Question

Grandma Jonesy died, leaving to her Grandson Bart, an insurance policy contract

that provides that the beneficiary (Bart) can choose any one of the following four options.

(a)        $200,000 immediate cash.

           

(b)       $12,000 every 3 months payable at the end of each quarter for 5 years.

           

(c)        $50,000 immediate cash and $5,000 every 3 months for 10 years, payable at the beginning of each 3-month period.

           

(d)       $12,000 every 3 months for 4 years and $3,750 each quarter for the following 10 quarters, all payments payable at the

            end of each quarter.

           

Instructions    

If money is worth 2% per quarter, compounded quarterly, which option would you recommend that Bart exercise?

Answer 1

We need to calculate present worth of each option which is calculated as follows:-

a) Present Value = Immediate Cash = $200,000

b) Total no. of quarters = 5 years*4 quarters in a year = 20

Present Value = $12,000*PVAF(20, 2%)

= $12,000*16.35143 = $196,217

c) Total No. of Quarters = 10 years*4 Qtrs in a year = 40

Present Value = Immediate Cash+[Amounts received in the beginning of Qtr*PVAF(40, 2%)

= $50,000+($5,000*27.90259) = $50,000+$139,513 = $189,513

d) Total Qtrs in 4 years = 4 years*4 qtrs in a year = 16

Present Value of Option = [$12,000*PVAF(16, 2%)]+[$3,750*PVAF(10, 2%)]

= ($12,000*13.57771)+($3,750*8.98259)

= $162,933+$33,685 = $196,618

Bart should exercise the option with highest present value. The highest present value of all the above four options is a) (i.e. immediate cash of $200,000). Therefore, Bart should exercise option a.