Final answer:
To calculate the PW of the base case, we need to determine the net cash flow for each year and find the present worth using the discount factor. The overall PW is the sum of all the present worth values.
Step-by-step explanation:
To calculate the present worth (PW) of the base case, we need to determine the net cash flow for each year. The net cash flow is calculated by subtracting the annual maintenance and operating cost from the annual revenue. Then, each net cash flow is divided by the appropriate discount factor to determine its present worth. The discount factor is calculated using the formula: (1 + MARR) ^ (-n), where MARR is the minimum attractive rate of return and n is the year. Finally, the present worth of each year is summed up to find the overall present worth of the base case.
Let's perform the calculations step by step:
- Year 1: Net cash flow = Revenue - Maintenance cost - Operating cost = $4,000,000 - $1,200,000 = $2,800,000
Discount factor = (1 + 0.18) ^ (-1) = 0.8475
Present worth = Net cash flow / Discount factor = $2,800,000 / 0.8475 = $3,301,839.08 - Year 2: Net cash flow = Revenue - Maintenance cost - Operating cost = $4,000,000 - $1,200,000 = $2,800,000
Discount factor = (1 + 0.18) ^ (-2) = 0.7172
Present worth = Net cash flow / Discount factor = $2,800,000 / 0.7172 = $3,899,182.66 - Repeat the above steps for the remaining years.
- Year 10: Net cash flow = Revenue - Maintenance cost - Operating cost = $4,000,000 - $1,200,000 = $2,800,000
Discount factor = (1 + 0.18) ^ (-10) = 0.2384
Present worth = Net cash flow / Discount factor = $2,800,000 / 0.2384 = $11,737,704.92
Finally, sum up the present worths of all the years to find the overall present worth of the base case:
$3,301,839.08 + $3,899,182.66 + ... + $11,737,704.92 = $41,705,591.81