Thank you for visiting Capital Recovery Cost 1 Ten years ago Johnson Recovery purchased a wrecker for 330 000 to move disabled 18 wheelers He received a salvage value. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
A. Johnson has not recovered his investment at a 12% per year return.
B. The average equivalent benefit/cost per vehicle moved is $240.
C. The annual equivalent worth at 12% per year, considering the increasing O&M costs, is approximately $49,107.14 in the first year.
How did we get these values?
a) To determine if Johnson has recovered his investment at a 12% per year return, we need to calculate the Capital Recovery cost and compare it to the Annual Equivalent Value (AEV) of the benefits.
The Capital Recovery cost can be calculated using the formula:
Capital Recovery cost = Initial cost - Salvage value
Capital Recovery cost = $330,000 - $25,000
Capital Recovery cost = $305,000
The AEV of the benefits can be calculated using the formula:
AEV = Annual revenue - Annual operating and maintenance cost
Given that the average annual revenue is $60,000 and there are no operating and maintenance costs mentioned yet, we can calculate the AEV without considering those costs initially.
AEV = $60,000
To determine if the AEV exceeds the Capital Recovery cost at a 12% per year return, we can compare the AEV to the Capital Recovery cost by discounting the AEV to present value using the interest rate of 12% over a 10-year period.
Present Value = AEV / (1 + interest rate)^number of years
Present Value = $60,000 / (1 + 0.12)¹â°
Present Value = $60,000 / (1.12)¹â°
Present Value = $60,000 / 1.5723
Present Value ≈ $38,103.66
Since the present value of the AEV is less than the Capital Recovery cost ($38,103.66 < $305,000), Johnson has not recovered his investment at a 12% per year return.
b) To calculate the average equivalent benefit/cost per vehicle moved, we need to consider the number of disabled 18-wheelers moved per year.
Average equivalent benefit/cost per vehicle moved = AEV / Number of vehicles moved per year
Given that Johnson moves, on average, 250 disabled 18-wheelers each year and the AEV is $60,000 (as calculated in part a), we can calculate the average equivalent benefit/cost per vehicle moved:
Average equivalent benefit/cost per vehicle moved = $60,000 / 250
Average equivalent benefit/cost per vehicle moved = $240
Therefore, the average equivalent benefit/cost per vehicle moved is $240.
c) Now let's incorporate annual operating and maintenance costs into the analysis. If the annual operating and maintenance cost was $5,000 in the first year and increased by a constant 10% per year, we need to calculate the AEV considering these costs.
To calculate the AEV, we subtract the annual operating and maintenance cost from the annual revenue and discount it to present value using a 12% interest rate.
AEV = (Annual revenue - Annual operating and maintenance cost) / (1 + interest rate)^number of years
In this case, we need to consider the increasing O&M costs over the 10-year period.
Year 1:
AEV = ($60,000 - $5,000) / (1 + 0.12)^1
AEV = $55,000 / 1.12
AEV ≈ $49,107.14
Year 2:
AEV = ($60,000 - $5,000 × 1.1) / (1 + 0.12)^2
AEV = ($60,000 - $5,500) / 1.2544
AEV ≈ $45,822.21
Similarly, we can calculate the AEV for the remaining years. However, since the question only asks for the AEV at a 12% per year rate, we don't need to calculate all the years.
Therefore, the annual equivalent worth at 12% per year, considering the increasing O&M costs, is approximately $49,107.14 in the first year.
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