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 13 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 | $ | 36,000 | 12/31/24 | |||
Evers | 41,000 | 12/31/25 | ||||
Chance | 46,000 | 12/31/26 | ||||
Required:
1. Compute the present value of the pension
obligation to these three employees as of December 31, 2021. Assume
an 11% 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 11% 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.)
CALCULATION OF PRESENT VALUE OF YEAR | |||||||
TINKERS | EVERS | CHANCE | |||||
YEAR | PRESENT VALUE | AMOUNT | PRESENT VALUE OF AMOUNT | AMOUNT | PRESENT VALUE OF AMOUNT | AMOUNT | PRESENT VALUE OF AMOUNT |
2021 | 1 | - | - | - | - | - | - |
2022 | 0.900900901 | - | - | - | - | - | - |
2023 | 0.811622433 | - | - | - | - | - | - |
2024 | 0.731191381 | 36,000.00 | 26,322.89 | - | - | - | - |
2025 | 0.658730974 | 36,000.00 | 23,714.32 | 41,000.00 | 27,007.97 | - | - |
2026 | 0.593451328 | 36,000.00 | 21,364.25 | 41,000.00 | 24,331.50 | 46,000.00 | 27,298.76 |
2027 | 0.534640836 | 36,000.00 | 19,247.07 | 41,000.00 | 21,920.27 | 46,000.00 | 24,593.48 |
2028 | 0.481658411 | 36,000.00 | 17,339.70 | 41,000.00 | 19,747.99 | 46,000.00 | 22,156.29 |
2029 | 0.433926496 | 36,000.00 | 15,621.35 | 41,000.00 | 17,790.99 | 46,000.00 | 19,960.62 |
2030 | 0.390924771 | 36,000.00 | 14,073.29 | 41,000.00 | 16,027.92 | 46,000.00 | 17,982.54 |
2031 | 0.352184479 | 36,000.00 | 12,678.64 | 41,000.00 | 14,439.56 | 46,000.00 | 16,200.49 |
2032 | 0.317283314 | 36,000.00 | 11,422.20 | 41,000.00 | 13,008.62 | 46,000.00 | 14,595.03 |
2033 | 0.285840824 | 36,000.00 | 10,290.27 | 41,000.00 | 11,719.47 | 46,000.00 | 13,148.68 |
2034 | 0.257514256 | 36,000.00 | 9,270.51 | 41,000.00 | 10,558.08 | 46,000.00 | 11,845.66 |
2035 | 0.231994825 | 36,000.00 | 8,351.81 | 41,000.00 | 9,511.79 | 46,000.00 | 10,671.76 |
2036 | 0.209004347 | 36,000.00 | 7,524.16 | 41,000.00 | 8,569.18 | 46,000.00 | 9,614.20 |
2037 | 0.188292204 | - | - | 41,000.00 | 7,719.98 | 46,000.00 | 8,661.44 |
2038 | 0.169632616 | - | - | - | - | 46,000.00 | 7,803.10 |
PRESENT VALUE | 1,97,220.46 | 2,02,353.33 | 2,04,532.04 | ||||
CALCULATION OF PRESENT VALUE OF PENSION ON 31.12.2021 | |||||||
TINKERS | FROM 31.12.2024 TO 31.12.2036 FOR 13 YEARS | ||||||
EVERS | FROM 31.12.2025 TO 31.12.2037 FOR 13 YEARS | ||||||
CHANCE | FROM 31.12.2026 TO 31.12.2038 FOR 13 YEARS | ||||||
WE CAN ALSO PUT A FORMULA FOR CALCULAION | |||||||
PRESENT VALUE = ANNUAL PENSION X PVAIF | |||||||
i.e. | |||||||
PVAIF = Present value Annuity Interest Factor | |||||||
TINKERS | = | ANNUAL PENSION X PVAIF (FROM 31.12.2024 TO 31.12.2036, 11%) | |||||
= | 36000 X 5.478346242 | ||||||
= | 1,97,220.46 | ||||||
EVERS | = | ANNUAL PENSION X PVAIF (FROM 31.12.2025 TO 31.12.2037, 11%) | |||||
= | 41000 X 4.935447065 | ||||||
= | 2,02,353.33 | ||||||
CHANCE | = | ANNUAL PENSION X PVAIF (FROM 31.12.2026 TO 31.12.2038, 11%) | |||||
= | 46000 X 4.446348707 | ||||||
= | 2,04,532.04 |
Three employees of the Horizon Distributing Company will receive annual pension payments from the company when...
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...
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: (EV of S1. PV of S1. FVA of $1. PVA of S1. FVAD of $1 and PVAD of...
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: Employee Annual Payment Date of First Payment Tinkers $ 37,000 12/31/24 Evers 42,000 12/31/25 Chance 47,000 12/31/26 Required:...
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