Suppose the government wants to reduce the total pollution emitted by three local firms. Currently, each firm is creating 4 units of pollution in the area, for a total of 12 pollution units. If the government wants to reduce total pollution in the area to 6 units, it can choose between the following two methods: Available Methods to Reduce Pollution
1. The government sets pollution standards using regulation.
2. The government allocates tradable pollution permits.
Each firm faces different costs, so reducing pollution is more difficult for some firms than others. The following table shows the cost each firm faces to eliminate each unit of pollution. For each firm, assume that the cost of reducing pollution to zero (that is, eliminating all 4 units of pollution) is prohibitively expensive.
Firm Cost of Eliminating the...
First Unit of Pollution Second Unit of Pollution Third Unit of Pollution
(Dollars) (Dollars) (Dollars)
Firm X 130 165 220
Firm Y 600 750 1,200
Firm Z 90 115 140
Now, imagine that two government employees proposed alternative plans for reducing pollution by 6 units.
Method 1: Regulation
The first government employee suggests to limit pollution through regulation. To meet the pollution goal, the government requires each firm to reduce its pollution by 2 units. Complete the following table with the total cost to each firm of reducing its pollution by 2 units.
Firm Total Cost of Eliminating Two Units of Pollution
(Dollars)
Firm X
Firm Y
Firm Z
Method 2: Tradable Permits
Meanwhile, the other employee proposes using a different strategy to achieve the government?s goal of reducing pollution in the area from 12 units to 6 units. He suggests that the government issues two pollution permits to each firm. For each permit a firm has in its possession, it can emit 1 unit of pollution. Firms are free to trade pollution permits with one another (that is, buy and sell them) as long as both firms can agree on a price. For example, if firm X agrees to sell a permit to firm Y at an agreed-upon price, then firm Y would end up with three permits and would need to reduce its pollution by only 1 unit while firm X would end up with only one permit and would have to reduce its pollution by 3 units. Assume the negotiation and exchange of permits are costless.
Because firm Y has high pollution-reduction costs, it thinks it might be better off buying a permit from firm Z and a permit from firm X so that it doesn't have to reduce its own pollution emissions. At which of the following prices are both firm Z and firm X willing to sell one of their permits to firm Y?
a. $127.
b. $199.
c. $207.
d. $244.
e. $345.
Suppose the the government has set the trading price of a permit at $523 per permit.
Complete the following table with the action each firm will take at this permit price, the amount of pollution each firm will eliminate, and the amount it costs each firm to reduce pollution to the necessary level. If a firm is willing to buy two permits, assume that it buys one permit from each of the other firms.
Firm Initial Pollution Action Final Amount of Cost of Pollution
Permit Allocation Pollution Eliminated Reduction
(Units of pollution) (Units of pollution) (Dollars)

Firm X 2
Firm Y 2
Firm Z 2
Regulation Versus Tradable Permits
Determine the total cost of eliminating six units of pollution using both methods, and enter the amounts in the following table.
Proposed Method Total Cost of Eliminating Six Units of Pollution
(Dollars)
Regulation
Tradable Permits
In this case, you can conclude that eliminating pollution is less/more? Costly to society when the government regulates each firm to eliminate a certain amount of pollution than when it allocates pollution permits that can be bought and sold.

Sabrina gupta, an investment advisor with a major brokerage firm, was examining wal-mart stores, inc. (wal-mart) stock and its valuation. gupta wondered whether to recommend the stock to any of her new clients or to existing clients who did not currently have wal-mart in their portfolios.her key task was to use an intrinsic value approach to price the shares and to then compare the resulting price with the price at which the stock was traded in the market. gupta wanted to use alternative valuation methods and assumptions to produce intrinsic value estimates for wal-mart stock.she was interested in seeing if the alternative methods would point to a consensus regarding the valuation of the stock and to see if the valuations suggested an investment opportunity given the current market price. methods she contemplated to use were: multi-stage growth modelprice earnings multiplemost valuation methods gupta considered required a common set of inputs: future cash flows to wal-mart investorsgrowth rate of future cash flowsdiscount factor or required rate of return by wal-mart investorsgupta gathered data to determine each of the above.gupta thought that dividends to wal-mart shareholders would adequately capture the cash flows to wal-mart shareholders; she also thought that this approach would simplify her task and she would revisit more complex valuation models if she felt the need.gupta thought that capm would provide her a relatively reliable estimate of the required rate of return. capm based required rate of return can be estimated by using a risk free rate, systematic risk of the firm and equity market risk premium. gupta thought that in a valuation exercise that involve long term cash flows, 10-year government bond yield would be an appropriate risk free rate of return estimate. she checked the 10 year note rate and found out that it was about 3.68%. gupta searched for wal-mart beta in bloomberg. bloomberg estimates betas by regressing the s& p 500 returns on the firm returns over the past two years and arrives at a “raw” beta estimate. bloomberg makes an adjustment in raw beta based on some academic research. gupta is confident that bloomberg adjustment is justified and she uses wal-mart beta estimate of 0.66 in her analysis.while gupta is aware of the importance of emrp assumption, she thinks that bloomberg’s historical estimate of 5.05% is a safe assumption. she is aware of the fact that some studies suggest a larger risk premium of approximately six per cent, while others suggest a much lower forward-looking premium of less than four per cent. she is mindful of the arbitrariness of her assumption, and she takes a note to revisit this issue if her valuations produce unreasonable estimates.anticipated dividend growth (g) is often estimated in a variety of ways.first, observed historical dividend growth can be assumed to continue in a perpetual fashion.second, future dividend growth can be estimated on the basis of recent estimates of analysts.gupta noted that the consensus annual wal-mart dividend for fiscal year 2011 was $1.21, and one respected analyst had estimated the expected constant dividend growth (in perpetuity) at approximately 3%.as the chart suggests, both earnings and dividend growth rates are declining but they seem to be higher than the “respected analyst’s” estimates. gupta decides to use several alternative perpetual growth assumptions to see the impact on price. since gupta decided to use variants of dividend discount model (ddm), she checked the anticipated earnings for 2011. analyst’s estimates suggested $4.10 earnings per share. gupta decided to use 10% growth rate from 2011 to 2012 and assumed a steady decline to 3% in 13 years (until 2024) where the perpetual growth rate of 3% resumes. she also assumed that walmart will increase its dividend payout ratio from 30% to 55% from years 2012 to 2024. you are asked to reproduce gupta’s analysis of multi-stage growth model and double check her valuation by using an earnings multiple. you have all the data you need to conduct the multi stage discounted growth model analysis, but you will need to do some research about the multiples valuation.