SOCIETY OF ACTUARIES. EXAM MLC Models for Life Contingencies ADDITIONAL MLC SAMPLE QUESTIONS AND SOLUTIONS

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1 SOCIETY OF ACTUARIES EXAM MLC Models for Life Contingencies ADDITIONAL MLC SAMPLE QUESTIONS AND SOLUTIONS Copyright 2016 by the Society of Actuaries

2 319. Kevin is a participant in a defined benefit pension plan at DMN Pharmaceuticals. You are given the following facts: (i) Kevin was born December 31, (ii) Kevin was hired on January 1, 2011 with an annual salary of 35,000. (iii) Kevin s salary has increased each year on January 1 by 3% in 2012 through (iv) The annual accrued benefit as of any date under the pension plan is 2% of the average annual salary over the three years prior to that date multiplied by the number of years of service as of that date. The accrued benefit is payable annually on the first of the month following the participant s birthday, beginning on the first of the month following the 65 th birthday. A valuation is performed as of December 31, 2015 using the Traditional Unit Credit cost method and the following assumptions: a) In the future, Kevin s salary will increase by 3% each year on January 1 (including on January 1, 2016) as long as Kevin remains employed by DMN. b) The retirement assumption is a single decrement of 100% at age 65. c) All other decrements combined equal 5% at July 1 each year before age 65. d) i = 0.04 e) a Calculate the actuarial liability for the retirement decrement under this valuation. (A) 2770 (B) 2790 (C) 2810 (D) 2830 (E) 2850

3 Solution: (Key = B) Following example on page 360 of the textbook, the actuarial liability under the Traditional Unit Credit cost method is the actuarial present value of the accrued benefit, which is calculated using the service and final average salary as of the valuation date. Thus the final average salary is the average of the salaries in the years 2013, 2014, and 2015, which is 35,000 x ( )/3 = 38,257. Valuation Date Average Salary Years of Service Accrued Benefit 12/31/ , The actuarial liability is the actuarial present value (as of the valuation date) of the accrued benefit and is given by AL = 3826 x 11.0 x (0.95) 30 / = 2785.

4 320. Kevin is a participant in a defined benefit pension plan at DMN Pharmaceuticals. You are given the following facts: (i) Kevin was born December 31, (ii) Kevin was hired on January 1, 2011 with an annual salary of 35,000. (iii) Kevin s salary has increased each year on January 1 by 3% in 2012 through (iv) The annual accrued benefit as of any date under the pension plan is 2% of pay in the prior 12-month period multiplied by the number of years of service as of that date. The accrued benefit is payable monthly on the first of each month, beginning on the first of the month following the 65 th birthday. A valuation is performed as of December 31, 2015 using the Traditional Unit Credit cost method and the following assumptions: a) In the future, Kevin s salary will increase by 3% each year on January 1 (including on January 1, 2016) as long as Kevin remains employed by DMN. b) The retirement assumption is a single decrement of 100% at age 65. c) All other decrements combined equal 5% at July 1 each year before age 65. d) i = 0.04 e) a f) Annuity values are calculated assuming deaths are uniformly distributed over each year of age. Calculate the normal contribution for the retirement decrement under this valuation. (A) 560 (B) 590 (C) 620 (D) 650 (E) 680

5 Solution. (Key = D) The normal contribution under the Traditional Unit Credit cost method is the actuarial present value of the difference between the expected accrued benefit one year from the valuation date and the accrued benefit at the valuation date. As of Date Pay in Prior Year Years of Service Accrued/ Expected Accrued Benefit 12/31/ , /31/ , Thus the expected accrued benefit on 12/31/2016 minus the accrued benefit on 12/31/2015 is = 930. Using UDD to approximate a (12) a65 at 4% interest we have i d i i and i d i d a (12) (12) (12) (12) (12) (12) (12) (12) (12) (12) The normal contribution is the actuarial present value (as of the valuation date) of this difference and is given by NC = 930 x x (0.95) 30 / = 648.

6 321. Kira is a participant in a defined benefit pension plan at DMN Pharmaceuticals. You are given the following facts: (i) Kira was born December 31, (ii) Kira was hired on January 1, 2011 with an annual salary of 35,000. (iii) Kira s salary has increased each year on January 1 by 3% in 2012 through (iv) The annual accrued benefit as of any date under the pension plan is 2% of the 3-year final average salary as of that date multiplied by the number of years of service as of that date. The accrued benefit is payable annually on the first of the month following the participant s birthday, beginning on the first of the month following the 65 th birthday. A valuation is performed as of December 31, 2015 using the Projected Unit Credit cost method and the following assumptions: a) In the future, Kira s salary will increase by 3% each year on January 1 (including on January 1, 2016) as long as Kira remains employed by DMN. b) The retirement assumption is a single decrement of 100% at age 65. c) All other decrements combined equal 5% at July 1 each year before age 65. d) i = 0.04 e) a Calculate the actuarial liability for the retirement decrement under this valuation. (A) 6660 (B) 6760 (C) 6860 (D) 6960 (E) 7060

7 Solution: (Key = B) Under the Projected Unit Credit cost method, the actuarial liability is the actuarial present value of the pay-projected benefit, which is calculated using the service as of the valuation date. We have the following information. Projected Final Average Salary at 35,000 x ( )/3 = 92, Service at valuation date 5 Pay-Projected Benefit.02 x 5 x 92,859 = 9286 The actuarial liability is the actuarial present value (as of the valuation date) of the payprojected benefit and is given by AL = 9286 x 11.0 x (0.95) 30 / = 6760.

8 322. Kira is a participant in a defined benefit pension plan at DMN Pharmaceuticals. You are given the following facts: (i) Kira was born December 31, (ii) Kira was hired on January 1, 2011 with an annual salary of 35,000. (iii) Kira s salary has increased each year on January 1 by 3% in 2012 through (iv) The annual accrued benefit as of any date under the pension plan is 2% of the 3-year final average salary as of that date multiplied by the number of years of service as of that date. The accrued benefit is payable annually on the first of the month following the participant s birthday, beginning on the first of the month following the 65 th birthday. A valuation is performed as of December 31, 2015 using the Projected Unit Credit cost method and the following assumptions: a) In the future, Kira s salary will increase by 3% each year on January 1 (including on January 1, 2016) as long as Kira remains employed by DMN. b) The retirement assumption is a single decrement of 100% at age 65. c) All other decrements combined equal 5% at July 1 each year before age 65. d) i = 0.04 e) a Calculate the normal contribution for the retirement decrement under this valuation. (A) 1050 (B) 1150 (C) 1250 (D) 1350 (E) 1450

9 Solution: (Key = D) Under the Projected Unit Credit cost method, the normal contribution is the actuarial present value of the difference between the expected pay-projected benefit one year after the valuation date and the pay-projected benefit at the valuation date. We have the following information. Projected Final Average Salary at 35,000 x ( )/3 = 92, Pay-projected benefit at 12/31/ x 5 x 92,859 = 9,286 Pay-projected benefit at 12/31/ x 6 x 92,859 = 11,143 Difference 11,143 9,286 = 1857 The normal contribution is the actuarial present value (as of the valuation date) of this difference and is given by: NC = 1857 x 11.0 x (0.95) 30 / = 1352.

10 Sample WA Question 22 On December 31, 2015, a defined benefit plan member, who is exactly age 55, has 25 years of service. Her salary in 2015 was 50,000. The annual accrued benefit as of any date is 1.6% of the three-year final average salary as of that date, multiplied by years of service as of that date. The pension is payable as a monthly single life annuity, with the first payment due at retirement. The valuation assumptions are as follows: Exits from employment follow the Illustrative Service Table, except that all lives surviving in employment to age 61 retire at that time. All retirements occur on the employee s birthday. After retirement, mortality follows the Illustrative Life Table. Annuities are valued using the 2-term Woolhouse formula. Salaries are increased by 3% each year on January 1. All contributions are paid on January 1 each year. i = 0.06 (a) (i) Calculate the actuarial liability for the member at December 31, 2015 using the Projected Unit Credit (PUC) cost method. (ii) Calculate the normal contribution for 2016 using PUC. (b) (i) Calculate the actuarial liability for the member at December 31, 2015 using the Traditional Unit Credit (TUC) cost method. (ii) Calculate the normal contribution for 2016 using TUC.

11 Solution Based on the December 31, 2015 valuation, let ABx be the accrued benefit at age x, with pay and service projected to age x, and let PBx be the benefit with pay projected to age x, but with service as of the valuation date. (a) (i) The actuarial liability as of December 31, 2015 is ( r) ( ) (12) 60 5 (12) V PB60a 60 v PB ( ) 61a61 v ( ) l55 l55 P d l We have PB (1.03) (1.03) (1.03) (.016)(25)(50, 000) 22, (1.03) (1.03) (1.03) PB61 (.016)(25)(50, 000) 23,192 3 Using the 2-term Woolhouse approximation we have (12) 11 (12) 11 a60 a and a61 a which gives P 0V 150, 072 P (ii) The NC in this case is 0 V / 25 = (b) (i) The TUC case is similar to PUC except that the accrued benefit is used in place of the pay-projected benefit. Hence we replace the PB60 and PB61 in the above with AB55. We have AB (1.03) (1.03) (.016)(25)(50,000) 19, P and thus 0 V (19,423)(6.5014) 126,277. (ii) For the NC, we must calculate expected increase in the accrued benefit over 2016 AB AB (.016)(26)(50, 000) 19, ,806 19, NC = (1383)(6.5014) = 8991.