Question

(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?

Short answer

The best option is option C which has the highest Present Value.

Step-by-step solution

Present Value of part A

The present value of is $55,000.

Calculation of present value of option B.

$$\begin{gathered} \mathbf{Present}\mathbf{}\mathbf{Value}\mathbf{=}\mathbf{Present}\mathbf{}\mathbf{value}\mathbf{}\mathbf{of}\mathbf{}\mathbf{quarterly}\mathbf{}\mathbf{payment} \\ \mathbf{=}\mathbf{4}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{15}\mathbf{.}\mathbf{58916} \\ \mathbf{=}\mathbf{\$}\mathbf{62}\mathbf{,}\mathbf{357} \end{gathered}$$

Calculation of present value of option C

$$\begin{gathered} \mathbf{Present}\mathbf{}\mathbf{Value}\mathbf{=}\mathbf{Initial}\mathbf{}\mathbf{Payment}\mathbf{+}\mathbf{Present}\mathbf{}\mathbf{value}\mathbf{}\mathbf{of}\mathbf{}\mathbf{quarterly}\mathbf{}\mathbf{payment} \\ \mathbf{=}\mathbf{18}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{1}\mathbf{,}\mathbf{800}\mathbf{\times }\mathbf{25}\mathbf{.}\mathbf{73034} \\ \mathbf{=}\mathbf{\$}\mathbf{64}\mathbf{,}\mathbf{315} \end{gathered}$$

Computation of present values of option D

$$\begin{gathered} \mathbf{Present}\mathbf{}\mathbf{Value}\mathbf{=}\mathbf{Present}\mathbf{}\mathbf{value}\mathbf{}\mathbf{of}\mathbf{}\mathbf{quarterly}\mathbf{}\mathbf{payment} \\ \mathbf{=}\mathbf{4}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{10}\mathbf{.}\mathbf{25776}\mathbf{+}\mathbf{1500}\mathbf{\times }\mathbf{18}\mathbf{.}\mathbf{42438}\mathbf{\times }\mathbf{0}\mathbf{.}\mathbf{74356} \\ \mathbf{=}\mathbf{41}\mathbf{,}\mathbf{031}\mathbf{+}\mathbf{20}\mathbf{,}\mathbf{549} \\ \mathbf{=}\mathbf{\$}\mathbf{61}\mathbf{,}\mathbf{580} \end{gathered}$$

The best option is option C.