Question

Problem 5-14 (Algo) Deferred annuities; pension obligation (LO5-8, 5-10] 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 12/31/24 12/31/25 12/31/26 Required: 1. Compute the present value of the pension obligation to these three employees as of December 31, 2021. Assume a 12% 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 12% 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.) Employee PV 1. Tinkers $ 130,309 Evers Chance 2. Amount of annual contribution

Answer 1

1) Present value of Pension Obligation

Tinkers = $24,000 * PVAF 12%, 15 * PV 12%, 3

= $24,000 * 7.62816 * 0.71178

Tinkers = $130,309.72 = $130,310

Evers = $29,000 * PVAF 12%, 15 * PV 12%, 3

= $29,000 * 7.62816 * 0.63551

Evers = $ 140,585.38 = $140,585

Chance = $34,000 * PVAF 12%, 15 * PV 12%, 3

= $34,000 * 7.62816 * 0.56742

Chance = $ 147,164.59 =$147,164

2) Calculation of Amount required for annual Contribution

Tinkers = $24,000 * PVAF 12%, 15

= $24,000 * 7.62816

Tinkers = $183,075.84

Evers = $29,000 * PVAF 12%, 15 * PV 12%,1

= $29,000 * 7.62816 *0.89285

Evers. = $197,513.27

Chance = $34,000 * PVAF 12%, 15 * PV 12%,2

= $34,000 * 7.62816 * 0.79719

Chance = $206,757.15

Total present value = $183,075.84 + $197,513.27 + $206,757.15 = $587,346.26 = $587,346

Annual Contribution = Total Present Value / FVAf 12%, 3

= $587,346 / 3.60477

Annual Contribution = $162,935.84 = $162,936