Kruger Industries Owns A Small Office Building Wo
Kruger Industries owns a small office building worth $400,000. Art Vandelay is the risk manager. Kruger faces the risk of fire which would completely destroy their building. The probability of a fire is known to be 3%. Kruger has a marginal tax rate of 40%. Kruger is considering the following risk management options to address the risk of fire to their building: 1. Retention 2. Full Insurance for a premium of $12,500. Safety Program + Retention 4. Safety Program + Full Insurance [premium falls to $9,500]. The cost of the Safety Program is $2,000. It has the impact of lowering the probability of a fire from 3% to 2%.
However, if a fire does occur it is still a total loss. The assignment involves constructing an after-tax loss matrix, calculating actuarially fair premiums (AFP), analyzing risk management options with worry values, and making decisions based on total costs and risk aversion. Additionally, it includes similar analyses for Kramerica Industries and Kramerica Company's small building, with various risk management strategies, premiums, and subjective risk valuations.
Paper For Above instruction
Kruger Industries’ decision to manage fire risk involves several analytical steps rooted in risk management theory and economic decision-making. The first step is constructing an after-tax loss matrix, which accounts for the financial outcomes of each risk management option under different loss scenarios, considering the tax implications. Next, the actuarially fair premium (AFP) is computed to determine the expected cost proportionate to the risk, serving as a baseline for evaluating insurance options.
Constructing the after-tax loss matrix involves identifying potential losses and their probabilities and then adjusting for tax effects. For Kruger, the total loss if a fire occurs is $400,000. Probabilities are 3% without safety measures and 2% with safety programs. The tax rate of 40% affects the financial impact, reducing the after-tax loss from gross losses. For instance, without safety measures, the expected loss is 0.03 x $400,000 = $12,000. After-tax, this becomes $12,000 x (1-0.4) = $7,200. With safety, the expected loss drops to 0.02 x $400,000 = $8,000, and after-tax, it becomes $8,000 x (1-0.4) = $4,800.
The AFP, calculated as the expected loss, is thus $12,000 without safety and $8,000 with safety, representing the amount that would be both fair and actuarially accurate for insurance premium setting. The introduction of safety measures effectively reduces the risk and therefore the AFP, aligning with risk mitigation strategies.
When considering subjective valuations of risk, expressed through worry values, Art's decision shifts
based on individual risk aversion. Worry values reflect how much Art is willing to pay to avoid risking a fire disaster. For the scenario without safety, WVR is $3,500, representing Art’s subjective valuation of risk retention. With safety, WVRS decreases to $2,000, indicating safety measures effectively reduce perceived risk.
The total cost minimization approach involves considering both monetary expenses (premiums, safety program costs) and worry values. Calculations show the total costs for each option, factoring in the premium, safety costs, and worry values. For example, opting for full insurance costs $12,500 (premium) plus $0 (loss risk), but with safety, the total cost includes the premium ($9,500), safety cost ($2,000), and worry valuation ($2,000), summing to $13,500. Among these, the option with the lowest total cost becomes optimal.
Art’s PMAX, representing the maximum premium he is willing to pay for full insurance considering his worry value, is calculated as the premium plus his worry value for the full insurance scenario. Using the example values, PMAX = $12,500 + $4,600 = $17,100.
The CRO’s worry value (WVR) for the most he is willing to pay is derived from the maximum premium limit mentioned by the CRO. If the CRO states that the most he would pay is $9,400, then WVR is the difference between this amount and the baseline premium, indicating his subjective valuation of risk.
Risk aversion comparisons between Art and CRO are based on these worry values and the subjective valuation process. Art, with a worry value of $3,500, shows a higher level of risk aversion compared to the CRO, who indicates a willingness to pay less, reflecting lower subjective risk valuation and thus lower risk aversion.
Similarly, Kramerica Industries’ risk management involves constructing an after-tax loss matrix for different options: retention, partial insurance, deductible insurance, and full insurance, with associated premiums and losses. The analysis incorporates subjective worry values to influence the decision-making criterion beyond pure expected loss calculations. Calculations show that without subjective valuation, partial insurance minimizes expected costs, but when subjective worry values are introduced, the preferred risk management option could shift, depending on individual risk attitudes.
For Kramerica, factors such as higher premiums and larger loss reductions influence the decision, with subjective worry values potentially favoring more comprehensive insurance if the perceived risk or worry is high enough. The calculations involve comparing total costs, including premiums and subjective worry
valuations, to determine the optimal risk management strategy. This analysis underscores the importance of subjective risk perception in insurance and risk management decisions, complementing quantitative expected loss calculations.
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