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PAM3240 Risk Management and Policy

The employer faces a 30 percent income tax rate and has an annual discount rate of 5 percent. Assume that maintenance and retained work-injury losses are realized at the end of the year, that insurance premiums are paid at the beginning of the year, and that income taxes are paid at the end of the year. Assume that the cost of implementing the ventilation system is realized at the beginning of the first year, and that 1/5 of the total costs of the system can be deducted from taxable income (as depreciation) in each of the five years (not 100% in the first year).

  1. Calculate the annual net savings from the ventilation system.
  2. Calculate the present value of the after-tax net annual savings from the ventilation system over the five years of its operation.
  3. Calculate the present value of the after-tax purchase cost of the ventilation system.
  4. Do your calculations suggest that the ventilation system should be introduced? Demonstrate and explain.
  5. Does changing the firm’s income tax rate to 15% affect your recommendation?  Demonstrate and explain. (note: if you do the problem using Excel this sensitivity check should be easy to calculate).
  6. Ignoring the changes you made in part e, does changing the firm’s annual discount rate to 10% affect your recommendation? Demonstrate and explain. (note: if you do the problem using Excel this sensitivity check should be easy to calculate).
  7. What other considerations should the risk manager include in his calculations  and/or report to management about this decision?

Using the simulation worksheet in the Excel file accompanying this problem set, construct by simulation the estimated true probability distribution of total accident costs for the firm, based on the observed data from the past year. What is the simulated mean and standard deviation of total accident costs?

What is the maximum probable loss (MPL) at the (approximate) 99% confidence level? What is the (approximate) probability that total accident costs will exceed $300,000? What is the (approximate) probability that total accident costs will exceed $1,000,000?

[Note: because simulation outcomes change each time the file isopened, save your results in a separate worksheet using the “values and formats” option in Excel. Submit both the “working” worksheet and the “results” worksheet.] c. Suppose that the firm believes that total accident costs have a Normal distribution with mean equal to the sample mean in part a. and standard deviation equal to the sample standard deviation in part a. What is the maximum probable loss (MPL) at the 99% confidence level? What is the probability that total accident costs will exceed $300,000? What is the probability that total accident costs will exceed $1,000,000?

Now suppose that firm believes that total accident costs have a Lognormal distribution with mean equal to 3.2 and standard deviation equal to 5.2 (this is based on the observed sample data, converting to natural logs). What is the maximum probable loss (MPL) at the 99% confidence level? What is the probability that total accident costs will exceed $300,000? What is the probability that total accident costs will exceed $1,000,000?


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