Question

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(Analysis of Alternatives) Julia Baker died, leaving to her husband Brent an insurance policy contract that...

(Analysis of Alternatives) Julia Baker died, leaving to her husband
Brent an insurance policy contract that provides that the beneficiary (Brent) can
choose any one of the following four options
a. €55,000 immediate cash.
b. €4,000 every 3 months payable at the end of each quarter for 5 years.
c. €18,000 immediate cash and $1,800 every 3 months for 10 years, payable at
the beginning of each 3-month period.
d. €4,000 every 3 months for 3 years and $1,500 each quarter for the following 25
quarters, all payments payable at the end of each quarter.

Instructions
If money is worth 2½% per quarter, compounded quarterly, which option would you
recommend that Brent exercise?

Solutions

Expert Solution

Quarter (no.) Amount $ PV Factor Present Value
Option 1 Immediate cash Immediate $       55,000 1.00000 $ 55,000
Quarter (no.) Amount $ PV Factor Present Value
Option 2 $4,000 every 3 months payable at the end of each quarter for 5 years. 20 $ 4,000 15.58916 $ 62,357
(period number = in 1 year, 4 quarters, for 5 years = 20 quarters)
(* Annuity table referred = ordinary annuity for 20th period for 2.5 %)
Quarter (no.) Amount $ PV Factor Present Value
Option 3 $18,000 immediate cash and $1,800 every 3 months for 10 years, payable at the beginning of each 3-month period Immediate $ 18,000 1.00000 $ 18,000
(period number = in 1 year, 4 quarters, for 10 years = 40 quarters) 40 $ 1,800 25.73034 $ 46,315
(* Annuity table referred = annuity due of 1 for 40th period for 2.5 %) $ 64,315
Quarter (no.) Amount $ PV Factor Present Value
Option 4 $4,000 every 3 months for 3 years and $1,500 each quarter for the following 25 quarters, all payments payable at the end of each quarter 12 $ 4,000 10.25776 $ 41,031
(period number = in 1 year, 4 quarters, for 3 years = 12 quarters + 25 quarters) 25 $ 1,500 (23.95732-10.25776) = 13.69956 $ 20,549
(* Annuity table referred = ordinary annuity for 12th period & 25th period for 2.5 % ) $ 61,580
So recommended option for Mr Brent would be Option # 3 as the pay out is high $ 64,315.

ekkarill92 answered 1 year ago
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