Question

anther Mail Homepage - Easter... Legfi Invoicing, pa... Chapter Officers M inufinancegmail... The BMP App YouTube M McGraw-Hill Cor hapter 6 0 Saved Help Save & Chi 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. EVA of $1. PVA of $1. EVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided. Employee Tinkers Evers Chance Annual Payment $32,000 37,000 42,000 Date of First Payment 12/31/21 12/31/22 12/31/23 Required: 1. Compute the present value of the pension obligation to these three employees as of December 31, 2018. Assume a 12 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 12% Interest compounded annually. The first contribution will be made on December 31, 2018. 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 Tinkers Prey 5 of 6 !! Next >

Answer 1

1.

PV of annuity = P x [1-(1+r)^-n/r] or P x PVIFA (r, n)

P = Periodic payment

r = Rate per period = 12 %

n = Number of periods = 13

PV of Tinkers pension obligation on 12/31/20 = $ 32,000 x PVIFA (12 %, 13)

= $ 32,000 x 6.4235 = $ 205,552

PV of Tinkers pension obligation on 12/31/18 = $ 205,552 x PVIF (12 %, 2)

                                                                         = $ 205,552 x 0.7972 = $ 163,866.0544 or $ 163,866

PV of Evers pension obligation on 12/31/21 = $ 37,000 x PVIFA (12 %, 13)

  = $ 37,000 x 6.4235 = $ 237,669.50

PV of Evers pension obligation on 12/31/18 = $ 237,669.50 x PVIF (12 %, 3)

                                                                       = $ 237,669.50 x 0.7118 = $ 169,173.1501 or $ 169,173

PV of pension obligation Chance on 12/31/22 = $ 42,000 x PVIFA (12 %, 13)

                                                                         = $ 42,000 x 6.4235 = $ 269,787

PV of Chance pension obligation on 12/31/18 = $ 269,787 x PVIF (12 %, 4)

= $ 269,787 x 0.6355 = $ 17,1449.6385 or $ 171,450

2.

Fund size needed on December 31, 2021 to facilitate pension obligations

= PV of pension obligation of Tinkers on 12/31/21 + PV of pension obligation of Evers on 12/31/21 + PV of pension obligation of Chance on 12/31/21

= PV of total pension obligation on 12/31/18 x FVIF (12 %, 3)

= ($ 163,866.0544 + $ 169,173.1501 + $ 17,1449.6385) x 1.4049

= $ 504,488.843 x 1.4049 = $ 708,756.3755307 or $ 708,756

Horizon Distributing should have $ 708,756 on 12/31/21

Future value of immediate annuity formula can be used to compute 3 annual contributions as:

FV_D = C x FVIFAD (12 %, 3)

$ 708,756.3755307 = C x 3.7793

C = $ 708,756.3755307/ 3.7793

    = $ 187,536.415614188 or $ 187,536

Annual contribution amount on 12/31/18, 12/31/19 and 12/31/20 is $ 187,536