Question

for your office work you need a high end photocopy machine which is available to rent for 150 usd per day and the operating cost is 25 usd. the price of this machine is 125,000 usd. you will need this machine for several months, therefore you start calculating whether you should purchase it or not. calculate the number of days after which it would be advisable to buy this machine.

Answer 1

After performing a break-even analysis, it is advisable to buy the photocopy machine after approximately 714 days or roughly 2 years, at which point the total cost of renting equals the purchase price.

Step-by-step explanation:

To determine whether you should rent or buy the high-end photocopy machine, you need to calculate the point at which the total costs of both options are equal. This involves understanding the concept of break-even analysis in mathematics and applying it to a practical financial decision.

Let's start by calculating the daily total cost if you were to rent the machine. Rent is $150 per day, and operating cost is $25 per day, so the total cost per day when renting is $175 (rent + operating cost).

Now, if you decide to buy the machine, the cost is $125,000, and we'll assume no operating cost apart from the daily expenses already accounted for when renting.

To find the number of days after which buying is advisable, we use the formula:

Cost to purchase / (Rent per day + Operating cost per day) = Break-even point in days.

So, $125,000 / $175 = 714.2857. After about 714 days or roughly 2 years, it would be advisable to buy the machine rather than rent it.