Question

HELP!

You have just been hired by your new employer and must choose between two retirement plan options...

You have just been hired by your new employer and must choose between two retirement plan options: (1) the state’s defined benefit plan and (2) a defined contribution plan under which the employer will contribute each year an amount equal to 8 % of your salary. The defined benefit plan will provide annual retirement benefits determined by the following formula: 1.5% x years of service x salary at retirement. It is assumed that your salary will rise about 3% a year, and the interest rate the company use in their calculation is 6%. It is also assume that you will retire after 40 years and draw retirement pay for 20 years.

Required –

1) You were hired at a beginning of 2017 at a salary of $100,000. If you choose the defined benefit plan and projections hold true, what will by your annual retirement pay? What is the present value of your retirement annuity as of the anticipated retirement date (end of 2056)?

2)Suppose instead that you choose the defined contribution plan. Assuming the rate of increase in salary is the same as the employer assumes and the rate of return on your retirement plan assets will be 6% compounded annually, what will be the future value of your plan assets as of the anticipated retirement date (end of 2056)? What will be your annual retirement pay (assuming continuing investments of remaining assets at 6%)?

3) Based on the numerical comparison, which plan would you choose?

Answer 1

		Current Salary	$100,000
		Number of years to retirement	40
		Rate of salary increase	3%
		Annual Slary at the time of retirement	$326,204	(100000*((1.03)^40))
	Pmt	Annual Retirement Pay	$195,722	(1.5%*40*326204)
	Rate	Annual interest rate	6%
	Nper	Number of years of retiremet payment	20
	1)	Present value of payments at end 2056	$2,244,916	(Using PV function of excel with Rate=6%, Nper=20, Pmt=-195722)
		Excel Command: PV(6%,20,-195722)
	2)	Defined contribution plan
		Future value of Cash Flow at end of N Years:
		Cash Flow*((1+i)^(N-t))
		i=interest rate =6%=0.06
		N=40
		t=time of cash flow
		Salary at end of year 1	$100,000
		Salary at end of year 2		(100000*1.03))
		Salary at end of year (t+1)=1.03*(Salary at end of year(t)
		t	A	B=A*(1.06^(40-t))
		Year	Salary	Future value at end 2056
		1	$100,000	$970,351
		2	$103,000	$942,888
		3	$106,090	$916,202
		4	$109,273	$890,272
		Future Value of pan asset at end 20156	$23,412,267
	3)	Based on above, we will choose:
		Defined contribution plan
		B-A (1.06 (40-t)) Future value at Year end 2056 1$100,000 $970,351 2$103,000 3 $106,090 $942,888 $916,202 4$109,273 5 $112,551 $890,272 $865,076 6 $115,927 $840,593 7 $119,405 $816,802 8 $122,987 9$126,677 $793,685 $771,222 10 $130,477 $749,395 728,186 $707,577 11$134,392 12$138,423 13 $142,576 $687,551 14$146,853 15$151,259 $668,092 $649,184 $630,811 16 $155,797 17$160,471 $612,958 18 $165,285 $595,610 19 $170,243 20$175,351 $578, 753 $562,373 19 $170,243 $578,753 20$175,351 $562,373 $546,457 530,991 $515,963 21 $180,611 22$186,029 23 $191,610 24 $197,359 25 $203,279 26$209,378 $501,360 $487,171 $473,383 27 $215,659 28$222,129 $459,985 $446,967 $434,317 $228, 793 29 30 $235,657 31 $242,726 $422,025 410,081 $398,475 32 $250,008 33 $257,508 387,197 34 $265,234 $376,239 35 $273,191 36 $281,386 $365,591 355,244 $345,190 37 $289,828 38 $298,523 $335,420 39 $307,478 40$316,703 $325,927 $316,703 23,412,267 SUM 23,412,267 Future Value of pan asset at end 20156