Question

he ABC company is considering the purchase of a new machine that will last 5 years and cost $100,000; maintenance will cost $12,000 per year. If the interest rate is 10% per year, compounded quarterly, a. how much money should the company set aside for this machine b. what is the future value, at the end of year 5, of the given cash flows

Answer 1

a.

$145,051.26

b.

$237,669.51

Step-by-step explanation:

First, calculate the equivalent annual interest rate

Equivalent annual interest rate = ( ( 1 + ( i / n ) )^n ) - 1

Equivalent annual interest rate = ( ( 1 + ( 10% / 4 ) )^4 ) - 1

Equivalent annual interest rate = 10.38%

a.

We will use the following formula to calculate the amount of money set aside.

Net Present value = Initial Cost + Maintainance cost x ( 1 - ( 1 + r )^-n / r

Net Present value = $100,000 + $12,000 x ( 1 - ( 1 + 10.38% )^-5 / 10.38%

Net Present value = $145,051.26

b.

We need to calculate the future value of using the following formula

Future value = $100,000 x ( 1 + 10.38% )^5 + [ $12,000 x ( ( 1 + 10.38% )^5 - 1 / 10.38%

Future value = $163,852.08 + $73,817.43 = $237,669.51