Question

A machine at a cost of $5,000 was purchased 3 years ago. It can be sold now for $3,000. If the machine is kept, the annual operating and maintenance costs will be $1,500. If it is kept and operated for next five years, determine the amount at time 0 (now) equivalent to the cost of owning and operating the machine for the next five-year period. It is anticipated that the machine can be sold for $1,000 at the end of the five-year period. Use an interest rate of 10%

Answer 1

$10,065.26

Step-by-step explanation:

First, we need to calculate the present value of machine operating cost using the following formula

PV of operating cost = Yearly Operating cost x ( 1 - ( 1 + Interest rate )^-numbers of years ) / Interest rate

Where

Yearly operating cost = $1,500

Interest rate = 10%

Numbers of years = 5 years

Placing values in the formula

PV of operating cost = $1500 x ( 1 - ( 1 + 10% )^-5 ) / 10%

PV of operating cost = $5,686.18

Now calculate the present vlaue of salvahge value

PV of SAlvage value = Slavage value / ( 1 + Interest rate )^Numbers of years

where

Salvage Value = $1,000

Interest rate = 10%

Numbers of years = 5 years

PLacing values in the formula

PV of SAlvage value = $1,000 / ( 1 + 10% )^5

PV of SAlvage value = $620.92

Net cost at time 0 = Initial purchase cost + PV of operating cost - Present value of salvage value = $5,000 + $5,686.18 - $620.92 = $10,065.26