Question

hree 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 Annual Payment Date of First Payment Tinkers $ 22,000 12/31/21 Evers 27,000 12/31/22 Chance 32,000 12/31/23 Required: 1. Compute the present value of the pension obligation to these three employees as of December 31, 2018. Assume a 10% interest rate. 2. The company wants to have enough cash invested at December 31, 2021, to provide for all three employees. To accumulate enough cash, they will make three equal annual contributions to a fund that will earn 10% interest compounded annually. The first contribution will be made on December 31, 2018. Compute the amount of this required annual contribution.

Answer 1

1
Tinkers:
PVA	7.60608*22000	167334
Present value of an ordinary annuity of $1:n= 15,i= 10%
PV	167334*0.82645	138293
2
Evers:
PVA	27,000*7.60608	205364
PV	205364* 0.75131	154292
3
Chance:
PVA	32,000*7.60608	243395
PV	243395*0.68301	166241

Tinkers:	138293
Evers:	154292
Chance:	166241

2
Present value of pension obligations as of December 31, 21
Employee PV as of 12/31/18		FV of $1 factor,n= 3,i= 10%
Tinkers:	138293	1.331	184068
Evers:	154292	1.331	205363
Chance:	166241	1.331	221267
Total present value,12/31/21			610698

Future value of an annuity due of $1:n= 3,i= 10% (from FVAD of $1) =( 3.6410)

610698/3.6410

167728