To find the future worth (FW) of the palletizer project, we need to calculate the future worth of the initial investment, the operating and maintenance costs, and the salvage value. Here’s a breakdown of the calculation:

1. Future Worth of the Initial Investment

The initial cost is $140,855, and this cost will grow over 30 years at an interest rate of 8%. We can use the formula for future worth of a single sum:

$FW_{\text{initial}} = P (1 + i)^n$

where:

• $P = 140,855$ (initial investment),
• $i = 0.08$ (interest rate),
• $n = 30$ (number of years).

$FW_{\text{initial}} = 140,855 \times (1 + 0.08)^{30}$

2. Future Worth of Operating and Maintenance Costs

Since the operating and maintenance costs occur annually, we use the future worth of a uniform series formula:

$FW_{\text{O\&M}} = A \times \frac{(1 + i)^n - 1}{i}$

where:

• $A = 13,484$ (annual cost),
• $i = 0.08$,
• $n = 30$.

$FW_{\text{O\&M}} = 13,484 \times \frac{(1 + 0.08)^{30} - 1}{0.08}$

3. Future Worth of Salvage Value

The salvage value is $70,966, which occurs at the end of 30 years. Therefore, it remains the same as the future worth at that point:

$FW_{\text{salvage}} = 70,966$

Total Future Worth

The total future worth of the project is the sum of the future worth of the initial investment, the future worth of the operating and maintenance costs, and the future worth of the salvage value:

$FW_{\text{total}} = FW_{\text{initial}} + FW_{\text{O\&M}} + FW_{\text{salvage}}$

Now, let's compute each part.The future worth of the palletizer project is 3,015,852.35.

Would you like further clarification or additional details? Here are five related questions to extend your understanding:

1. How does the interest rate affect the future worth calculation?
2. What is the significance of net salvage value in future worth analysis?
3. How would the future worth change if the operating costs increased annually?
4. Can this future worth method be applied to other project investment evaluations?
5. What would be the effect of using a different interest rate, say 10% instead of 8%?

Tip: Always break down complex financial problems into smaller parts, like calculating individual future values for initial costs, recurring costs, and final values (e.g., salvage). This helps ensure accuracy.