**Essay**

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**381**

1. A firm’s current profits are $1,000,000. These profits are expected to grow indefinitely at a constant annual rate of 3.5 percent. If the firm’s opportunity cost of funds is 5.5 percent, determine the value of the firm:

Instructions: Round your responses to 2 decimal places.

a. The instant before it pays out current profits as dividends.

$ million

b. The instant after it pays out current profits as dividends.

$ million

(page 18)

Explanation:

a. The value of the firm before it pays out current dividends is:

PVfirm = ,000,000((1 + 0.

06) / (0.06 – 0.04) = $52.75 million

b. The value of the firm immediately after paying the dividend is:

PVEx-Dividend firm= $1,000,000((1 + 0.04) / (0.06 – 0.04) = $51.75 millio

2, What is the value of a preferred stock that pays a perpetual dividend of $215 at the end of each year when the interest rate is 8 percent?

Instruction: Round your response to the nearest dollar.

$

The dividend divided by the interest rate

explanation:

The present value of the perpetual stream of cash flows. This is given by PVPerpetuity = CF / i = $215 / 0.08 = $2,688.

3. Jaynet spends $20,000 per year on painting supplies and storage space.

She recently received two job offers from a famous marketing firm – one offer was for $105,000 per year, and the other was for $85,000. However, she turned both jobs down to continue a painting career. If Jaynet sells 35 paintings per year at a price of $6,000 each:

a. What are her accounting profits?

$

b. What are her economic profits?

$

Explanation:

a. Her accounting profits are $190,000. These are computed as the difference between revenues ($210,000) and explicit costs ($20,000).

b. By working as a painter, Jaynet gives up the $105,000 she could have earned under her next best alternative. This implicit cost of $105,000 is in addition to the $20,000 in explicit costs. Since her economic costs are $125,000, her economic profits are $210,000 – $125,000 = $85,000.

4. You’ve recently learned that the company where you work is being sold for $440,000. The company’s income statement indicates current profits of $16,000, which have yet to be paid out as dividends. Assuming the company will remain a “going concern” indefinitely and that the interest rate will remain constant at 9 percent, at what constant rate does the owner believe that profits will grow?

Instruction: Round your response to 2 decimal places.

Growth rate of: 5.04 percent.

Explanation:

First, recall the equation for the value of a firm: . Next, solve this equation for g to obtain . Substituting in the known values implies a growth rate of 0.09 – ((1 + 0.09)16000) / 440000 or 5.04 percent.

5. Approximately 14 million Americans are addicted to drugs and alcohol. The federal government estimates that these addicts cost the U.S. economy $300 billion in medical expenses and lost productivity. Despite the enormous potential market, many biotech companies have shied away from funding research and development (R&D) initiatives to find a cure for drug and alcohol addiction. Your firm – Drug Abuse Sciences (DAS) – is a notable exception. It has spent $185 million to date working on a cure, but is now at a crossroads. It can either abandon its program or invest another $40 million today. Unfortunately, the firm’s opportunity cost of funds is 9 percent and it will take another five years before final approval from the Federal Drug Administration is achieved and the product is actually sold. Expected (year-end) profits from selling the drug are presented in the accompanying table.

Year 1

Year 2

Year 3

Year 4

Year 5

Year 6

Year 7

Year 8

Year 9

$0

$0

$0

$0

$10,600,000

$12,300,000

$14,100,000

$15,800,000

$18,200,000

What is the net present value of the project?

Instruction: Round your answer to the nearest penny (2 decimal places). Use a negative sign (-) where appropriate.

$

Should DAS continue with its plan to bring the drug to market, or should it abandon the project?

Explanation:

First, note that the $185 million spent to date is irrelevant. It is a sunk cost that will be lost regardless of the decision. The relevant question is whether the incremental benefits (the present value of the profits generated from the drug) exceed the incremental costs (the $40 million needed to keep the project alive). Since these costs and benefits span time, it is appropriate to compute the net present value. Here, the net present value of DAS’s R&D initiative is:

NPV = 10,600,000 / (1 + 0.09)5 + 12,300,000 / (1 + 0.09)6 + 14,100,000 / (1 + 0.09)7 + 15,800,000 / (1 + 0.09)8 + 18,200,000 / (1 + 0.09)9 – 40,000,000 = $-1,754,183.53

Since this is negative, DAS should not spend the $40 million.

6. The head of the accounting department at a major software manufacturer has asked you to put together a pro forma statement of the company’s value under several possible growth scenarios and the assumption that the company’s many divisions will remain a single entity forever. The manager is concerned that, despite the fact that the firm’s competitors are comparatively small, collectively their annual revenue growth has exceeded 50 percent over each of the last five years. She has requested that the value projections be

based on the firm’s current profits of $4.5 billion (which have yet to be paid out to stockholders) and the average interest rate over the past 20 years (8 percent) in each of the following profit growth scenarios:

a. Profits grow at an annual rate of 10 percent. (This one is tricky.)

Instructions: Round your responses to 2 decimal places.

b. Profits grow at an annual rate of 2 percent.

billion

c. Profits grow at an annual rate of 0 percent.

billion

d. Profits decline at an annual rate of 5 percent.

billion

Explanation:

a. Since the profits grow faster than the interest rate, the value of the firm would be infinite. This illustrates a limitation of using these simple formulas to estimate the value of a firm when the assumed growth rate is greater than the interest rate.

b. PVfirm = π((1 + i) / (i – g)) = $4.5(1.08 / 0.06) = $81 billion

c. PVfirm = π((1 + i) / (i – g)) = $4.5(1.08 / 0.08) = $60.75 billion

d. PVfirm = π((1 + i) / (i – g)) = $4.5(1.08 / 0.13) = $37.38 billion

7. The demand curve for product X is given by QXd = 420 – 4PX.

a. Find the inverse demand curve.

PX = – QXd

Instructions: Round your answer to the nearest penny (2 decimal places).

b. How much consumer surplus do consumers receive when Px = $50?

$

c. How much consumer surplus do consumers receive when Px = $25?

$

d. In general, what happens to the level of consumer surplus as the price of a good falls?

The level of consumer surplus as the price of a good falls. Explanation:

a. Solve the demand function for Px to obtain the following inverse demand function: PX = 105 – 0.25QXd.

b. Notice that when Px = $50, QXd = 420 – 4(50) = 220 units. Also, from part a, we know the vertical intercept of the inverse demand equation is 105. Thus, consumer surplus is $6,050.00 (computed as (0.5)($105 – $50)220 = $6,050.00).

c. When price decreases to $25, quantity demanded increases to 320 units, so consumer surplus increases to $12,800.00 (computed as (0.5)($105-$25)320 = $12,800.00).

d. So long as the law of demand holds, a decrease in price leads to an increase in consumer surplus, and vice versa. In general, there is an inverse relationship between the price of a product and consumer surplus.

8. Suppose demand and supply are given by Qd = 50 – P and Qs = 1.0P – 10.

a. What are the equilibrium quantity and price in this market?

Equilibrium quantity:

Equilibrium price: $

b. Determine the quantity demanded, the quantity supplied, and the magnitude of the surplus if a price floor of $45 is imposed in this market.

Quantity demanded:

Quantity supplied:

Surplus:

c. Determine the quantity demanded, the quantity supplied, and the magnitude of the shortage if a price ceiling of $25 is imposed in the market. Also, determine the full economic price paid by consumers.

Quantity demanded:

Quantity supplied:

Shortage:

Full economic price: $

Explanation:

a. Equating quantity supplied and quantity demanded yields the equation 50 – P = 1.0P -10. Solving for P yields the equilibrium price of $30 per unit. Plugging this into the demand equation yields the equilibrium quantity of 20 units (since quantity demanded at the equilibrium price is Qd = 50 – 30 = 20).

b. A price floor of $45 is effective since it is above the equilibrium price of $30. As a result, quantity demanded will fall to 5 units (Qd = 50- 45), while quantity supplied will increase to 35 units (Qs = 1.0*45 – 10). That is, firms produce 35 units but consumers are willing and able to purchase only 5 units. Therefore, at a price floor of $45, 5 units will be exchanged. Since Qd Qs, there is a shortage amounting to 25 – 15 = 10 units. Since only 15 units are available at a price of $25, the full economic price is the price such that quantity demanded equals the 15 available units: 15 = 50 – PF. Solving yields the full economic price of $35.

9. The supply curve for product X is given by QXS = -400 + 10PX .

a. Find the inverse supply curve.

P = + Q

b. How much surplus do producers receive when Qx = 500? When Qx = 1,250?

When QX = 500: $

When QX = 1,250: $

Explanation:

a. The inverse supply curve is P = 40 + 0.1Q.

b. When Qx = 500, producer surplus is (90-40)*500/2 = $12,500. When Qx = 1250, producer surplus is (165-40)*1250/2 = $78,125.

10. Consider a market where supply and demand are given by QXS = -18 + PX and QXd = 78 – 2PX. Suppose the government imposes a price floor of $36, and agrees to purchase any and all units consumers do not buy at the floor price of $36 per unit.

a. Determine the cost to the government of buying firms’ unsold units.

$

b. Compute the lost social welfare (deadweight loss) that stems from the $36 price floor.

$

Explanation:

a. The supply at the price floor is -18 + 36 = 18 and the demand at the price floor is 78 – 2(36) = 6. The cost of purchasing the surplus then is $36*(18-6) = $432.

b. With no price floor, the equilibrium quantity (found by setting supply equal to demand) would be 14. Also, the price that would generate a supply of 6 is $24. Therefore, the deadweight loss resulting from a $36 price floor is 0.5*(36 – 24)*(14 – 6) = $48 .

11. You are an assistant to a senator who chairs an ad hoc committee on reforming taxes on telecommunication services. Based on your research, AT&T has spent over $15 million on related paperwork and compliance costs. Moreover, depending on the locale, telecom taxes can amount to as much as 25 percent of a consumer’s phone bill. These high tax rates on telecom services have become quite controversial, due to the fact that the deregulation of the telecom industry has led to a highly competitive market. Your best estimates indicate that, based on current tax rates, the monthly market demand for telecommunication services is given by Qd = 300 – 4P and the market supply (including taxes) is QS = 2P – 120 (both in millions), where P is the monthly price of the telecommunication services.

The senator is considering tax reform that would dramatically cut tax rates, leading to a supply function under the new tax policy of QS = 2.5P – 120. How much money per unit would a typical consumer save each month as a result of the proposed legislation?

Instruction: Round your answer to the nearest penny (2 decimal places).

$

Explanation:

Equating the initial quantity demanded and quantity supplied gives the equation: 300 – 4P = 2P – 120. Solving for price, we see that the initial equilibrium price is $70.00 per month. When the tax rate is reduced, equilibrium is determined by the following equation: 300 – 4P = 2.5P – 120. Solving, we see that the new equilibrium price is about $64.62 per month.

In other words, a typical subscriber would save about $5.38 (the difference between $70.00 and $64.62).

12. From California to New York, legislative bodies across the United States are considering eliminating or reducing the surcharges that banks impose on noncustomers, who make $14 million in withdrawals from other banks’ ATM machines. On average, noncustomers earn a wage of $20 per hour and pay ATM fees of $3.25 per transaction. It is estimated that banks would be willing to maintain services for 5 million transactions at $1.25 per transaction, while noncustomers would attempt to conduct 22 million transactions at that price. Estimates suggest that, for every 1 million gap between the desired and available transactions, a typical consumer will have to spend an extra minute traveling to another machine to withdraw cash.

Based on this information, what would be the nonpecuniary cost of legislation that would place a $1.25 cap on the fees banks can charge for noncustomer transactions?

Instructions: Round your answer to the nearest penny (2 decimal places).

$

What would be the full economic price of this legislation?

$

Explanation:

The equilibrium price is $3.25, but the ceiling price is $1.25. Notice that, given the shortage of 17 million transactions caused by the ceiling price of $1.25, the average consumer spends an extra 17 minutes traveling to another ATM machine. Since the opportunity cost of time is $20 per hour, the non-pecuniary price of an ATM transaction is $5.67 (the $20 per hour wage times the fractional hour, 17/60, spent searching for another machine).

Thus, the full economic price under the price ceiling is $6.92 per transaction.

13. Suppose the own price elasticity of demand for good X is -3, its income elasticity is 1, its advertising elasticity is 2, and the cross-price elasticity of demand between it and good Y is -4. Determine how much the consumption of this good will change if:

Instructions: Enter your answers as percentages. Include a minus (-) sign for all negative answers.

a. The price of good X decreases by 5 percent.

percent

b. The price of good Y increases by 8 percent.

percent

c. Advertising decreases by 4 percent.

percent

d. Income increases by 4 percent.

percent

Explanation:

a. Use the own price elasticity of demand formula to write %ΔQXd / (-5) = -3. Solving, we see that the quantity demanded of good X will change by 15 percent if the price of good X decreases by 5 percent.

b. Use the cross-price elasticity of demand formula to write %ΔQXd / (8) =

-4. Solving, we see that the demand for X will change by -32 percent if the price of good Y increases by 8 percent.

c. Use the formula for the advertising elasticity of demand to write %ΔQXd / (-4) = 2. Solving, we see that the demand for good X will change by -8 percent if advertising decreases by 4 percent.

d. Use the income elasticity of demand formula to write %ΔQXd / (4) = 1. Solving, we see that the demand of good X will change by 4 percent if income increases by 4 percent.

14. Suppose the cross-price elasticity of demand between goods X and Y is 1. How much would the price of good Y have to change in order to change the consumption of good X by 20 percent?

percent

Explanation:

Using the cross price elasticity formula, (20 / %ΔPY) = 1. Solving, we see that the price of good Y would have to change by 20 percent in order to change the consumption of good X by 20 percent.

15. You are the manager of a firm that receives revenues of $50,000 per year from product X and $90,000 per year from product Y. The own price elasticity of demand for product X is -3, and the cross-price elasticity of demand between product Y and X is 1.6.

How much will your firm’s total revenues (revenues from both products) change if you increase the price of good X by 2 percent?

Instructions: Round your answer to the nearest dollar. Include a minus (-) sign if applicable.

$

Explanation:

Using the change in revenue formula for two products, ΔR = [$50,000(1 -3) +

$90,000(1.6)](0.02) = 880. Thus, a 2 percent increase in the price of good X would cause revenues from both goods to change by 880 dollars.

16. Revenue at a major cellular telephone manufacturer was $2.3 billion for the nine months ending March 2, up 85 percent over revenues for the same period last year. Management attributes the increase in revenues to a 108 percent increase in shipments, despite a 21 percent drop in the average blended selling price of its line of phones.

Given this information, is it surprising that the company’s revenue increased when it decreased the average selling price of its phones?

No. Own price elasticity is -0.19, which means demand is elastic and a decrease in price will raise revenues.

No. Own price elasticity is -5.14, which means demand is elastic and a decrease in price will raise revenues.

Yes. Own price elasticity is -0.19, which means demand is inelastic and a decrease in price will decrease revenues.

Yes. Own price elasticity is -5.14, which means demand is elastic and a decrease in price will decrease revenues.

Explanation:

The result is not surprising. Given the available information, the own price elasticity of demand for major cellular telephone manufacturer is EQ,P = 108 / (-21) = -5.14. Since this number is greater than one in absolute value, demand is elastic. By the total revenue test, this means that a reduction in price will increase revenues.

17. For the first time in two years, Big G (the cereal division of General Mills) raised cereal prices by 4 percent. If, as a result of this price increase, the volume of all cereal sold by Big G changed by -3 percent, what can you infer about the own price elasticity of demand for Big G cereal?

It is .

Can you predict whether revenues on sales of its Lucky Charms brand increased or decreased?

No – you can’t tell.

Yes – it increased.

Yes – it decreased.

Explanation:

Based on this information, the own price elasticity of demand for Big G cereal is EQ,P = -3 / 4 = -0.75. Thus, demand for Big G cereal is inelastic. (since this number is less than one in absolute value). Since Lucky Charms is one particular brand of cereal for which even more substitutes exist, you would expect the demand for Lucky Charms to be more elastic than the demand for Big G cereal. The fact that Big G cereal is inelastic means we cannot tell whether demand for Lucky Charms is elastic or inelastic so one cannot predict the effect of the price increase on revenues for Lucky Charms.

18. If Starbucks’s marketing department estimates the income elasticity of demand for its coffee to be 1.95, how will the prospect of an economic bust (expected to decrease consumers’ incomes by 6 percent over the next year) impact the quantity of coffee Starbucks expects to sell?

Instruction: Round your response to 2 decimal places.

It will change by percent.

Explanation:

Use the income elasticity formula to write %ΔQd / -6 = 1.95. Solving, we see that coffee purchases are expected to change by -11.70 percent.

19. Suppose the Kalamazoo Brewing Company (KBC) currently sells its microbrews in a seven-state area: Illinois, Indiana, Michigan, Minnesota, Mississippi, Ohio, and Wisconsin. The company’s marketing department has collected data from its distributors in each state. This data consists of the quantity and price (per case) of microbrews sold in each state, as well as the average income (in thousands of dollars) of consumers living in various regions of each state. The data for each state are available via the link below–please note there are multiple tabs at the bottom of the spreadsheet, each refers to one of the seven states selling the Kalamazoo Brewing Company’s microbrews.

Excel Data File

Assuming that the underlying demand relation is a linear function of price and income, use your spreadsheet program to obtain least squares estimates of Mississippi’s demand for KBC microbrews.

Instruction: If the estimate is negative, enter a negative number in the equation. Round your answer to two decimal places.

Q = + Price + Income

Explanation:

The estimated demand equation is Q = 124.31 + (-0.79)P + (7.45)M.

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