RMI 2101 SPRING 2016 Homework Assignment 3 30 points Due: Wednesday, March 16, 2016 at the beginning of class This homework does not need to be typed. Do your homework on lined 8 x 11 paper....not paper torn out from a spiral notebook. All matrices are to be constructed with the Risk Management Alternatives as the rows and the States of the World as the columns, as we did in class. Show ALL of your work in order to receive full credit for an answer. Indicate your after-tax numbers in the matrix by placing parentheses around them as we did in class. At the beginning of each problem, show how you calculated one of the after-tax numbers in the matrix. Then you do not have to show the work for all of the after-tax numbers. Remember that you still need to provide a cover page and also indicate your name and TU ID on each page of your stapled homework. 1. 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. 2. 3. 4. Retention Full Insurance for a premium of $12,500 Safety Program + Retention 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. a) Construct an after-tax loss matrix. (4 points) b) What is the actuarially fair premium [AFP] in this case (hint: AFP = P*)? (1 point) c) What is the AFP when safety is introduced? (2 points) Assume Art's worry value for retention (WVR) is $3,500 and for retention and safety (WVRS) is $2,000. d) If Art decides to minimize TOTAL COST, what risk management option does he choose? Make sure that you show all calculations and clearly define TOTAL COST in each case. (4 points) e) What is Art's PMAX for full insurance? (2 points) f) During a meeting, the Chief Risk Officer (CRO) told Art that the most he would pay for full insurance is $9,400. What is the CRO's WVR? (2 points) g) Who is more risk averse, the CRO or Art? Explain. (2 points) 2. Kramerica Industries has a small plant worth $100,000. The plant is subject to physical damages and total destruction as a result of fire. Firm has 30% tax rate. Probability Distribution as follows: Loss Amt ($) 0 1,000 7,000 10,000 100,000 Probability of Loss .5 .4 .06 .03 ? Kramerica is considering the following risk management options: 1. Retention 2. Partial insurance - Face Amount = $8,000; Premium = $700 3. Deductible insurance - Face Amount = $100,000; Deductible per occurrence = $1000; Premium = $2,000 4. Full insurance - Face Amount = $100,000; Premium = $6,000 a) Construct the after-tax loss matrix. (5 points) b) Assume that the firm decides to choose a risk management alternative without including valuation for subjective risk. What risk management option is chosen? Show all work and calculations? (4 points) The firm would like to add worry value to their analysis. For the following questions, when using worry values, use the following abbreviations. WVR (retention); WVP (partial insurance); WVD (deductible insurance); WVF (full insurance). c) What worry value(s) would make full insurance preferred to partial insurance? Show all work and calculations and explain your numerical answer. (2 points) d) What worry value(s) would make deductible insurance preferred to partial insurance? Show all work and calculations and explain your numerical answer. (2 points)