320W 2023 Final Exam Practice Solutions(2)

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320

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Accounting

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Feb 20, 2024

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RM 320 Final Exam Practice Solutions 1) An insurance company opens on 12/31/15. It has $2 million in investments and $2 million in cash as its total assets upon opening. It has not sold any policies yet. On 1/1/16, the insurer sells policies and collects $9 million in premiums. It has initial expenses associated with selling the policies of $3 million. (a) Fill in the balance sheet below for 1/1/16 without insurance. Calculate the Kenney ratio. The insurer then decides to enter a quota share reinsurance treaty. They cede 45% of the premiums and losses and collect a 30% commission. (b) Fill in the balance sheet below for 1/1/16 with reinsurance. Calculate the Kenney ratio. Balance Sheet . 12/31/15 1/1/16 1/1/16 w/ reinsurance Assets Cash $2 8 mil 5.165 mil Investments $2 mil 2 mil 2 mil Total Assets $4 mil 10 mil 7.165 mil Liabilities UPR 9 mil 4.95 mil Policyholder Surplus $4 mil 1 mil 2.215 Kenney Ratio 9 2.2348 2) Fill in this table for this set of policies under surplus share treaty with a retention of $10 million: Amount Paid by Reinsurer Amount of Insurance % Retained % Reinsured if a $1 million Loss Occurs $5 million 100% 0% $0 $10 million 100% 0% $0 $20 million 50% 50% $500,000 $30 million 33.3333% 66.6667% $666,667 $40 million 25% 75% $750,000 $50 million 20% 80% $800,000

3) The following is a sample experience rating worksheet: COMPENSATION RATING BUREAU EXPERIENCE RATING CALCULATION Policy Effective Date: 2/1/23 Losses as Part I Year Indemnity Medical Total Used = A Exhibit of Actual Losses 20 160,000 312,000 472,000 254,500 21 113,000 327,000 440,000 240,000 22 43,000 62,000 105,000 100,500 Total 316,000 701,000 1,017,000 595,000 Part II Policy Claim # Losses as Losses as Exhibit of Losses Year Number Reported Used Subject to Limiting 20 20-2 150,000 42,500 Values 20 20-3 55,000 42,500 20 20-5 140,000 42,500 21 21-2 170,000 42,500 21 21-5 60,000 42,500 21 21-6 55,000 42,500 21 21-7 85,000 42,500 22 22-2 47,000 42,500 Total 762,000 340,000 Part III Class Policy Expected Expected Exhibit of Code Year Payroll Loss Factor Losses = E Payrolls, Expected 20 15,000,000 2.26 339,000 Losses, 21 11,000,000 1.91 210,100 Authorized 22 2,000,000 1.48 29,600 Classes, etc. 551 20 50,000 .47 235 21 100,000 .41 410 22 200,000 .32 640 951 20 2,000,000 .23 4,600 21 2,500,000 .20 5,000 22 1,000,000 .15 1,500 953 Total N/A 591,085

a. Use the expected loss factors and payrolls given in Part III of the experience rating calculation worksheet to fill in the final column (expected losses = E). Use the following claims data for Parts I and II of the worksheet. b. The limit placed on severity is $42,500. This means that any claim with a total larger than $42,500 will be treated as $42,500 instead of its full amount. Any claim subject to this limit must be recorded in Part II of the worksheet. c. Fill in the last 2 columns in the chart below (using the $42,500 limit where appropriate in the last column) and calculate the totals for each year. d. Complete Part I using the totals from below. Total Indemnity Total Year Claim # Indemnity Medical Plus Medical Amount used 20 20-1 20,000 6,000 26,000 26,000 20 20-2 10,000 140,000 150,000 42,500 20 20-3 45,000 10,000 55,000 42,500 20 20-4 30,000 5,000 35,000 35,000 20 20-5 30,000 110,000 140,000 42,500 20 20-6 5,000 30,000 35,000 35,000 20 20-7 20,000 11,000 31,000 31,000 Total 160,000 312,000 472,000 254,500 21 21-1 6,000 2,000 8,000 8,000 21 21-2 40,000 130,000 170,000 42,500 21 21-3 15,000 25,000 40,000 40,000 21 21-4 7,000 15,000 22,000 22,000 21 21-5 30,000 30,000 60,000 42,500 21 21-6 5,000 50,000 55,000 42,500 21 21-7 10,000 75,000 85,000 42,500 Total 113,000 327,000 440,000 240,000 22 22-1 5,000 15,000 20,000 20,000 22 22-2 12,000 35,000 47,000 42,500 22 22-3 1,000 2,000 3,000 3,000 22 22-4 25,000 10,000 35,000 35,000 Total 43,000 62,000 105,000 100,500

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e. Calculate the Experience Modification factor for this firm using the following information: A = Actual Losses = Losses as Used = A from Part I of worksheet E = Expected Losses = E from Part III of worksheet C = Credibility = .6 LC = Limit charge = .1 M = Experience Modification Factor Recall that the formula for the Experience Modification factor is M = A·C + E·(1-C) + E·LC E = (595,000)(.6) + (591,085)(.4) + (591,085)(.1) 591,085 = 1.10397 Then, using the following information: 1) the class rate that the insurer has quoted is $2 and 2) the employer's payroll is $15,000,000, f. Calculate the workers compensation premium that this firm will be quoted given the formula: Premium = (Payroll/100)·(Class Rate)·(Experience Mod. Factor). Premium = (15,000,000/100) · (2) · (1.10397) = (300,000) · (1.10397) = $331,191