John Roberts is 51 years old and has been asked to accept early retirement from his company. On July 1, the company offered John three alternative compensation packages to induce John to retire: 1. $180,000 cash payment to be paid immediately.
2. A 16-year annuity of $18,000 beginning immediately.
3. A 10-year annuity of $52,000 beginning on July 1 of the year John reaches age 61 (after 10 years).

Required:
Determine the present value, assuming that he is able to invest funds at a 7% rate, which alternative should John choose?

John should choose option 3 which is a 10 year annuity starting after 10 years from today as the present value of this option which is $185662.50 is higher than the present value of option 1 and option 2 which are $180000 and $181942.45 respectively.

Explanation:

1.

The present value of option 1 is equal to the cash payment received today. Thus, it is the same.

PV - Option1 = $180000

2.

The option 2 is an annuity due as the annuity is beginning immediately. The formula to calculate the present value of annuity due is attached in attachment.

PV - Option 2 = 18000 * [(1 - (1+0.07)^-16) / 0.07] * (1+0.07)

PV - Option 2 = $181942.4521 rounded off to $181942.45

3.

To calculate the present value of option 3 which is an ordinary annuity of 10 years and which will start after 10 years, we will use the present value of annuity ordinary formula as provided in the attachment to calculate the value of annuity when John will be 61 that is 10 years from now. Then we will discount that value of annuity to today's value to calculate the present value.

Value of Ordinary annuity (10 years from now) = 52000 * [(1 - (1+0.07)^-10) / 0.07]

Value of Ordinary annuity (10 years from now) = 365226.2401

The present value of this annuity will be = 365226.2401 / (1+0.07)^10

PV - Option 3 = $185662.5006 rounded off to $185662.50

b is the correct answer