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Reserves

Reserves. James Miles, FSA, MAAA October 5, 2006. What is a reserve?. Current income set aside, or reserved, for a future contingent payment. An accounting device for matching revenues of one period with benefits and expenses in another period. An estimate.

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Reserves

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  1. Reserves James Miles, FSA, MAAA October 5, 2006 Purdue University

  2. What is a reserve? • Current income set aside, or reserved, for a future contingent payment. • An accounting device for matching revenues of one period with benefits and expenses in another period. • An estimate. Purdue University

  3. A Life Insurance Company Balance Sheet Purdue University

  4. A Life Insurance Company Income Statement Purdue University

  5. Impact • For an insurance company reserves are the major item on the balance sheet. • A small change or error in the reserves can have a major impact on income. • Actuaries calculate the reserves! Purdue University

  6. Impact Potential • Reserves: $1,346,059,480 • Change in reserves: $72,169,080 • Net income: $1,328,303 • In this example a 0.1% error in the reserves would wipe out the net income. • A company • A career Purdue University

  7. Differing Points of View • A US life insurance company will calculate at least three reserve values for every policy every financial reporting period. • Statutory reserve using methods specified by state insurance departments • GAAP reserve using methods specified by the Financial Accounting Standards Board (FASB) • Tax reserve using methods specified in the Internal Revenue Code Purdue University

  8. A simple case • Your six-month automobile insurance premium is $600. • After you mail in your payment the insurance company has $600 of cash. • The company wants to present a pro-rata portion of the premium in their income statement each month. • The company sets up an unearned premium reserve as a liability. Purdue University

  9. Unearned Premium Reserve Purdue University

  10. A simple case continued • During the sixth month of your automobile policy you are involved in a traffic accident. The estimated damage to the other car is $1,350. • As the sixth month comes to a close the other driver has not settled with your insurance company. • Your insurance company wants the claim to be reported on their income statement in the month of the accident. • The company sets up a claim reserve as a liability. Purdue University

  11. Claim Reserve Purdue University

  12. Claim Reserve Purdue University

  13. Claim Reserve Purdue University

  14. A Life Insurance Example • You purchase a ten-year term life insurance policy. • You agree to pay a premium of $170 each year. • If you die during the ten year period your beneficiary will receive $100,000. • Should the company set up a benefit reserve as a liability? Purdue University

  15. Premium versus Expected Loss Purdue University

  16. Benefit Reserve The present value of future benefits less the present value of future premium Purdue University

  17. Benefit Reserve Purdue University

  18. Expected Loss versus Change in Benefit Reserve Purdue University

  19. Expected Loss plus Change in Benefit Reserve Purdue University

  20. Simple Life • Two-year term life insurance • The death benefit is $100,000 • The premium each year is $115 • The annual interest rate is 4% • The probability of death in the • First year is 0.0011 • Second year is 0.0012 Purdue University

  21. Benefit Reserve The present value of future benefits less the present value of future premium Purdue University

  22. Benefit Reserve Calculation • Calculate the benefit reserve immediately after the first premium payment. • Assume premium is paid at the beginning of each year. • Assume death benefits are paid at the end of each year. Purdue University

  23. Present value of future benefits The expected value of each benefit payment after the valuation date is discounted with interest to the date of valuation. [100,000 x 0.0011 ]/ (1.04) + [100,000 x (1 – 0.0011) x 0.0012] / ((1.04)^2) = 216.59 Purdue University

  24. Present value of future premium Each premium after the valuation date is discounted back to the date of valuation. In this example, only one premium remains to be paid. 115 x (1- 0.0011) / (1.04) = 110.46 Purdue University

  25. Benefit Reserve 216.59 – 110.46 = 106.13 • $115 premium was received. • $106.13 is reserved for expected benefit payments. • If no deaths occur the reported income in year one is $115.00 - $106.13 or $8.87. Purdue University

  26. Assumptions • Mortality rates • Interest rates • Premium is paid at the beginning of each policy year. • Death benefits are paid at the end of each policy year. Purdue University

  27. Approaches • Standards • Formula based • Principles based • Level of Detail • Seriatim • Grouped • Projection • Deterministic • Stochastic Purdue University

  28. Expected Loss plus Change in Benefit Reserve Purdue University

  29. Exercise 1 Purdue University

  30. Exercise 2 Purdue University

  31. Questions Purdue University

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