Company XYZ provides a hybrid pension plan to its employees. At retirement, its
ID: 2725107 • Letter: C
Question
Company XYZ provides a hybrid pension plan to its employees. At retirement, its employee receives whichever of the following with greater value: A whole life annuity with an annual payment of [2% times service year times average annual salary in the last three years of employment), payable at the beginning of each year. The total value of the contribution account. An employee entered the plan when he just turned 25, on January 1, 2012. You are given that: The contribution from the employee and the employer is 14% of the annual salary in total, paid at the end of each year. The salary scale is s_x = 1.05^x. Salary is increased every year, at the end of each calendar year. The retirement age is 65. His annual salary is $60,000 in 2012. The investment return on the contribution account is 6% per year. delta^12_65 = 10. What is the value of this employee's pension plan upon retirement?Explanation / Answer
First let us calculate the pension under alternative (a).
Pension = (2% X Service Yeras X Averarge annual salary in the last 3 years of employment)
Service Years = (Retirement age - Joining age) = 65 - 25 = 40 years
To get this we have to calculate average annual salary in the last 3 years of employment.
Given Anuual income in 2012 = $ 60,000
Growth rate = 1.05 i.e., 5% each year.
Annual Salary at the age of 63 (i.e 38th service year) = $ 60,000 X (1+ Growth Rate)n-1
= $ 60,000 X (1+0.05)38-1
= $ 60,000 X 6.08
= $ 364,800
Annual Income in the 39th service year = $ 364,800 X 1.05 = $ 383,040
in the 40th service year = $ 383,040 X 1.05 = $ 402,192
Therefore Average annual income = (364,800 + 383,040 + 402,192 ) / 3 = $ 383,344
Therefore, Pension = (2% X Service Year X Averarge annual salary in the last 3 years of employment)
Annual Payments are as follows.
Now let us calculate the pension under alternative (b)
Contribution in the first year = $ 60,000 X 14% = $ 8,400
Rate of return on investment = 6%
Growth Rate of Annual salary = 5%
Total yearly increase in Contribution = 6% + 5% = 11%
Therefore, Value of Pension after 40 years = $ 8,400 X FVAF(11%, 40 Years)*
= $ 8,400 X 581.83
= $ 4,887,372
* Future Value Annuity Factor (FVAF) = (1+R)n/R, where R is yearly increase rate and n is No. of years.
Therefore, it is observed from both the alternatives that the Value of Pension will be $ 6,286,841
Year Payment 1 7,667 2 15,334 3 23,001 4 30,668 5 38,334 6 46,001 7 53,668 8 61,335 9 69,002 10 76,669 11 84,336 12 92,003 13 99,669 14 107,336 15 115,003 16 122,670 17 130,336 18 138,004 19 145,671 20 153,338 21 161,004 22 168,671 23 176,338 24 184,005 25 191,672 26 199,339 27 207,006 28 214,673 29 222,340 30 230,006 31 237,673 32 245,340 33 253,007 34 260,674 35 268,341 36 276,008 37 283,675 38 291,341 39 299,008 40 306,675 Total 6,286,841Related Questions
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