A hamburger factory produces 40,000 hamburgers each week. The equipment used costs $5,000 and will remain productive for 4 years. The labor cost per year is $9,500. a. What is the productivity measure of “units of output per dollar of input” averaged over the 3-year period? b. We have the option of $10,000 equipment, with an operating life of 5 years. It would reduce labor costs to $6,000 per year. Should we consider purchasing this equipment (using productivity arguments alone)?
The correct answer and explanation is :
Solution:
Let’s break this into two parts:
a. Current Productivity Measure
Given:
- Output: 40,000 hamburgers/week
- Weeks/year: 52
- Total hamburgers/year = 40,000 × 52 = 2,080,000 hamburgers/year
- Equipment cost: \$5,000 (used over 4 years → annualized = 5,000 / 4 = \$1,250/year)
- Labor cost/year = \$9,500
- Time period = 3 years
Total Input Cost over 3 years =
= 3 × (\$1,250 + \$9,500) = 3 × \$10,750 = \$32,250
Total Output over 3 years =
= 3 × 2,080,000 = 6,240,000 hamburgers
Productivity = Output / Input =
= 6,240,000 / 32,250 ≈ 193.48 hamburgers per dollar
b. New Equipment Option
New Equipment Cost = \$10,000 (5-year life → annualized = 10,000 / 5 = \$2,000/year)
Labor cost/year = \$6,000
Time period = 3 years
Total Input Cost over 3 years =
= 3 × (\$2,000 + \$6,000) = 3 × \$8,000 = \$24,000
Total Output = Same as before = 6,240,000 hamburgers
New Productivity =
= 6,240,000 / 24,000 = 260 hamburgers per dollar
Conclusion & Explanation (Approx. 300 Words)
Productivity is a key performance metric that measures the efficiency of input use in producing output. In this scenario, the productivity is expressed as the number of hamburgers produced per dollar spent on inputs over a 3-year period.
For the current system, using the \$5,000 equipment with higher annual labor costs of \$9,500 results in a total 3-year input cost of \$32,250. This leads to a productivity of approximately 193.48 hamburgers per dollar.
However, the proposed equipment, though more expensive upfront at \$10,000, is more efficient in the long term with a 5-year life and significantly lower labor costs (\$6,000 per year). Over the same 3-year period, this results in a lower total input cost of \$24,000 and a higher productivity of 260 hamburgers per dollar.
From a purely productivity-based perspective, the new equipment is a better investment. It offers approximately 34% higher productivity compared to the current setup (260 vs. 193.48). This means each dollar invested in the new system yields more output, reducing operational inefficiencies and cost per unit.
Therefore, based on productivity arguments alone, it is advisable to consider purchasing the new equipment, as it provides better output per dollar and could lead to greater profitability and operational efficiency in the long run.