Question

Your grandfather would like to share some of his fortune with you. He offers to give

you money under one of the following scenarios (you get to choose):

1. \(8,750 per year at the end of each of the next six years

2. \)49,650 (lump sum) now

3. $100,450 (lump sum) six years from now

C H A P T E R 1 2

Requirements

1. Calculate the present value of each scenario using a 6% discount rate. Which scenario

yields the highest present value? Round to the nearest dollar.

2. Would your preference change if you used a 12% discount rate?

Short answer

Present value of scenario 1,2 and 3 are $54,336, $49650 and $63,108. Scenario 3 has highest yield among all scenarios.

Step-by-step solution

Definition of present value

The current value calculated by using the specified formula for the amount invested by the investor in future date.

calculation of present value

1.Present value:

$\begin{array}{c}\text{Present\hspace{0.17em}Value=\hspace{0.17em}Principal\hspace{0.17em}Amount×\hspace{0.17em}PV\hspace{0.17em}factor\hspace{0.17em}i=6\%,\hspace{0.17em}n=\hspace{0.17em}8}\\ \text{=\$8,750×\hspace{0.17em}6.20979}\\ \text{=\$54,336}\end{array}$

2.Present Value of this scenario is $49,650

3.Present Value:

$\begin{array}{c}\text{Present\hspace{0.17em}Value=\hspace{0.17em}Principal\hspace{0.17em}Amount×\hspace{0.17em}PV\hspace{0.17em}factor\hspace{0.17em}i=6\%,\hspace{0.17em}n=\hspace{0.17em}8}\\ \text{=\$100,650×\hspace{0.17em}\hspace{0.17em}}0.627\\ \text{=\$63,108}\end{array}$