare Advantage

Aetna announced on August 19, 2012, that it would buy Coventry Health Care for nearly $6 billion (de

la Merced 2012). The acquisition represents a strategy to expand its Medicaid managed care, Medicare Advantage, and health insurance marketplace lines of business. Most analysts anticipate rapid growth in these markets.

These markets do present major risks, however. First, much of the growth in Medicaid managed care will be due to expanded coverage of aged or disabled beneficiaries. These new enrollees tend to have multiple, complex health problems, meaning that prior experience with Medicaid managed care plans may be of little help. Prior to the pas- sage of the Affordable Care Act in 2010, Medicaid managed care enroll- ees were largely children, pregnant women, and parents. Second, prof- itability in Medicaid managed care and Medicare Advantage depends on government rates. Medicare Advantage rates are scheduled to be gradually cut to bring them in line with costs in traditional Medicare, and no one can really forecast what will happen to rates for Medicaid managed care or marketplace products. Third, no one knows what will happen to Medicare Advantage enrollment if the structure or payment systems of traditional Medicare are changed. Fourth, some time will be needed to sort out who will sign up for coverage via health insurance marketplaces. If too few low-risk individuals sign up, insurers could lose substantial amounts of money.

Risk is intrinsic to the health insurance business. Insurers take on risk by selling coverage for consumers’ variable medical expenditures. When you average risk over the spending patterns of tens of thou- sands of consumers, however, the risk becomes less uncertain—in most cases. In 2008, Humana nearly halved its profit forecast because claims for its Medicare prescription drug plan ran much higher than anticipated (Donley and Britt 2008). Apparently, its emphasis on

Case 4.1

(continued)

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4.3 Evaluating Outcomes

The next step is to evaluate possible outcomes. This chapter focuses on financial outcomes, typically profits. Financial outcomes are usually difficult to project. Skilled analysts commonly arrive at different answers when asked to calculate how much a therapy will cost under well-defined circumstances. Attempts at forecasting costs and revenues for a new project result in an even greater range of plausible outcomes because of all the uncertainties inherent in such an undertaking. Analysts may have ways of improving their forecasts, but in general, forecasts will never be more than educated guesses.

The problems mount when no simple measurement system, like profits, exists. How valuable is a new surgical procedure that reduces the chance of abdominal scarring from 0.12 to 0.08 but reduces the chance that the operation will succeed from 0.68 to 0.66? Any time a scenario involves opposing probabilities, evaluation becomes a challenge. Even though

covering well-known, branded pharmaceuticals attracted a large number of customers with above- average utilization patterns. (This situation is an

example of adverse selection.) But the main perils do not come from the operational issues

mentioned previously. The real risks spring from strategic decisions that could go wrong if an insurer misjudges the market. For example, Humana’s decision to serve Medicare Advantage customers in 2007 was a major gamble, but it appears to have paid off. Humana has gained nearly 2.5 million new customers (Gold et al. 2013). That result does not guarantee that Aetna’s similar bet will work out as well.

Discussion questions: • What has happened to Medicare Advantage enrollment since 2012?

• What has happened to Medicaid managed care enrollment since 2012?

• Have any insurers pulled out of Medicaid managed care markets during the past year?

• Medicare Advantage contracts last a year. What is Aetna risking by betting that Medicare Advantage will be an attractive opportunity?

• Is Medicare Advantage riskier than other forms of private health insurance?

• What other healthcare firms also face risks due to changes in government policy?

Case 4.1 (continued)

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scholars have made progress in evaluating complex outcomes, considerable uncertainty remains. Chapter 14 will tackle this problem in more detail.

Calculating descriptive statistics is the final step in the process of evaluating outcomes. The most common statistic is the expected value. To calculate an expected value, multiply the value of each outcome by its prob- ability of occurrence and then add the resulting products. For example, sup- pose your organization is contemplating buying a skilled nursing facility that currently has profits of $20,000. The price of the nursing home is $1 million, meaning that the return on investment would be only 2 percent, which is too low from your organization’s point of view. (Return on investment equals annual profit divided by your investment.) One of your managers, however, has identified a number of operational improvements that she forecasts will boost profits to $120,000. Although this manager’s improvements are rea- sonable, a consultant points out that, in his experience, ambitious propos- als to increase profits fail about 40 percent of the time. So, the consultant estimates that the expected profit is $80,000 = (0.6 × $120,000) + (0.4 × $20,000).

This level of precision (e.g., “about 40 percent of the time”) is repre- sentative of the reliability of managerial forecasts—they are inexact at best. Despite imprecise forecasts, managers must make a choice. In many cases, calculating the expected profit and then conducting a sensitivity analysis will help managers avoid bad decisions.

Formally, an expected value equals P 1 X

1 + P

2 X

2 + . . . + P

n X

n , where P

i

represents the probability that an outcome will occur and X i represents the

value of that outcome. An expected value differs from an average because the probabilities of some outcomes will be higher than the probabilities of others, so they get more weight. For example, the average of $120,000 and $20,000—the two estimates from our example above—is $70,000. But the expected value is $80,000 because the probability of earning $120,000 is larger than the probability of earning $20,000.

Does buying the skilled nursing home make sense? It might. The expected return on investment is 8 percent. Given that the worst-case sce- nario is a 2 percent return on investment, this gamble will seem reasonable to many firms, depending on the alternative investments the firm is considering.

Good decisions usually require more information than just an expected value because typically the expected value is not the outcome that occurs. Most decision makers find that a list of the best and worst outcomes is valuable. A list of the most likely outcomes can also be useful. Graphs, too, can help decision makers understand their choices. Many people find a well-designed graph more valuable than a calculation. Finally, remember that estimates are estimates; writing them down does not make them more reli- able. The less mathematically sophisticated your target audience is, the more you need to emphasize that forecasts are imprecise.

Expected value The sum of the probability of each possible outcome multiplied by the value of the outcome

Sensitivity analysis The process of varying the assumptions in an analysis over a reasonable range and observing how the outcome changes

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This simple example can be illustrated with a decision tree, which is a way of presenting information about a choice. A decision tree visually links a decision maker’s choices with the outcomes that are likely to result. It is called a tree because the possible outcomes branch from a choice. For the analyst, much of the value lies in the process of constructing the decision tree because it highlights his or her perception of what will happen and where the information is weakest. In addition, many people find that examining a deci- sion tree helps them understand the issues involved because it lays out their best estimates of the cost or payoff and the probability associated with each possible outcome. As you can see in Exhibit 4.1, the worst-case forecast is a profit of $20,000, which is less than ideal but not a catastrophe. Similarly, the best-case forecast is a profit of $120,000, which is good but not superb. As is usually the case, laying out the decision tree helps clarify the situation by making the probability and profit estimates explicit. It does not tell managers what decision to make. Alternatives have not yet been laid out, so a sensible decision cannot be made.

Calculating the expected values of alternatives is sometimes called rolling back a decision tree. Rolling back a decision tree means calculating its expected value. In Exhibit 4.1, the expected return is $80,000.

Decision trees probably don’t need to be drawn for scenarios as simple as this example, but a little more complexity can make construction of a tree worthwhile (see Exhibit 4.2). The consultant might have noted that there is one chance in four that the state will reduce nursing home payments. If pay- ments are reduced, profits will be $100,000 if the improvements succeed or $0 if they fail. The chance of rate cuts reduces expected profits to $75,000. The updated decision tree also displays the profit available from an alterna- tive investment, in this case a short-term bond that returns $40,000. Most profit-oriented decision makers would prefer to invest in the nursing home

Decision tree A visual decision support tool that depicts the values and probabilities of the outcomes of a choice

Improvements fail

Expected Profit = $80,000

Improvements succeed

P = 0.6

P = 0.4

Profit = $120,000 P = 0.60

Profit = $20,000 P = 0.40

EXHIBIT 4.1 A Nursing Home

Decision Tree

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because its expected profit is higher and its outcomes with low profits do not entail losses.

To make sure that you understand Exhibit 4.2, answer the following questions.

• Why does the probability that the improvements fail and rates are cut equal 0.10?

• Why does profit equal $0 if the improvements fail and rates are cut? • Why is expected profit less in Exhibit 4.2 than in Exhibit 4.1?

Estimates of the variability of outcomes can be useful for making comparisons. Variability is typically measured by listing the range of possible values or by listing the standard deviation (which is the square root of the variance). If you are not comparing outcomes, the standard deviation is not helpful. In contrast, the range can convey useful information even if you are not comparing outcomes. The range helps you see the best- and worst-case scenarios. To know whether a risk is worth taking, you need to know the size of the risk and the potential payoff. Few people will want to take a risk

Range The difference between the largest and smallest values of a variable

Standard deviation The square root of a variance

Profit = $100,000 P =0.15

Profit = $120,000 P = 0.45

Profit = $0 P = 0.10

$20,000 P = 0.30

Short-term bond = $40,000

Expected Profit = $75,000

Rate cuts

No rate cuts

P = 0.25

P = 0.75

Rate cuts

No rate cuts

P = 0.25

P = 0.75

Improvements succeed

Improvements fail

P = 0.6

P = 0.4

EXHIBIT 4.2 A Nursing Home Decision Tree with the Possibility of Rate Cuts

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if the best possible payoff is small or if the worst payoff is disastrous. On the other hand, if the best payoff is large, some people will be willing to accept significant risks.

To calculate variance, multiply the squared difference between the value of each outcome and the expected value by its probability of occur- rence and then add the resulting products. (Find the appropriate probability of occurrence by multiplying the probability on the “branch” of the outcome by the probability on the preceding branch.) So, in our example, the variance equals 0.15 × ($100,000 − $75,000)2 + 0.45 × ($120,000 − $75,000)2 + 0.10 × ($0 − $75,000)2 + 0.3 × ($20,000 − $75,000)2, or $2,475,000,000. The standard deviation is the square root of $2,475,000,000, which is $49,749.

A standard deviation or variance has meaning only when you are com- paring options. If two choices have similar expected values, the one with the higher standard deviation carries a higher risk because a larger standard devia- tion means that the bad outcomes are either more likely or much worse. For example, a project that has an 85 percent chance of earning $0 and a 15 per- cent chance of earning $500,000 also has an expected profit of $75,000. The standard deviation for this project is $178,536, confirming its higher risk.

Variance The squared deviation of a random variable from its expected value (If a variable takes the value 3 with a probability of 0.2, the value 6 with a probability of 0.3, and the value 9 with a probability of 0.5, its expected value is 6.9. Its variance is 5.49, which is 0.2 × [3 − 6.9]2 + 0.3 × [6 − 6.9]2 + 0.5 × [9 − 6.9]2.)

Investing in Cardiology Services

“It’s time for us to commit to building a center of excellence in cardiac care,” said Shea, the hospi-

tal’s chief financial officer. “Mercy and Central did it three years ago, and they are doing extremely well. Medicare pays well, and the private insurers pay even better. We cannot afford to miss this opportunity.”

“Perhaps,” said Emerson, the hospital’s chief medical officer. “Let me lay out a couple of issues that we need to consider. First, there’s no guarantee that the insurers will keep on paying so well for cardiology services. Most observers think that prices are higher than they need to be, and Medicare is facing a financial crisis. I think that Medicare will move to a bundled payment for many cardiology services before too long. The cardiologists will continue to do nicely, but they will have powerful incentives to cut back on imaging, to cut back on catheteriza- tions, and to switch to less invasive interventions. The net effect will be to slash hospital revenues. Second, there’s no guarantee that we will be able to attract a team of top-notch cardiologists. Those guys are in short supply these days. Without a really superb team, we will not get this off the ground.”

Case 4.2

(continued)

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Remember, though, the point of these calculations is to improve your analysis. The analysis should include an understanding of the size of the risk, how likely it is to occur, and whether it is worth taking. If your target audi- ence, which might include members of the board or nonfinancial managers, is puzzled by your analysis and does not really understand the issues, you have failed to present it effectively. Your audience will not be able to offer useful feedback, and the decision to take or not take the risk will be all yours. Managers could be terminated for taking risks that the board and other man- agers understood and approved. Managers will be terminated for taking risks that the board and other managers did not understand.

4.3.1 Risk Preferences Risk preferences may influence choices. A risk-seeking person prefers more variability. Someone who gambles in a casino must be a risk seeker because

Risk seeker A decision maker who prefers more risk to less (A risk seeker would prefer a gamble with a 50 percent chance of getting nothing and a 50 percent chance of getting $10 to getting $5 for sure.)

“OK,” said Shea. “Here is what the planning team has forecast. We will need a 24-bed unit, office space for three cardiologists, a 64-slice CT

scanner, and a cardiac catheterization lab. We estimate that this setup will cost us $10 million. We estimate that this change will increase inpa- tient days by 1,500, resulting in profits of $2 million. We also estimate that we will have 1,000 new outpatient procedures, which will generate $500,000 in profits. That represents a very nice return on our investment and leaves us some room for error in our cost and revenue forecasts. Personally, I do not think that Medicare will make any changes fast. The ability of the federal government to avoid taking action is unsurpassed. And I am confident that we will be able to recruit cardiologists.”

Discussion questions: • How likely is a change in Medicare payment? What probability

should you assign to it?

• What will happen to hospital profits if Medicare does switch to bundled payments?

• How likely is a failure to recruit three excellent cardiologists? What probability should you assign to this endeavor? What will happen to profits if you are able to recruit only two excellent cardiologists?

• If you set up this scenario as a decision tree, which of your assumptions become clear to other decision makers?

• What are the advantages of making your assumptions clear? What are the disadvantages?

Case 4.2 (continued)

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the expected payoff from a dollar bet will always be less than a dollar because of taxes and the casino’s take. Likewise, a patient who can expect to live 18 months if he undergoes standard therapy may be a risk seeker. He may prefer a therapy that gives him an expected life span of only 13 months if it increases his chances of significant recovery. The manager of a nearly bankrupt business is likely also a risk seeker. Taking chances, even chances with low expected payoffs, may be the only way to survive.

A risk-neutral person does not care about variability and will always choose the outcome with the highest expected value. Large organizations with substantial reserves can afford to be risk neutral. For example, a firm with $400 million in cash reserves will probably not buy fire insurance for a $200,000 clinic. If the expected loss is $4,000 per year (a 2 percent chance of a $200,000 loss), the organization’s fire insurance will cost at least $4,400 because of processing costs and insurer profits. On average, the firm will have higher profits if it does not insure this risk, and it can afford not to. Spending $200,000 for a new clinic will not put much of a dent in the organization’s reserves.

A risk-averse person avoids variability and will sometimes choose strate- gies with smaller expected values to avoid risk. An individual who buys health insurance is likely to demonstrate risk aversion because the expected value of his or her covered expenses will usually be less than the premium. Insurance premiums must cover the insurer’s expected payout, its cost of operation, and some return on invested capital. Unless a beneficiary’s expected benefits (the insurer’s expected payouts) have been incorrectly estimated, the insurer’s costs and profits will push insurance premiums above expected losses. By definition, someone who will pay an insurance premium is risk averse.

4.3.2 Decision Analysis Formal decision analysis has three steps, and only one of them is difficult (Hammond, Keeney, and Raiffa 1998). The steps are setting up a decision tree, identifying the alternative with the largest expected value, and using sensitivity analysis to assess the robustness of the analysis. Setting up a deci- sion tree is the hardest and most important part of decision analysis. Most insights are gained, but also most mistakes are made, in this step. Six steps are involved in setting up a decision tree.

1. Carefully define the problem. Often this task is harder than it sounds. 2. Identify the alternative courses of action. Serious mistakes are often

made here. 3. Identify the outcomes associated with each alternative. 4. Identify the sequence of events leading to final outcomes. This

sequence may include choices and chance events.

Risk neutral Indifferent to risk in decision making (A risk-neutral person would think that getting $5 for sure is as good as a gamble with a 50 percent chance of getting nothing and a 50 percent chance of getting $10.)

Risk aversion The reluctance of a decision maker to accept an outcome with an uncertain payoff rather than a smaller, more certain outcome (A risk-averse person would prefer getting $5 for sure to a gamble with a 50 percent chance of getting nothing and a 50 percent chance of getting $10.)

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5. Calculate the probability of each outcome. 6. Calculate the value of each outcome.

Each of these steps is more difficult than it sounds, so often the first decision is whether to do a decision analysis at all.

4.3.3 Sensitivity Analysis Any time setting up and solving a decision tree are worthwhile, performing a sensitivity analysis is equally worthwhile. A sensitivity analysis substitutes different, but plausible, values for the values in a decision tree. Gauging the effects of minor data changes on the results is always helpful. The data are never perfect, and using them as if they were would not make sense.

The decision tree for the nursing facility purchase tells us that the key issue is whether its manager can realize the operational improvements and product line changes that she is contemplating. If she can, the return on equity will be no less than 8.3 percent, no matter what Medicare does. A sensitivity analysis tells us that if she can realize about 70 percent of her projected gains, she can expect a 7 percent return on equity, no matter what Medicare does. What could she do to increase the odds of full improvement? The sensitivity analysis indicates that we can fall somewhat short of the man- ager’s prediction and still hit the target rate of return.

4.4 Managing Risk

Risk sharing and diversification are the only two strategies for managing risk. Buying an insurance policy is the obvious way to share risk, although joint ventures or options can serve the same function. For insurance, consumers pay a fee to induce another organization to share risks; joint ventures or options share costs and profits with partners. Diversification can take a number of forms. Horizontal integration (creating an organization that can offer the full spectrum of healthcare services) is one diversification strategy because some aspects of healthcare are likely to be profitable no matter what the environment. All of these strategies limit potential losses, but they also limit potential profitability.

4.4.1 Risk Sharing Joint ventures and options are common risk-sharing methods in the biotech- nology and pharmaceutical fields. For example, in 2012 Pfizer and Zhejiang Hisun Pharmaceutical Company launched a joint venture to offer products for cardiovascular disease, infectious disease, oncology, and mental health in China (Khan 2012). This venture will be a full-service pharmaceutical company with manufacturing, marketing, and research capabilities. Likewise, Pfenex and

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Agila Biotech announced a joint venture in 2013 to develop, manufacture, and commercialize an initial group of six products for the global market (Pfenex 2013). The two firms will share product development and marketing decisions. In 2013 Novartis purchased an option to buy Sideris Pharmaceuticals (Car- roll 2013). Sideris, which got initial funding from a number of venture capital firms, was working on a drug that flushes iron from the body. Novartis has the option to complete the purchase if clinical trials confirm the drug’s safety and efficacy. As a result, Novartis and the current owners share the risk that the drug will not be commercially viable. In a very different type of joint venture, Microsoft joined with General Electric to connect software applications with healthcare hardware. The objective was to offer a performance management suite that supports decision support and analysis (Tu 2012).

This example illustrates another facet of risk sharing. Often the cost that an organization seeks to share is the enormous cost of acquiring a key competency. Working with a knowledgeable partner allows the organization to gain experience. A lot of time and money is needed to build expertise, and joint ventures can reduce the risk of expending these resources needlessly. Of course, the organization must also assess what the gains are for the partner, such as expertise and profits.

4.4.2 Diversification Diversification consists of identifying a portfolio of projects or therapies that are not highly positively correlated. Exhibit 4.3 compares investing in a clinic, investing in a trauma unit, and investing in a portfolio of 50 percent shares of each. Forecasts of return on investment for the projects depend on whether the growth of an HMO is rapid, moderate, or slow. The clinic is a better investment than the trauma unit (higher expected profits and lower standard

HMO Growth

Rapid Moderate Slow

Growth probabilities 0.160 0.700 0.140

Profits Expected Standard Deviation

Clinic profits 10.0% 4.0% −1.0% 4.3% 3.0%

Trauma unit profits −3.0% 2.0% 13.0% 2.7% 4.5%

Portfolio profits (50% of each) 3.5% 3.0% 6.0% 3.5% 1.0%

EXHIBIT 4.3 Diversification

and Risk Reduction

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deviation of profits). The portfolio is also a better investment than the trauma unit (higher expected profits and lower standard deviation of profits). The portfolio might be a better investment than the clinic for a risk-averse inves- tor (lower expected profits but a lower standard deviation of profits).

Joint ventures can make diversification less risky, as Case 4.3 illustrates.

Diversification by Joint Venture

As of 2013 the University of Pittsburgh Medical Center (UPMC) had international operations in

seven countries. It operates cancer centers and a full-service hospital in Ireland; transplantation, radiotherapy, and biotechnology centers in Italy; information technology and cancer centers in the United King- dom; cancer center consults in Kazakhstan; transplantation in Singa- pore; pathology consulting in China; and educational training in pri- mary care in Japan. UPMC is exploring expansion in Cyprus and Qatar. Most of these represent joint ventures with local partners (UPMC 2013).

In addition to its international operations, UPMC launched a domestic joint venture in 2011 with the Advisory Board, a consulting firm (Kliff 2013). Each partner invested $20 million in Evolent Health, which provides consulting services to other healthcare organiza- tions. In addition, the Advisory Board brought consulting experience and a list of potential customers. UPMC brought years of experience in operating its own insurance plan, clinical expertise, and the infra- structure to coordinate care. Evolent Health supports the development strategies to reduce readmissions, to start medical homes, to create accountable care organizations, and even to form HMOs.

UPMC is headquartered in Pittsburgh, where it has a commanding presence. The largest employer in western Pennsylvania, with more than 50,000 employees and nearly $8 billion in revenue, UPMC owns 20 hospitals, 400 outpatient sites, a large insurance plan, and a num- ber of other healthcare ventures (UPMC 2013).

Discussion questions: • Why is expansion outside the United States an attractive form of

diversification?

• What are the pitfalls of international expansion?

• What are the potential pitfalls of other diversification efforts?

• What are the main risks that UPMC faces in its Pittsburgh operations?

Case 4.3

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4.5 Conclusion

The goal of describing, evaluating, and managing risk is improving choices, not identifying perfect choices. Even when the evidence available to a deci- sion maker is good and he or she makes a good decision, bad outcomes can result. More often, though, medical and managerial decisions are made with inadequate information. For example, managers often must make invest- ment decisions long before they know how well technology will work, what volumes will be, and what rivals will do. Even when a manager has access to good information (which will never be the case with innovative choices), the possible consequences of his or her choices remain uncertain.

Good management, however, can reduce risk and reduce the con- sequences of risk. Some risks need not be taken because the payoff would not be adequate. Some risks can be shared via joint ventures or insurance. Some risks can be hedged via diversification. A balanced portfolio of projects and lines of business can be profitable in any market environment. Reduc- ing variations in costs (so that risks are lower in capitated environments) or reducing fixed costs (so that sales slumps have fewer negative effects) can cut risk sharply. Finally, there’s nothing like a high margin to reduce risk. If pos- sible outcomes are a 15 percent return on equity or an 11 percent return on equity, most managers will sleep well.

Exercises

4.1 Five of ten people earn $0, four earn $100, and one loses $100. What is the expected payoff? What is the variance of the payoff?

4.2 There is a 50 percent chance of making $0, a 40 percent chance of making $100, and a 10 percent chance of losing $100. Calculate the expected value and variance of the payoff. How does your estimate compare to the previous problem?

4.3 There is a 1 percent chance that you will have healthcare bills of $100,000, a 19 percent chance that you will have healthcare bills of $10,000, a 60 percent chance that you will have healthcare bills of $500, and a 20 percent chance that you will have healthcare bills of $0. What is your expected healthcare spending?

4.4 There is a 1 percent chance that you will have healthcare bills of $100,000, a 19 percent chance that you will have healthcare bills of $10,000, a 60 percent chance that you will have healthcare bills of $500, and a 20 percent chance that you will have healthcare bills of $0. What will your expected insurance benefits be? Would you be willing to buy complete insurance coverage if it cost $3,712? Explain.

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4.5 Instead of complete insurance as in Exercise 4.4, you have a policy with a $5,000 deductible. What will your expected out-of- pocket spending be? What will your expected insurance benefits be? Assuming that the premium equals 116 percent of expected insurance benefits, do you prefer the policy with a $5,000 deductible or complete coverage? Explain.

4.6 Your firm, which operates a nationwide system of cancer clinics, has annual profits of $800 million and cash reserves of $500 million. Your clinics have a replacement value of $200 million, and fire insurance for them would cost $5 million per year. Actuarial data show that your expected losses due to fire are $4 million. Should you buy insurance?

4.7 Your firm rents a supply management system to hospitals. You have received a buyout offer of $5 million. You forecast a 25 percent chance that you will have profits of $10 million, a 35 percent chance that you will have profits of $6 million, and a 40 percent chance that you will have profits of $2 million. Should you accept the offer? Explain.

4.8 You were given a lottery ticket. The drawing will be held in 5 minutes. You have a 0.1 percent chance of winning $10,000. You refuse an offer of $11 for your ticket. Are you risk averse? Explain.

4.9 Your house is worth $200,000. Your risk of a catastrophic flood is 0.5 percent. Such a flood would destroy your house and would not be covered by homeowner’s insurance. Although you grumble, you buy flood coverage for $1,200. Are you risk averse or risk seeking?

4.10 Your firm faces considerable revenue uncertainty because you have to negotiate contracts with several customers. You forecast a 20 percent chance that your revenues will be $200,000, a 30 percent chance that your revenues will be $300,000, and a 50 percent chance that your revenues will be $500,000. Your costs are also uncertain because the prices of your supplies fluctuate considerably. You forecast a 40 percent chance that your costs will be $400,000 and a 60 percent chance that your costs will be $250,000. Use Excel to set up a decision tree for your profit forecast (it does not matter whether costs or revenues come first). How many possible profit outcomes do you have? What is your expected profit?

4.11 Your firm has been sued for $3 million by a supplier for breach of contract. Your lawyers believe that there are three possible outcomes if the suit goes to trial. One, which the lawyers term highly improbable, is that your supplier will win the lawsuit and be awarded $3 million. Another, which the lawyers term unlikely, is that your supplier will win the lawsuit and be awarded $500,000.

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The third, which the lawyers term likely, is that your supplier will lose the lawsuit and be awarded $0. You have to decide whether to try to settle the case. To do so you need to assign probabilities to “highly improbable,” “unlikely,” and “likely.” What probabilities correspond to these statements? Going to trial will cost you $100,000 in legal fees. One of your lawyers believes that your supplier will settle for $100,000 (and you will have legal fees of $25,000). Should you settle?

References

Carroll, J. 2013. “Novartis Grabs an Option to Buy Biotech Startup for Up to $300M.” FierceBiotech. Published October 22. www.fiercebiotech.com/story/ novartis-grabs-option-buy-biotech-startup-300m/2013-10-22.

de la Merced, M. J. 2012. “Aetna Agrees to Buy Coventry in $5.7 Billion Deal.” New York Times, August 12.

Donley, M., and R. Britt. 2008. “Humana Slides Again on Profit Warning.” Market-Watch. Published March 12. www.marketwatch.com/story/humana- warns-on-profit-shares-slide-for-second-day.

Gold, M., G. Jacobson, A. Damico, and T. Neuman. 2013. Medicare Advan- tage 2013 Spotlight: Enrollment Market Update. Kaiser Family Foundation Issue Brief. Published June. http://kaiserfamilyfoundation.files.wordpress. com/2013/06/8448.pdf.

Hammond, J. S., R. L. Keeney, and H. Raiffa. 1998. Smart Choices: A Practical Guide to Making Better Decisions. Boston: Harvard Business Review Press.

Khan, N. 2012. “Hisun-Pfizer Pharmaceutical to Hire 600 China Staff by Year-End.” Bloomberg. Published September 13. www.bloomberg.com/news/2012-09- 13/hisun-pfizer-pharmaceutical-to-hire-600-china-staff-by-year-end.html.

Kliff, S. 2013. “Is This the End of Health Insurers?” Washington Post, July 5. Pfenex. 2013. “Pfenex Inc. and Agila Biotech Private Limited Announce Joint Ven-

ture to Develop Biosimilar Products for the Global Market.” Published April 16. www.pfenex.com/news/details/31.

Tu, J. I. 2012. “Microsoft, GE Uniting to Create Better Health-Care Data Systems.” Seattle Times. Published September 26. http://seattletimes.com/html/ businesstechnology/2019270995_microsoftcaradigmxml.html.

University of Pittsburgh Medical Center (UPMC). 2013. “Business Ventures.” Accessed July 2, 2014. www.upmc.com/about/partners/ventures/Pages/ default.aspx.

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CHAPTER

73

5UNDERSTANDING COSTS Learning Objectives

After reading this chapter, students will be able to

• calculate average and marginal costs, • articulate why efficiency is important, • identify opportunity costs, • forecast how changes in technology and prices will change costs, and • discuss the relationship between cost and quality.

Key Concepts

• Costs depend on perspective. • Costs can be hard to measure. • Good managers have an accurate understanding of costs. • Goods and services an organization produces are called outputs. • Goods and services an organization uses in production are called

inputs. • Incremental cost equals the change in cost resulting from a change in

output. • Average cost equals the total cost of a process divided by the total

output of a process. • Large firms have a cost advantage if there are economies of scale. • Multiproduct firms have a cost advantage if there are economies of scope. • Higher quality should mean higher costs. If not, the organization is

inefficient. • Higher input prices mean higher costs. • Costs depend on outputs, technology, input prices, and efficiency. • Opportunity cost is the value of a resource in its best alternative use. • Sunk costs, which are costs you cannot change, should be ignored.

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