AACE CCP Full Course Free

Given that the average life span of the lithium battery is 24 months with a standard deviation of 2 months, we need to calculate the probability that the battery will last between 20 and 26 months.

Using the Z-score formula:

Z=X−μσZ = \frac{X - \mu}{\sigma}Z=σX−μ​

For 20 months: Z=20−242=−2Z = \frac{20 - 24}{2} = -2Z=220−24​=−2

For 26 months: Z=26−242=1Z = \frac{26 - 24}{2} = 1Z=226−24​=1

Looking up these Z-scores in the standard normal distribution table:

Z = -2 corresponds to approximately 2.28%

Z = 1 corresponds to approximately 84.13%

The probability that the battery will last between 20 and 26 months is approximately84%.

Thelearning curvedescribes the phenomenon where productivity increases with time as workers become more experienced and efficient in their tasks. This improvement is often associated with repetitive tasks where increased familiarity leads to greater speed and reduced errors, thereby enhancing overall productivity. The learning curve is a fundamental concept in project management and operations, as it predicts how labor efficiency improves as a function of cumulative production or time spent on a task. It is an important factor in cost estimation and scheduling as it can lead to reduced labor costs and shorter project timelines.

In a construction company, profitability analysis typically involves calculating theReturn on Investment (ROI)andRate of Return (ROR). ROI measures the profitability of an investment by comparing the gain from the investment to its cost, while ROR calculates the percentage return on each dollar invested. These metrics are critical in determining the financial performance and efficiency of investments in the construction industry.

To calculate the 25-year after-tax present worth of this project, we need to consider the income, expenses, depreciation, and taxes.

First, calculate the annual depreciation:

Depreciation=Initial CostLife=80,00025=3,200\text{Depreciation} = \frac{\text{Initial Cost}}{\text{Life}} = \frac{80,000}{25} = 3,200Depreciation=LifeInitial Cost​=2580,000​=3,200

Now, calculate the taxable income each year:

Taxable Income=Revenue−Expenses−Depreciation=22,500−12,000−3,200=7,300\text{Taxable Income} = \text{Revenue} - \text{Expenses} - \text{Depreciation} = 22,500 - 12,000 - 3,200 = 7,300Taxable Income=Revenue−Expenses−Depreciation=22,500−12,000−3,200=7,300

Calculate the tax:

Tax=Taxable Income×Tax Rate=7,300×0.53=3,869\text{Tax} = \text{Taxable Income} \times \text{Tax Rate} = 7,300 \times 0.53 = 3,869Tax=Taxable Income×Tax Rate=7,300×0.53=3,869

Net income after tax:

Net Income=Taxable Income−Tax=7,300−3,869=3,431\text{Net Income} = \text{Taxable Income} - \text{Tax} = 7,300 - 3,869 = 3,431Net Income=Taxable Income−Tax=7,300−3,869=3,431

Add back depreciation (since it’s a non-cash expense):

Cash Flow=3,431+3,200=6,631\text{Cash Flow} = 3,431 + 3,200 = 6,631Cash Flow=3,431+3,200=6,631

Finally, calculate the present worth using the formula for the present worth of an annuity:

Present Worth=6,631×(1−(1+0.10)−250.10)≈137,466\text{Present Worth} = 6,631 \times \left(\frac{1-(1+0.10)^{-25}}{0.10}\right) \approx 137,466Present Worth=6,631×(0.101−(1+0.10)−25​)≈137,466

So, the correct answer isB. $137,466.