You are given:

1. An insurance company was formed to write workers compensation business in CY1.
2. Earned premium in CY1 was 1,000,000.
3. Earned premium growth through CY3 has been constant at 20% per year (compounded).
4. The expected loss ratio for AY1 is 60%.
5. As of December 31, CY3, the company’s reserving actuary believes the expected loss ratio has increased two percentage points each accident year since the company’s inception.
6. Selected incurred loss development factors are as follows:

12 to 24 months	1.500
24 to 36 months	1.336
36 to 48 months	1.126
48 to 60 months	1.057
60 to 72 months	1.050
72 to ultimate	1.000

Calculate the total IBNR reserve as of December 31, CY3 using the Bornhuetter-Ferguson method.

• 964,000
• 966,000
• 968,000
• 970,000
• 972,000

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Key: E

CY1: ELR = 60%, earned premium = 1,000,000, expected losses = 0.6(1,000,000) = 600,000. Cumulative development factor (CDF) = (1.05)(1.057)(1.126) = 1.250. Reserve using BF method = 600,000(1 – 1/1.250) = 120,000.

CY2: ELR = 62%, earned premium = 1,200,000, expected losses = 0.62(1,200,000) = 744,000. CDF = (1.05)(1.057)(1.126)(1.336) = 1.670. Reserve using BF method = 744,000(1 – 1/1.670) = 298,491.

CY3: ELR = 64%, earned premium = 1,440,000, expected losses = 0.64(1,440,000) =921,600. CDF = (1.05)(1.057)(1.126)(1.336)(1.5) = 2.504. Reserve using BF method = 921,600(1 – 1/2.504) = 553,549. Total reserve = 120,000 + 298,491 + 553,549 = 972,040.

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.