Three employees of the Horizon Distributing Company will receive annual pension

Question

Three employees of the Horizon Distributing Company will receive annual pension payments from the company when they retire. The employees will receive their annual payments for as long as they live. Life expectancy for each employee is 15 years beyond retirement. Their names, the amount of their annual pension payments, and the date they will receive their first payment are shown below: (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided.) Employee Tinkers Evers Chance Annual Payment $24,000 29,000 34,000 Date of First Payment 12/31/19 12/31/20 12/31/21 Required 1. Compute the present value of the pension obligation to these three employees as of December 31 2016. Assume a 12% interest rate Employee Tinkers Evers Chance PV 2. The company wants to have enough cash invested at December 31, 2019, to provide for all three employees. To accumulate enough cash, they will make three equal annual contributions to a fund that will earn 12% interest compounded annually. The first contribution will be made on December 31, 2016 Compute the amount of this required annual contribution ount of annual contribution

Explanation / Answer

1. Calculation of present value of the pension obligation

Tinker :

PVA = $24000*6.81086** = 163461

**Present value of an ordinary annuity of $1:n= 15,i= 12% (from PVA of $1)

PV = 163461*0.79719** = 130309

**Present value of $1:n= 2,i= 11% (from PV of $1)

Evers :

PVA = $29000*6.81086** = 19751

**Present value of an ordinary annuity of $1:n= 15,i= 12% (from PVA of $1)

PV = 19751*0.733119** = 14480

**Present value of $1:n= 3,i= 11% (from PV of $1)

Chance :

PVA = $34000*6.81086** = 23157

**Present value of an ordinary annuity of $1:n= 15,i= 12% (from PVA of $1)

PV = 23157*0.65873** = 15254

**Present value of $1:n= 4,i= 11% (from PV of $1)

2. Present value of pension obligations as of December 31, 2019

Amount of annual contribution:

FVAD = Annuity amount × Annuity factor

Annuity amount = FVAD/Annuity factor

= 218880/3.7097** = 59002

***Future value of an annuity due of $1:n= 3,i= 11% (from FVAD of $1)

Employee PV as of 12/31/16 FV of $1 factor,n= 3,i= 11% FV as of 12/31/16 Tinker 130309 1.36763 178215 Evers 14480 1.36763 19804 Chance 15254 1.36763 20862 Total 218880

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