Final answer:
The breakeven point, without considering the interest rate, for the company to recover the extra initial cost of the automated system over hand tools with an annual volume of 5000 units, is approximately 1.93 years.
Step-by-step explanation:
To calculate the breakeven point for the company considering the two manufacturing scenarios, we need to compare the total cost of each method and find out when they are equal. The breakeven point will tell us when the investment in the automated system begins to pay off over the use of hand tools.
For the hand tools approach, the initial cost is $1000, and the cost per unit is $1.50. Over one year, with an annual volume of 5000 units, the total cost would be:
Initial Hand Tools Cost + (Annual Volume × Cost per Unit with Hand Tools)
$1000 + (5000 × $1.50) = $8500
For the automated system, the initial cost is $15000, and the cost per unit is $0.05. The total cost over one year would be:
Initial Automated System Cost + (Annual Volume × Cost per Unit with Automated System)
$15000 + (5000 × $0.05) = $15250
The difference in total cost after one year is $15250 - $8500 = $6750. To find out when the savings in unit cost with the automated system will cover the initial extra cost, we divide the extra initial cost by the annual savings:
$15000 - $1000 = $14000 (Extra initial cost)
The savings per unit is $1.50 - $0.05 = $1.45
Annual savings is 5000 units × $1.45 = $7250
Breakeven point in years = $14000 / $7250 = approximately 1.93 years
Considering a 10% interest rate, the value of money changes every year. To include this in our calculation, we would need to calculate the present value of the annual savings over the years and determine when it equals the initial cost difference. This requires a more complex financial analysis, like Net Present Value (NPV) or Internal Rate of Return (IRR), which is not performed here.