Question

A car manufacturer is considering one of two systems for its windshield assembly line.  

The first is a robotic system that should save money due to a reduction in labor and materials costs. The robotic system will cost $400,000, and requires 1 full-time technician and 1 full-time material handler will be needed with this system.  The full-time technician costs $60,000 per year and the material handler costs $52,000 per year.  The expectation is to recover the cost of the robotic system over the first two years.

The second option is to select the manual system. The manual system requires 4 full-time material handlers at a cost of $52,000 each per year.  If the manual system is selected, the company will incur additional costs of $0.50 per windshield installed.

Assume that only one windshield is installed per automobile.

1. How many automobiles are needed to be produced over the next two years to make the manufacturer indifferent economically between the two systems?  Ignore the time value money and assume that the entire cost of the robotic system will be recovered during the first two years.

Answer 1

To be calculated:

Number of automobiles to be produced in 2 years

Given values:

System 1

Robotic system cost = $400,000

Technician costs = $60,000 per year

Material handler cost = $52,000 per year

System 2

4 full-time material handlers = $52,000 each per year

Additional costs = $0.50 per windshield

Solution:

In order to be indifferent economically between the two systems, the cost of manufacturing should be equal for the two systems over the next two years.

For system 1, the total costs for the two years is calculated as;

= $400,000 + ($60,000 + $52,000) x 2 years

= $624,000

For system 2, the total costs for the two years is calculated as;

Let the number of windshields installed = W units

Total costs is given as;

= ($52,000 x 4 handlers x 2 years) + ($0.50 x W)

= $416,000 + 0.50W

To be indifferent economically between the two system, the total costs for the two systems should be equal.

$416,000 + 0.50W = $624,000

Solving for W;

W = ($624,000 - $416,000) / 0.50

W = 416,000

At 416,000 units of windshields, the costs of two systems will be equal.

The number of automobiles needed to be produced over the next two years to make the manufacturer indifferent economically between the two systems = 416,000 units