Assume, over time, air quality has been annually declining in Columbia, South Carolina. Heavy

traffic loads, growth in industrial activity, and poor geography have combined to produce

frequent health warnings in the city, especially in summer. Violations of the Environmental

Protection Agencies O$3($ozone$)$ standard are particularly frequent. During the last year, the city

had more than $148$ days in which the EPA $0\mathrm{.}12-$ppm $1-$hour standard was exceeded. Of equal

concern is the fact that O$3$ measurements have been as much as $3-$times the EPA standard on

violation days. On the worst days, schoolchildren are not permitted to go outside for recess and

sick and elderly individuals are advised to stay inside.

A recent study of air pollution by the Office of Technology Assessment has developed policies

reduce emission of volatile organic compounds $($VOCs$).$ A reduction in VOC emissions will

alleviate some $($but not all$)$ of the O$3$ problem in Columbia.

Assume the two most promising strategies for reducing VOCs in Columbia have been identified.

You have been asked by the state legislature to assess these two strategies using Benefit$-$Cost

Analysis $($BCA$).$ The legislature has asked for a comprehensive study of benefits and costs for a

ten$-$year planning horizon, spanning the years $2024-2033.$ The two VOC$-$reduction strategies

are as follows:

Policy I: Involves using an existing combination of pollution control measures that consist of a

reduction in the volatility of gasoline, and substitution of methanol for gasoline in state and

private vehicles. Initial costs are low but costs are expected to rise over time because the ability

to apply existing pollution control measures to new situations $($especially industrial sources$)$ is

expected to become costlier$.$

Policy II: Requires substantial investment in research and development to foster technological

breakthroughs in the elimination$/$reduction of VOCs in the production and transportation of some

products. Research and implementation costs will be extremely high during the first two years,

but will rapidly decrease as the new technology becomes readily available through mass

production.

The state will choose either Policy I or Policy II based on your analysis. Your task, therefore, is

to compare two air quality improvement strategies: one that relies only on Policy I measures, and

the other that relies only on Policy II measures. The annual expected costs of each strategy is

listed in Table $1$ on the next page.

Epidemiological $($long$-$term medical$)$ studies have estimated the annual expected health benefits

of VOC reductions. These annual benefits fall into three categories as listed in Table $2.$ For

simplicity it is assumed that both polices provide the same annual dollar benefit for each type of

health benefit. To simply the analysis, assume the undiscounted annual health benefit for each of

the three health benefits is constant over the ten$-$year period.

You can complete this assignment using a pocket calculator, but you will find it much easier to

use a computer spreadsheet program like Excel. I suggest you begin by making a ten$-$period

$($year$)$ table that contains the information provided in Table $1.$ You will find it easier if you have

a column that contains time period $($year$)$ starting at $0$ and going to $9.$ Another column can

contain the actual years $(2024-2033).$

Make sure you include a column for the cost data associated with each pollution reduction

strategy in each year. You will also need columns for each annual benefit value in each year there is a benefit and an additional column for the sum of all annual benefits provided by the program each year. For simplicity, the annual benefit value is constant over time $($since the comparisons are based on reduction of $1$ ton of VOC$)$ but you will need to report a total benefit. You need to calculate the column sums, $($totals$)$ to find the present value of benefits and costs

over the $10-$year horizon. Before doing this, however, you will need to construct a formula to

discount each future value into a current value before summing. The easiest way to do this is to

place the discount rate in a single cell somewhere at the top of your spreadsheet.

QUESTION$-$ PLEASE FOLLOW AND ANSWER

The state legislature tells you to use a low discount rate of $4\mathrm{.}0\%$ reflecting the current

short term interest rate $($low cost of money$)$ in your analysis. Using this discount rate and

$2024$ as the base year $($i$.$e$.$ t $=0),$ calculate the present value of benefits and the present

value of costs under the two strategies. In present value terms, do the benefits exceed the

costs of either strategy? What is the net present value of each policy and associated

benefit$-$cost ratio? Is each policy equally preferred? If not, which is the preferred policy?

Why?