The College of Business is deciding between two photocopier options. The first is to lease a high-end machine for $8,400/year. The lease is all-inclusive so the only additional costs are the cost of paper, which is $0.01/sheet. The other option is to purchase a machine. The cost is $5,000 and the per sheet cost increases (toner, maintenance) to $0.02.

Which option is preferred if the annual copy volume is expected to be 270,000? b. What if the copy volume is reduced to 240,000? c. At what volume is the College indifferent between the two options?
What if the copy volume is reduced to 240,000?
At what volume is the College indifferent between the two options?

At 270, 000 copies, option 2 is preferred

At 240, 000 copies, option 2 is preferred.

the college will be indifferent when the volume is 340, 000

Explanation:

When deciding which option to choose, the college of business need to consider that the cost is divided into two: fixed and variable costs.

Fixed costs: Fixed costs are the costs that do no change regardless of the number of copies that will be made. In this instance, fixed costs are the Lease value for option 1 and the cost price of the machine for the second option.

Variable Costs: Variable costs are the costs that will vary depending n the number of copies that will be made. In this instance, variable costs will be the total cost of making copies (per sheet cost x number of copies made)

Option 1: to lease the machine

Fixed cost = $8, 400

Variable cost (@270, 000 copies) = $0.01 x 270, 000 = $2, 700

Total cost = $11, 100

Option 2: to purchase the machine

Fixed cost = $5, 000

Variable cost (@270, 000 copies) = $0.02 x 270, 000 = $5, 400

Total cost = $10, 400

Between option 1 and Option 2, at 270, 000 copies, option 2 is preferred as it has a lesser cost.

Option 1: to lease the machine

Fixed cost = $8, 400

Variable cost (@240, 000 copies) = $0.01 x 240, 000 = $2, 400

Total cost = $10, 800

Option 2: to purchase the machine

Fixed cost = $5, 000

Variable cost (@240, 000 copies) = $0.02 x 240, 000 = $4, 800

Total cost = $9, 800

Between option 1 and Option 2, at 270, 000 copies, option 2 is preferred as it has a lesser total cost.

Now we need to determine at which volume will the college be indifferent between the two option, i.e. when the costs that will be incurred for Option 1 are equal to the costs that will be incurred for Option 2

$8, 400 + 0.01x = $5, 000 + 0.02x  

$8, 400 - $5, 000 = 0.02x – 0.01x

$3, 400 = 0.01x

$340, 000 = x

The college will be indifferent between the 2 options when the volume is 340, 000 copies.  

Proof:  

Option 1: $8, 400 + [0.01 x 340, 000] = $11, 800

Option 2: $5, 000 + [0.02 x 340, 000] = $11, 800

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