Question

John Roberts is 55 years old and has been asked to accept early retirement from his company. The company has offered John three alternative compensation packages to induce John to retire: (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.) 1.$180,000 cash payment to be paid immediately.2. A 20-year annuity of $16,000 beginning immediately.3. A 10-year annuity of $50,000 beginning at age 65. Required:Determine the present value, assuming that he is able to invest funds at a 7% rate, which alternative should John choose? (Round your final answers to nearest whole dollar amount

Answer 1

Answer:

The best alternative will be of 180,000 today.

Explanation:

We calculate the present value of the second and third alternatives and compare with the cash received today:

.2. A 20-year annuity of $16,000 beginning immediately

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 16,000

time 20

rate 0.07

$16000 \times \frac{1-(1+0.07)^{-20} }{0.07} = PV$

PV $169,504.2279

3.- A 10-year annuity of $50,000 beginning at age 65.

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C       $  50,000

time 10 years

rate 0.07

$50000 \times \frac{1-(1+0.07)^{-10} }{0.07} = PV$

PV $351,179.0770

This start at age 65 currently he's 55 so we bring it to present:

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity $  351,179.08

time   10 years

rate  0.07

$\frac{351179.07704663}{(1 + 0.07)^{10} } = PV$  

PV   178,521.64

As non of the alternatives is better than 180,000 today we pick this alternative.

Answer 2

Answer: John Roberts should take the lump sum of $180 000

Explanation:

option 1

lump sum = $180 000

option 2

Present Value = P(1-(1+r)^-n)/r

Present Value = 16000(1-(1+0.07)^-20)/0.07

Present Value = 169504.22789 = 169504.23

The present value of option 2 = $169504

option 3

Present Value = P(1-(1+r)^-n)/r

Present Value = 50000(1-(1+0.07)^-10)/0.07

present value (at age 65) = 351179.07643

the annuity of option 3 will start in future when john is 65 years old. the present value of $ 35179.07643  is the present of the annuity at the age of 65. john is 55 years old,We need to discount the present value of $ 35179.07643  to determine how much is option 3 future annuity worth today.

Present value= 351179.07643

N = 65 - 55 =10

present value (at age 55) = (present value at 65)/(1+r)^n

present value (at age 55) = 351179.07643/(1+0.07)^10  

present value (at age 55) = 178521.63491 = 178521.64