PAM 3240 Ventilation Method Cost
reduce the employer’s retained work-injury losses by $35,000. In addition, the insurer that writes the employer’s workers compensation insurance is willing to reduce the insurance premium by $45,000 per year if the method is used. The employer faces a 30 percent income tax rate and has an annual discount rate of 5 percent.
a. Calculate the annual net savings from the ventilation system.
b. Calculate the present value of the after-tax net annual savings from the ventilation system over the five years of its operation.
c. Calculate the present value of the after-tax purchase cost of the ventilation system.
d. Do your calculations suggest that the ventilation system should be introduced? Demonstrate and explain.
e. 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).
f. 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).
g. What other considerations should the risk manager include in his calculations and/or report to management about this decision?
Answer:
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| Accident Severity | Natural log of Accident Severity | Distribution of Accidents | Natural log of Distribution of Accidents | Mean of Distribution of Accidents | Variance of distribution of Accidents | Standard Deviation of distribution of Accidents | Normal distribution less that 90 |
| 500 | 2.698970004 | 50 | 1.698970004 | 19.5 | 473 | 21.74856317 | 0.999405683 |
| 1000 | 3 | 20 | 1.301029996 | Mean of Accident Severity | Variance of Accident Severity | Standard Deviation of Accident Severity | Normal distribution for equal to or more than 90 |
| 5000 | 3.698970004 | 6 | 0.77815125 | 4125 | 19395833.33 | 4404.070087 | 0.000594317 |
| Mean of total accident cost | 990000 | 990053.4241 | 5.99565863 | c.) | MPL at 99 % | Probability that the Total accident cost will exceed $300,000 | 0.293609757 |
| standard deviation of total accident bcost | 1271023.21 | Probability that the Total accident cost will exceed $300,000 | 0.293609757 | 0.500016768 | Probability that the Total accident cost will exceed $1,000,000 | 0.503138717 |
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