Question

A car salesperson offers you two alternative payment option:

- Buy new car for $25,000 cash today, or

- pay $5000 today and $22,500 two years from now

If the interest rate in the economy is 7%,

1. What is the present value of the first option?
2. What is the present value of the second option?
3. Which option is preferable?

Answer 1

Will use time of value of money to analyze the two options. Option with lowest present value cost will be preferred.

a) Option 1 : Buy new car for $25,000 cash today

Present Value of Option 1 = $25,000

(If cash is paid today then the present value will be equal to cash paid)

b) Option 2 : Pay $5000 today and $22,500 two years from now

i = interest rate = 7%
n = no. of periods =2yrs

Present Value = Cash Flow today + [ 1 / (1 + i )ⁿ ] * Cash flow two years from now
= $5,000 + [ 1 / (1 + 0.07)² ] * $22,500
= $5,000 + 0.87344 * $22,500
= $5,000 + $19652.37
= $24,652.37

c) Option 2 is preferred since the Present Value Cost of Option 2 is less than Option 1.