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9

Making Decisions 1.

Hiro owns and operates a small business that provides economic consulting services. During the year he spends $55,000 on travel to clients and other expenses, and the computer that he owns depreciates by $2,000. If he didn’t use the computer, he could sell it and earn yearly interest of $100 on the money created through this sale. Hiro’s total revenue for the year is $100,000. Instead of working as a consultant for the year, he could teach economics at a small local college and make a salary of $50,000. a. What is Hiro’s accounting profit? b. What is Hiro’s economic profit? c. Should Hiro continue working as a consultant, or should he teach economics instead?

1. Solution

a. Hiro’s accounting profit is: $100,000 (total revenue) − $55,000 (travel and other expenses) − $2,000 (depreciation) $43,000 (accounting profit)

b. Hiro’s economic profit is: $43,000 (accounting profit) − $100 (interest forgone) − $50,000 (salary as economics professor) −

$7,100 (economic profit)

c. Since Hiro’s economic profit is negative, he would be better off if he didn’t operate the consulting business and taught economics instead.

2.

Jackie owns and operates a web-design business. Her computing equipment depreciates by $5,000 per year. She runs the business out of a room in her home. If she didn’t use the room as her business office, she could rent it out for $2,000 per year. Jackie knows that if she didn’t run her own business, she could return to her previous job at a large software company that would pay her a salary of $60,000 per year. Jackie has no other expenses. a. How much total revenue does Jackie need to make in order to break even in the eyes of her accountant? That is, how much total revenue would give Jackie an accounting profit of just zero? b. How much total revenue does Jackie need to make in order for her to want to remain self-employed? That is, how much total revenue would give Jackie an economic profit of just zero?

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Solution 2.

a. Jackie’s accounting profit is: Total revenue − $5,000. (The only cost that her accountant would add into the accounting profit calculation is depreciation.) For her accounting profit to be just equal to zero, her total revenue would have to be $5,000. b. Jackie’s economic profit is: Total revenue − $5,000 − $2,000 − $60,000 = Total revenue − $67,000. (Depreciation, the opportunity cost of not renting out the room, and the opportunity cost of Jackie’s time are all costs that figure into the calculation of economic profit.) For this to be just equal to zero, Jackie’s total revenue would have to be $67,000.

3.

You own and operate a bike store. Each year, you receive revenue of $200,000 from your bike sales, and it costs you $100,000 to obtain the bikes. In addition, you pay $20,000 for electricity, taxes, and other expenses per year. Instead of running the bike store, you could become an accountant and receive a yearly salary of $40,000. A large clothing retail chain wants to expand and offers to rent the store from you for $50,000 per year. How do you explain to your friends that despite making a profit, it is too costly for you to continue running your store?

Solution 3.

Your yearly accounting profit is: $200,000 (total revenue) − $100,000 (cost of bikes) − $20,000 (electricity, taxes, and other expenses) $80,000 (accounting profit)

But not renting the store to the retail chain is an opportunity cost, and not being able to make $40,000 as an accountant is also an opportunity cost, so your yearly economic profit is: − −

$80,000 (accounting profit) $40,000 (opportunity cost of your time) $50,000 (opportunity cost of not renting the store)

−

$10,000 (economic profit)

So although you make an accounting profit each year, you would be better off renting the store to the large chain and becoming an accountant yourself, since your opportunity cost of continuing to run your own store is too high.

4.

Suppose you have just paid a nonrefundable fee of $1,000 for your meal plan for this academic term. This allows you to eat dinner in the cafeteria every evening. a. You are offered a part-time job in a restaurant where you can eat for free each evening. Your parents say that you should eat dinner in the cafeteria anyway, since you have already paid for those meals. Are your parents right? Explain why or why not. b. You are offered a part-time job in a different restaurant where, rather than being able to eat for free, you receive only a large discount on your meals. Each meal there will cost you $2; if you eat there each evening this semester, it will add up to $200. Your roommate says that you should eat in the restaurant since it costs less than the $1,000 that you paid for the meal plan. Is your roommate right? Explain why or why not.


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Solution 4.

a. Your parents are wrong. They are making the mistake of considering sunk costs. Since the $1,000 that you have already paid for the meal plan is nonrefundable, it should not enter into your decision making now. Your decision of where to eat should depend only on those costs and benefits that are affected by your decision. Since both the cafeteria meals and the restaurant meals are free, you should choose to eat where the benefit to you (convenience, quality of food, and so on) is greater. b. Your roommate is wrong. Since the $1,000 that you have already paid for the meal plan is nonrefundable, it should not enter into your decision making now. It is a sunk cost. In deciding where to eat, you should weigh the benefit and cost of eating in the restaurant (where each meal costs $2) against the benefit and cost of eating in the cafeteria (where meals are free). You may decide to eat in the restaurant, but only if that gives you a benefit that is at least $2 greater than the benefit you get from eating in the cafeteria.

5.

You have bought a $10 ticket in advance for the college soccer game, a ticket that cannot be resold. You know that going to the soccer game will give you a benefit equal to $20. After you have bought the ticket, you hear that there will be a professional baseball post-season game at the same time. Tickets to the baseball game cost $20, and you know that going to the baseball game will give you a benefit equal to $35. You tell your friends the following: “If I had known about the baseball game before buying the ticket to the soccer game, I would have gone to the baseball game instead. But now that I already have the ticket to the soccer game, it’s better for me to just go to the soccer game.” Are you making the correct decision? Justify your answer by calculating the benefits and costs of your decision.

Solution 5.

Yes, you are making the correct decision. If you had known about the baseball game before buying the ticket to the soccer game, your decision would have been as follows: Go to the soccer game

Go to the baseball game

$20 (benefit) −$10 (cost of ticket)

$35 (benefit) −$20 (cost of ticket)

$10

$15

Since the baseball game would have given you the greater total net gain, you should have gone to the baseball game. But after you have already bought the ticket to the soccer game, your decision is different: the ticket to the soccer game (since it cannot be resold) is now a sunk cost, and you should no longer take it into account. Your decision now looks as follows: Go to the soccer game $20 (benefit) $20

Go to the baseball game $35 (benefit) −$20 (cost of ticket) $15

So, since you had already bought the ticket to the soccer game before you heard about the baseball game, it is optimal for you to go to the soccer game.

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6.

Amy, Bill, and Carla all mow lawns for money. Each of them operates a different lawn mower. The accompanying table shows the total cost to Amy, Bill, and Carla of mowing lawns. Quantity of lawns mowed

Amy’s total cost

Bill’s total cost

Carla’s total cost

0

$0

$0

$0

1

20

10

2

2

35

20

7

3

45

30

17

4

50

40

32

5

52

50

52

6

53

60

82

a. Calculate Amy’s, Bill’s, and Carla’s marginal costs, and draw each of their marginal cost curves. b. Who has increasing marginal cost, who has decreasing marginal cost, and who has constant marginal cost?

Solution 6.

a. The accompanying table shows Amy’s, Bill’s, and Carla’s marginal costs. Amy’s marginal Amy’s cost of total cost lawn mowed

Quantity of lawns mowed

0

Bill’s total cost

$0

Bill’s marginal cost of Carla’s lawn mowed total cost

$0

$0

$20 1

20

2

35

3

45

4

50

5

52

6

53

Carla’s marginal cost of lawn mowed

$10 10

$2 2

15

10 20

5 7

10

10 30

10 17

5

10 40

15 32

2

10 50

20 52

1

10 60

30 82

The accompanying diagram shows Amy’s, Bill’s, and Carla’s marginal cost curves. Marginal cost of lawn mowed $30

Amy’s MC

Carla’s MC Bill’s MC

20

10

0

1

2

3 4 5 6 Quantity of lawns mowed


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b. From the information in the table or from the diagram, you can see that Amy has decreasing marginal cost, Bill has constant marginal cost, and Carla has increasing marginal cost. (Also note that all of them have increasing total cost.)

7.

You are the manager of a gym, and you have to decide how many customers to admit each hour. Assume that each customer stays exactly one hour. Customers are costly to admit because they inflict wear and tear on the exercise equipment. Moreover, each additional customer generates more wear and tear than the customer before. As a result, the gym faces increasing marginal cost. The accompanying table shows the marginal costs associated with each number of customers per hour. Quantity of customers per hour

Marginal cost of customer

0 $14.00 1 $14.50 2 $15.00 3 $15.50 4 $16.00 5 $16.50 6 $17.00 7

a. Suppose that each customer pays $15.25 for a one-hour workout. Use the principle of marginal analysis to find the optimal number of customers that you should admit per hour. b. You increase the price of a one-hour workout to $16.25. What is the optimal number of customers per hour that you should admit now?

Solution 7.

a. The marginal benefit of each customer is $15.25: each additional customer you admit increases the total benefit to the gym by $15.25. So you should admit three customers per hour. Here is how you could think about that decision. Suppose you currently admit no customers. Admitting the first customer gives the gym a marginal benefit of $15.25 and a marginal cost of $14.00. Since the marginal benefit of that first customer exceeds the marginal cost, you want to admit the first customer. For the second customer, the marginal benefit ($15.25) also exceeds the marginal cost ($14.50), so you want to admit the second customer, too. The same is true for the third customer: the marginal benefit ($15.25) exceeds the marginal cost ($15.00), so you also want to admit the third customer. For the fourth customer, however, the marginal cost ($15.50) exceeds the marginal benefit ($15.25), so you do not want to admit a fourth customer. b. By reasoning similar to that in part a, you now want to admit five customers: for the fifth customer, the marginal benefit ($16.25) exceeds the marginal cost ($16.00). For the sixth customer, however, the marginal cost ($16.50) exceeds the marginal benefit, so you do not want to admit a sixth customer.

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8.

Georgia and Lauren are economics students who go to a karate class together. Both have to choose how many classes to go to per week. Each class costs $20. The accompanying table shows Georgia’s and Lauren’s estimates of the marginal benefit that each of them gets from each class per week. Quantity of classes

Lauren’s marginal benefit of each class

Georgia’s marginal benefit of each class

$23

$28

$19

22

$14

15

$08

7

0 1 2 3 4

a. Use marginal analysis to find Lauren’s optimal number of karate classes per week. Explain your answer. b. Use marginal analysis to find Georgia’s optimal number of karate classes per week. Explain your answer.

Solution 8.

The marginal cost of one more class is always $20: each additional class that Lauren or Georgia takes will cost an additional $20. a. The optimal number of classes per week for Lauren is one. The marginal benefit to Lauren of the first class is $23, and the marginal cost is $20. Since the marginal benefit exceeds the marginal cost, Lauren wants to take that first class. For the second class, Lauren’s marginal benefit ($19) is less than the marginal cost ($20), so she does not want to take a second class. b. Georgia would be better off adding a second class per week. For the second class, the marginal benefit to Georgia ($22) exceeds the marginal cost ($20), so she wants to take the second class. For the third class, the marginal cost ($20) would exceed the marginal benefit ($15), so Georgia does not want to take the third class. For Georgia, the optimal number of classes per week is two.

9.

The Centers for Disease Control and Prevention (CDC) recommended against vaccinating the whole population against the smallpox virus because the vaccination has undesirable, and sometimes fatal, side effects. Suppose the accompanying table gives the data that are available about the effects of a smallpox vaccination program. Percent of population vaccinated

0%

Deaths due to smallpox

Deaths due to vaccination side effects

200

0

10

180

4

20

160

10

30

140

18

40

120

33

50

100

50

60

80

74

a. Calculate the marginal benefit (in terms of lives saved) and the marginal cost (in terms of lives lost) of each 10% increment of smallpox vaccination. Calculate the net gain for each 10% increment in population vaccinated. b. Using marginal analysis, determine the optimal percentage of the population that should be vaccinated.


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Solution 9.

a. The accompanying table gives the marginal benefit and the marginal cost of smallpox vaccination. The marginal benefit is the additional number of lives saved if we vaccinate an additional 10% of the population. For instance, if instead of vaccinating 0% of the population (resulting in 200 deaths from smallpox), we vaccinate 10% of the population (resulting in 180 deaths from smallpox), we have saved 20 lives. That is, the marginal benefit of vaccinating 10% (instead of 0%) of the population is 20 lives. Repeating this for the step from 10% to 20% vaccination, and so on, gives us the marginal benefit numbers in the table. The marginal cost is the additional number of lives lost if we vaccinate an additional 10% of the population. For instance, if instead of vaccinating 0% of the population (resulting in 0 deaths due to side effects), we vaccinate 10% of the population (resulting in 4 deaths due to side effects), we have lost 4 lives. That is, the marginal cost of vaccinating 10% (instead of 0%) of the population is 4 lives. Repeating this for the step from 10% to 20% vaccination, and so on, gives us the marginal cost numbers in the table.

Percent of population vaccinated

Marginal benefit in lives saved

Marginal cost in lives lost

Net gain of 10% increment in population vaccinated

0 20

4

16

20

6

14

20

8

12

20

15

5

20

17

3

20

24

−4

10 20 30 40 50 60

b. The optimal percentage of the population that should be vaccinated is 50%. Suppose we were vaccinating 40% of the population. Then vaccinating an additional 10% (to bring the total up to 50%) would give us a marginal benefit of 20 lives saved. And vaccinating that additional 10% would give us a marginal cost of 17 lives lost. Since the marginal benefit exceeds the marginal cost, we do indeed want to vaccinate that additional 10% of the population. But do we want to go beyond 50% vaccination? Vaccinating an additional 10% (to bring the total up to 60%) would result in a marginal benefit of 20 lives saved and a marginal cost of 24 lives lost due to side effects. Since the marginal cost exceeds the marginal benefit, we do not want to increase the vaccination rate from 50% to 60%.

10.

In 2007, the online medical journal Circulation published a study that analyzed the cost-effectiveness of standard-dosage versus high-dosage amounts of statins, drugs designed to lower cholesterol. Patients of approximately 60 years of age were divided into two groups: ACS, or acute coronary syndrome, patients who had recently suffered a heart attack or chest pains severe enough for hospitalization; and CAD, or stable coronary artery disease, patients who had less severe cases of heart disease. The benefit of a dose of statins was measured in terms of the number of additional years of lifespan lived in a quality way—or QALYs (Quality-Adjusted Life Years). The table below gives some data from the study, where for each group, the outcome from the standard dose was the baseline. ACS

CAD

Standard dose

Baseline

Baseline

High dose

Additional 0.35 QALY

Additional 0.096 QALY

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In the following table, we have posed two assumptions about the value of a QALY: in the first case it is worth $30,000 and in the second case it is worth $50,000. We have assumed that ACS patients live an average of 6 additional years with the high dose than with the standard dose, and CAD patients live an average of 10 additional years with the high dose than with the standard dose. Both sets of patients must take the high dose for their entire future life span to receive the additional QALY benefits from it. We have also made two assumptions about the additional cost of a high dose versus a standard dose of statin: in the first case the high dose costs an additional $3.50 per day and in the second case the high dose costs an additional $1.25 per day. In the empty cells in the table, indicate whether the high dose therapy should be prescribed from weighing its marginal benefits and marginal costs. Explain your choices. Disregard the fact that some benefits and costs arrive at different times. Also assume that all years have 365 days (i.e., no leap years). QALY = $30,000

QALY = $50,000

ACS (additional 6 years over standard dose; high dose costs additional $3.50/day)

?

?


?

?

CAD (additional 10 years over standard dose; high dose costs additional $3.50/day)

?

?


?

?

10. Solution QALY = $30,000

QALY = $50,000


Yes

Yes


Yes

Yes


No

No


No

Yes

For an ACS patient, when a QALY = $30,000, a high dose therapy leads to a marginal benefit of 0.35 × $30,000 = $10,500; when a QALY = $50,000, a high dose therapy leads to a marginal benefit of 0.35 × $50,000 = $17,500. When the marginal cost of the high dose therapy is $3.50/day, the ACS patient must pay 365 days/year × $3.50/day × 6 years = $7,665 to receive the marginal benefit of the high-dose statin. Because the marginal cost is greater than the marginal benefit under both assumptions about QALY, the high dose therapy should be prescribed for ACS patients both when a QALY is worth $30,000 and when it is worth $50,000. This, clearly, also means that the high dose therapy should be prescribed for the ACS patients when the marginal cost per day is only $1.25.


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For a CAD patient, when a QALY is worth $30,000, a high dose therapy leads to a marginal benefit of 0.096 × $30,000 = $2,880; when a QALY is worth $50,000, a high dose therapy leads to a marginal benefit of 0.096 × $50,000 = $4,800. When the marginal cost of the high dose therapy is $3.50/day, the CAD patient must pay 365 days/year × $3.50/day × 10 years = $12,775 to receive the marginal benefit of the high statin. Because $12,775 is more than the marginal benefit under both assumptions about QALY, the high-dose statin therapy is not justified for CAD patients when it has a marginal cost of $3.50/day. When the marginal cost of the high dose therapy is $1.25/day, the CAD patient must pay 365 days/year × $1.25/day × 10 years = $4,562.50 to receive the marginal benefit of the high statin. $4,562.50 is more than the marginal benefit when a QALY is worth $30,000, but less than the marginal benefit when a QALY is worth $50,000. So the high-dose statin therapy should be prescribed only in the high QALY case.

11.

Patty delivers pizza using her own car, and she is paid according to the number of pizzas she delivers. The accompanying table shows Patty’s total benefit and total cost when she works a specific number of hours. Quantity of hours worked

Total benefit

Total cost

0

$0

$0

1

30

10

2

55

21

3

75

34

4

90

50

5

100

70

a. Use marginal analysis to determine Patty’s optimal number of hours worked. b. Calculate the total net gain to Patty from working 0 hours, 1 hour, 2 hours, and so on. Now suppose Patty chooses to work for 1 hour. Compare her total net gain from working for 1 hour with her total net gain from working the optimal number of hours. How much would she lose by working for only 1 hour?

Solution 11.

a. We first need to work out Patty’s marginal benefit and marginal cost of each additional hour worked, which are shown in the accompanying table. For instance, as Patty increases the number of hours worked from 2 to 3, her benefit increases from $55 to $75; that is, her marginal benefit is $20. Similarly, as she increases the number of hours worked from 2 to 3, her cost increases from $21 to $34; that is, her marginal cost is $13. Repeating this for increases in the number of hours from 0 to 1, from 1 to 2, and so on, gives the data in the accompanying table. Quantity of hours worked

Marginal benefit of hour worked

Marginal cost of hour worked

Net gain of hour worked

$30

$10

$20

25

11

14

20

13

7

15

16

–1

10

20

–10

0 1 2 3 4 5

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Patty should work for 3 hours because her marginal benefit of going from 2 hours to 3 hours ($20) exceeds the marginal cost of going from 2 hours to 3 hours ($13). But if she went from 3 hours to 4 hours, Patty’s marginal cost ($16) would exceed her marginal benefit ($15). So working that fourth hour is not optimal. b. The accompanying table shows Patty’s total net gain in the fourth column. The total net gain is the difference between total benefit and total cost. Quantity of hours worked

Total benefit

Total cost

Total net gain

0

$0

$0

$0

1

30

10

20

2

55

21

34

3

75

34

41

4

90

50

40

5

100

70

30

Patty’s loss from working for only 1 hour instead of the optimal 3 hours is $41 − $20 = $21.

12.

Assume De Beers is the sole producer of diamonds. When it wants to sell more diamonds, it must lower its price in order to induce consumers to buy more. Furthermore, each additional diamond that is produced costs more than the previous one due to the difficulty of mining for diamonds. De Beers’s total benefit schedule is given in the accompanying table, along with its total cost schedule. Quantity of diamonds

Total benefit

Total cost

0

$0

$0

1

1,000

50

2

1,900

100

3

2,700

200

4

3,400

400

5

4,000

800

6

4,500

1,500

7

4,900

2,500

8

5,200

3,800

a. Draw the marginal cost curve and the marginal benefit curve and, from your diagram, graphically derive the optimal quantity of diamonds to produce. b. Calculate the total net gain to De Beers from producing each quantity of diamonds. Which quantity gives De Beers the highest total net gain?


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Solution 12.

a. The accompanying table shows the marginal benefit and marginal cost of each diamond. The accompanying diagram graphs marginal benefit and marginal cost. From the diagram, you can conclude that the optimal number of diamonds to produce is 5. Quantity of diamonds

Total benefit

0

Marginal benefit

Total cost

$0

$0 $1,000

1

1,000

2

1,900

3

2,700

4

3,400

5

4,000

6

4,500

7

4,900

8

5,200

$50 50

900

50 100

800

100 200

700

200 400

600

400 800

500

700 1,500

400

1,000 2,500

300

Marginal benefit, marginal cost of diamond

Marginal cost

1,300 3,800

Optimal point

MC

$1,400 1,200 1,000 800 600 400

MB

200 0

1

2

3

4

5

6

7

8

Optimal quantity Quantity of diamonds

b. The accompanying table calculates the total net gain to De Beers from producing each quantity of diamonds. The quantity that gives De Beers the greatest total net gain is 5 diamonds. This is, of course, just what you found in part a. Quantity of diamonds

Total benefit

Total cost

Total net gain

0

$0

$0

$0

1

1,000

50

950

2

1,900

100

1,800

3

2,700

200

2,500

4

3,400

400

3,000

5

4,000

800

3,200

6

4,500

1,500

3,000

7

4,900

2,500

2,400

8

5,200

3,800

1,400

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13.

According to a report in the St. Louis (Missouri) Post-Dispatch, that city’s main thoroughfare, Interstate 64, will be completely closed to traffic for two years, from January 2008 to December 2009, for reconstruction at a cost of $535 million. If the construction company were to keep the highway open for traffic during construction, the highway reconstruction project would take much longer and be more expensive. Suppose that construction would take four years if the highway were kept open, at a total cost of $800 million. The Missouri Department of Transportation had to make its decision in 2007, one year before the start of construction (so that the first payment is one year away). So the Missouri Department of Transportation had the following choices: (i) Close Interstate 64 during construction, at an annual cost of $267.5 million per year for two years. (ii) Keep Interstate 64 open during construction, at an annual cost of $200 million per year for four years. a. Suppose the interest rate is 10%. Calculate the present value of the costs incurred under each plan. Which reconstruction plan is less expensive? b. Now suppose the interest rate is 80%. Calculate the present value of the costs incurred under each plan. Which reconstruction plan is now less expensive?

Solution 13.

a. The present value of plan (i) is: $267.5 million $267.5 million + = $243.18 million + $221.07 million = 1.1 1.12 $464.25 million The present value of plan (ii) is: $200 million $200 million $200 million $200 million + + + = 1.1 1.12 1.13 1.14 $181.82 million + $165.29 million + $150.26 million + 136.60 million = $633.97 million So plan (i) is less expensive. b. The present value of plan (i) is: $267.5 million $267.5 million + + $148.61 million + $82.56 million = 1.8 1.82 $231.17 million The present value of plan (ii) is: $200 million $200 million $200 million $200 million + + + = 1.8 1.82 1.83 1.84 $111.11 million + $61.73 million + $34.29 million + 19.05 million = $226.18 million Plan (ii) is now less expensive.

14.

You have won the state lottery. There are two ways in which you can receive your prize. You can either have $1 million in cash now, or you can have $1.2 million that is paid out as follows: $300,000 now, $300,000 in one year’s time, $300,000 in two years’ time, and $300,000 in three years’ time. The interest rate is 20%. How would you prefer to receive your prize?


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Solution 14.

If you choose to get $1.2 million paid out over the next three years, the present value of those payments is: $300,000 +

$300,000 $300,000 $300,000 + + = 1.2 1.22 1.23

$300,000 +

$300,000 $300,000 $300,000 + + = 1.2 1.44 1.728

$300,000 + $250,000 + $208,333 + $173,611 = $931,944 Since this is less than $1 million, you would prefer to get $1 million now instead of $1.2 million over four years.

15.

The drug company Pfizer is considering whether to invest in the development of a new cancer drug. Development will require an initial investment of $10 million now; beginning one year from now, the drug will generate annual profits of $4 million for three years. a. If the interest rate is 12%, should Pfizer invest in the development of the new drug? Why or why not? b. If the interest rate is 8%, should Pfizer invest in the development of the new drug? Why or why not?

Solution 15.

a. The net present value is: $4 million $4 million $4 million −$10 million + + + = −$392,675 1.12 1.122 1.123 Since the net present value is negative, Pfizer should not invest in the development of this drug: it would be better off putting the $10 million into a bank account that pays 12% interest. b. The net present value is: −$10 million +

$4 million $4 million $4 million + + = $308,387 1.08 1.082 1.083

Since the net present value is positive, Pfizer should invest in the development of this drug: the return on its initial investment of $10 million would be better than what it could get if it put the $10 million into a bank account paying 8% interest.

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