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CPD CO. produces a product using an expensive proprietary machine that can onlybe leased. The leasing company offers two contracts. The first (unit-rate lease) is onewhere CPD would pay $4 per unit produced, regardless of the number of productionunits. The second lease option (flat-rate lease) is one where CPD would pay $60,000per month, regardless of the number produced. The lease will run one year, and thelease option chosen cannot be changed during the year. All other lease terms are thesame.The product sells for $35 per unit and unit variable cost (excluding any machine leasecosts) are $17. Monthly fixed costs (excluding any machine lease costs) are $205,000.The sales volume is the same as the production volume. At what volume would theoperating profit be the same regardless of the lease option chosen?A. 13000 unitsB. 10000 unitsC. 12500 unitsD. 15000 units

Question

CPD CO. produces a product using an expensive proprietary machine that can onlybe leased. The leasing company offers two contracts. The first (unit-rate lease) is onewhere CPD would pay 4perunitproduced,regardlessofthenumberofproductionunits.Thesecondleaseoption(flatratelease)isonewhereCPDwouldpay4 per unit produced, regardless of the number of productionunits. The second lease option (flat-rate lease) is one where CPD would pay 60,000per month, regardless of the number produced. The lease will run one year, and thelease option chosen cannot be changed during the year. All other lease terms are thesame.The product sells for 35perunitandunitvariablecost(excludinganymachineleasecosts)are35 per unit and unit variable cost (excluding any machine leasecosts) are 17. Monthly fixed costs (excluding any machine lease costs) are $205,000.The sales volume is the same as the production volume. At what volume would theoperating profit be the same regardless of the lease option chosen?A. 13000 unitsB. 10000 unitsC. 12500 unitsD. 15000 units

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Solution

To find the volume at which the operating profit would be the same regardless of the lease option chosen, we need to set the total cost for both lease options equal to each other and solve for the volume.

Let's denote the volume as X.

For the unit-rate lease, the total cost is the sum of the variable costs, fixed costs, and the lease cost per unit. This can be expressed as:

Total Cost (unit-rate) = 17X(variablecost)+17X (variable cost) + 205,000 (fixed cost) + $4X (lease cost)

For the flat-rate lease, the total cost is the sum of the variable costs, fixed costs, and the flat lease cost. This can be expressed as:

Total Cost (flat-rate) = 17X(variablecost)+17X (variable cost) + 205,000 (fixed cost) + $60,000 (lease cost)

Setting these two equations equal to each other gives us:

17X+17X + 205,000 + 4X=4X = 17X + 205,000+205,000 + 60,000

Solving for X gives us:

4X=4X = 60,000

X = 60,000/60,000 / 4

X = 15,000 units

So, the operating profit would be the same regardless of the lease option chosen at a volume of 15,000 units. Therefore, the correct answer is D. 15000 units.

This problem has been solved

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