SHORT ANSWER. question Write the word or phrase that best completes each stateme

Question

SHORT ANSWER. question Write the word or phrase that best completes each statement or answers the 24) Three employees of Sharp Communication 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 S 37,000 42,000 47,000 12/31/19 12/31/20 12/31/21 Samuel Lisa Kyle Required: (24 points) date of the first payment is different for each employee) a) Compute the TOTAL present value of the pension obligation for all threse employees as of December 31, 2016, Assume a 12% interest rate. (Hint: the b) To accumulate enough cash, the company will make three equal annual contributions to a fund that will earn 12% interest compounded annually over the next 3 years starting on December 31, 2016. What will be the TOTAL value of the obligation for all three employees as of December 31, 2019? c)How much will the annual payments have to be to meet the TOTAL obligation for these 3 employees at December 31, 2019 caclulated in part b? Assume the payments are made at the BEGINNING of each of the next 3 years.

Explanation / Answer

a)

Samuel

Present Value of Annuity = $37,000 x PVAF(12%, 15 year) i.e. 6.8109

.........................................= $252,003

Present Value = $252,003 x PVIF (12%, 2 year) i.e. 0.7972

.......................= $200,897

Lisa

Present Value of Annuity = $42,000 x PVAF(12%, 15 year) i.e. 6.8109

.........................................= $286,058

Present Value = $286,058 x PVIF (12%, 3 year) i.e. 0.7118

.......................= $203,616

Kyle

Present Value of Annuity = $47,000 x PVAF(12%, 15 year) i.e. 6.8109

.........................................= $320,112

Present Value = $320,112 x PVIF (12%, 4 year) i.e. 0.6355

.......................= $203,431

b)

c

Annual payments = $854,101 / (Future value of annuity due of $1 , n= 3, i= 12%) i.e. 3.7793

.............................= $225,994

Employee PV as of 12/31/16 x FV of $1 factor, n=3, i=12% = FV as of 12/31/16 Samuel $200,897 x 1.4049 = $282,240 Lisa $203,616 x 1.4049 = $286,060 Kyle $203,431 x 1.4049 = $285,800 Total present value, 12/31/19 $854,101

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