An automobile company is planning to convert a plant from manufacturing economy cars to manufacturing sports cars. The initial cost for equipment conversion will be $200 million with a 20% salvage value anytime within a 5-year period. The cost of producing a car will be $21,000, and it will be sold for $33,000. The production capacity for the first year will be 4,000 units. At an interest rate of 12% per year, by what uniform amount will production have to increase each year for the next 4 years to achieve a breakeven point?

The company will need to produce each sports car at a uniform amount of $28,914.12 to cover the conversion cost and generate a 12% return on investment.

Explanation:

To calculate the uniform amount the company needs to produce each sports car, we can use the concept of Present Value (PV) and the Uniform Series formula.

Calculate the present value of the conversion cost. The initial cost for equipment conversion is $200 million, and it has a 20% salvage value within a 5-year period. Using the salvage value, we can calculate the present value of the conversion cost:

PV = Initial Cost - Salvage Value = $200 million - ($200 million * 20%) = $160 million.

Calculate the annual revenue and costs. The company plans to produce 4,000 sports cars in the first year, each sold for $33,000, with a production cost of $21,000 per car.

Annual Revenue = 4,000 cars * $33,000 = $132 million.

Annual Cost = 4,000 cars * $21,000 = $84 million.

Calculate the required uniform amount. We need to find the uniform amount that, when compounded at an interest rate of 12% per year for 5 years, equals the difference between annual revenue and annual cost, while also covering the present value of the conversion cost:

Uniform Amount = (PV + Annual Cost - Annual Revenue) / [(1 - (1 + r)^(-n)) / r],

where r is the interest rate (0.12) and n is the number of years (5).

Uniform Amount = ($160 million + $84 million - $132 million) / [(1 - (1 + 0.12)^(-5)) / 0.12] ≈ $28,914.12.

Therefore, the company will need to produce each sports car at a uniform amount of $28,914.12 to cover the conversion cost and generate a 12% return on investment.

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