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 14 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	$	38,000			12/31/24
Evers		43,000			12/31/25
Chance		48,000			12/31/26

Required:
1. Compute the present value of the pension obligation to these three employees as of December 31, 2021. Assume a 10% interest rate.
2. The company wants to have enough cash invested at December 31, 2024, 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, 2021. Compute the amount of this required annual contribution.
(For all requirements, Do not round intermediate calculations. Round your final answers to nearest whole dollar amount.)

Answer 1

Answer:

1.

Employee	PV
Tinkers	231,352
Evers	237,991
Chance	241,513

2.

Amount of annual contribution

259,860

Calculation

1.

Present value of the pension obligation

Tinkers:

Present value of an ordinary annuity :

n = 14

rate = 10%

If using MS Exce, formula will be = PV(10%,14,1,0,0)

PVAD = 7.36669

PVA = 38,000 * 7.36669 = 279,934

Present value :

n = 2

rate = 10%

If using MS Exce, formula will be = PV(10%,2,0,1,0)

Present value of $1 = 0.82645

PV = $279,934 * 0.82645 = 231,351

Evers:

Present value of an ordinary annuity :

n = 14

rate = 10%

If using MS Exce, formula will be = PV(10%,14,1,0,0)

PVAD = 7.36669

PVA = 43,000* 7.36669 = 316,768

Present value :

n = 3

rate = 10%

If using MS Exce, formula will be = PV(10%,3,0,1,0)

Present value of $1 = 0.75131

PV = $316,777* 0.75131= 237,991

Chance:

Present value of an ordinary annuity :

n = 14

rate = 10%

If using MS Exce, formula will be = PV(10%,14,1,0,0)

PVAD = 7.36669

PVA = 48,000 * 7.36669 = 353,601

Present value :

n = 4

rate = 10%

If using MS Exce, formula will be = PV(10%,4,0,1,0)

Present value of $1 = 0.68301

PV = $353,611* 0.68301= 241,513

2.

Amount of annual contribution

Employee	PV as of 12/31/21	FV of $1 factor, n = 3, i = 10%	FV as of 12/31/21
Tinkers	231,351	1.33100	307,928
Evers	237,992	1.33100	316,767
Chance	241,514	1.33100	321,455
		Total present value	946,151

FVAD = Annuity amount * Annuity factor

Annuity factor :

n = 3

rate = 10%

FV = 3.6410

Using MS Excel = FV(10%,3,1,0,1) = 3.6410

Annuity amount = FVAD / Annuity factor

Annuity amount = 946,151 / 3.6410 = 259,860