When businesses face the decision to invest in equipment or methods for manufacturing certain parts, they must consider various factors, including initial costs, annual operating expenses, salvage values, and the prevailing interest rate. In this scenario, we will evaluate two manufacturing alternatives: Method R and Method S, using both the present worth and annual worth comparison methods. The goal is to determine which alternative is the most financially viable option at an interest rate of 12% per year.
Method R has an initial cost of $40,000, an annual operating cost of $25,000, and a $10,000 salvage value after its five-year life. To calculate the present worth of Method R, we need to find the present value of both the initial cost and the annual operating costs over five years, considering the salvage value.
Initial Cost: $40,000
Annual Operating Cost: $25,000
Salvage Value: $10,000
Using the present worth formula:
PW(R) = Initial Cost – Annual Operating Cost * (P/A, 12%, 5) + Salvage Value * (P/F, 12%, 5)
PW(R) = $40,000 – $25,000 * (3.6048) + $10,000 * (0.5674) PW(R) = $40,000 – $90,120 + $5,674 PW(R) = -$44,446
Method S entails an initial cost of $100,000, an annual operating cost of $15,000 increasing by $600 each year, and a $13,000 salvage value after its 10-year life. To compute the present worth of Method S, we need to determine the present value of both the initial cost, the increasing annual operating costs, and the salvage value over ten years.
Present Worth of Method S:
Initial Cost: $100,000
Annual Operating Cost (Year 1): $15,000
Annual Operating Cost (Year 2): $15,600 (increasing by $600)
Salvage Value: $13,000
Using the present worth formula:
PW(S) = Initial Cost – Annual Operating Costs * (P/A, 12%, 10) + Salvage Value * (P/F, 12%, 10)
PW(S) = $100,000 – [$15,000 * (6.3522) + $15,600 * (5.6509)] + $13,000 * (0.322)
PW(S) = $100,000 – [$95,283 + $87,860] + $4,186 PW(S) = $100,000 – $183,143 + $4,186 PW(S) = -$78,957
Present Worth Comparison
The present worth of Method R is -$44,446, while the present worth of Method S is -$78,957. Since the goal is to minimize costs, Method R is the preferable option as it has a less negative present worth compared to Method S.
Annual Worth Comparison
To calculate the annual worth of each method, we can use the following formula:
AW = PW * (A/P, i, n)
For Method R: AW(R) = -$44,446 * (0.1625) AW(R) = -$7,236
For Method S: AW(S) = -$78,957 * (0.1625) AW(S) = -$12,846
In conclusion, when considering an interest rate of 12% per year, Method R is the economically superior choice for manufacturing the certain part, both in terms of present worth and annual worth. It is essential for businesses to carefully analyze such decisions, as they can significantly impact their financial performance over time.
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