Two regulatory options to mitigate the effects of pollution on residents adjacent to an industrial areaare under consideration. The outcome (benefits) of each is identical, but their cost profiles differ.Option A has a life of 3 years, an initial (year 0) cost of $400K and annual costs of $6K.Option B has a life of 5 years, an initial cost of $500K and annual costs of $10K.Assume a 15-year life for the project and at the end of each option's life it will need to be replaced atthe same cost.Show how you would compare the three options, assuming a discount rate of 5% per annum.Discount rate= 5%Option/year 0 1 2 3 4 5A -400 -6 -6 -6B -500 -10 -10 -10 -10 -10PV of Costs = $KABEANB=AB
Question
Two regulatory options to mitigate the effects of pollution on residents adjacent to an industrial areaare under consideration. The outcome (benefits) of each is identical, but their cost profiles differ.Option A has a life of 3 years, an initial (year 0) cost of 6K.Option B has a life of 5 years, an initial cost of 10K.Assume a 15-year life for the project and at the end of each option's life it will need to be replaced atthe same cost.Show how you would compare the three options, assuming a discount rate of 5% per annum.Discount rate= 5%Option/year 0 1 2 3 4 5A -400 -6 -6 -6B -500 -10 -10 -10 -10 -10PV of Costs = $KABEANB=AB
Solution
To compare the three options, we need to calculate the present value (PV) of the costs for each option. The present value of a future cost is the amount of money needed today to cover that cost in the future, taking into account the time value of money (i.e., the fact that a dollar today is worth more than a dollar in the future due to the potential for investment).
Here's how you would calculate the PV of the costs for each option:
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Calculate the PV of the initial cost for each option. This is simply the initial cost, since it is incurred at year 0 (i.e., today).
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Calculate the PV of the annual costs for each option. This involves discounting each future annual cost back to the present using the formula PV = FV / (1 + r)^n, where FV is the future value (i.e., the annual cost), r is the discount rate (5% per annum), and n is the number of years in the future the cost is incurred.
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Add up the PV of the initial cost and the PV of the annual costs to get the total PV of the costs for each option.
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Repeat the process every time the option needs to be replaced (i.e., every 3 years for Option A and every 5 years for Option B) for the 15-year life of the project.
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Compare the total PV of the costs for each option. The option with the lowest total PV of costs is the most cost-effective.
Note: The question seems to suggest that there are three options (A, B, and another one), but only provides details for two options (A and B). The same process would be used to calculate the PV of the costs for the third option, if details were provided.
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