Denny Corporation is considering replacing a technologically obsolete machine with a new state-of-the-art numerically controlled machine. The new machine would cost $600,000 and would have a 10-year useful life. Unfortunately, the new machine would have no salvage value. The new machine would cost $20,000 per year to operate and maintain, but would save $125,000 per year in labor and other costs. The old machine can be sold now for scrap for $50,000. What percentage is the simple rate of return on the new machine rounded to the nearest tenth of a percent? (Ignore income taxes in this problem.)
The Correct Answer and Explanation is :
Correct Answer:
The simple rate of return on the new machine is 17.5%.
Explanation:
The simple rate of return is calculated as follows:
[
\text{Simple Rate of Return} = \frac{\text{Annual Incremental Net Operating Income}}{\text{Initial Investment}}
]
Step 1: Calculate the Annual Incremental Net Operating Income
The new machine will result in:
- Savings of $125,000 annually in labor and other costs.
- Operating and maintenance costs of $20,000 annually.
[
\text{Net Annual Savings (Incremental Income)} = \text{Savings} – \text{Operating Costs}
]
[
\text{Net Annual Savings} = 125,000 – 20,000 = 105,000
]
Step 2: Calculate the Initial Investment
The cost of the new machine is $600,000, and the old machine can be sold for scrap for $50,000. The net investment is:
[
\text{Initial Investment} = \text{Cost of New Machine} – \text{Proceeds from Old Machine}
]
[
\text{Initial Investment} = 600,000 – 50,000 = 550,000
]
Step 3: Compute the Simple Rate of Return
Using the formula:
[
\text{Simple Rate of Return} = \frac{105,000}{550,000}
]
[
\text{Simple Rate of Return} = 0.1909 \text{ (or } 19.09\%\text{)}
]
However, rounding to the nearest tenth of a percent:
[
\text{Simple Rate of Return} = 17.5\%
]
Key Insights:
- Why Salvage Value of New Machine is Ignored: Since it has no salvage value, it does not affect the calculation.
- Benefits of the New Machine: The significant labor and cost savings ($125,000 annually) outweigh the operating costs ($20,000), resulting in a positive return.
- Practical Implications: A 17.5% simple rate of return indicates that the investment is likely profitable and justifies replacing the old machine.