To solve this problem, we need to calculate the future worth (FW) of each machine, considering all relevant costs and the corporate Minimum Attractive Rate of Return (MARR) of 15% per year.

We'll use the formula for the future worth of cash flows:

$\text{FW} = \text{First Cost} \times (F/P, 15\%, n) + \text{AOC} \times (F/A, 15\%, n) + \text{Salvage Value} \times (F/F, 15\%, n)$

Where:

• $F/P$ is the future worth factor for a single payment at the present
• $F/A$ is the future worth factor for a uniform series of payments (AOC in this case)
• $F/F$ is the future worth factor for a future payment (Salvage value in this case)

The factors can be calculated from standard future worth factor tables or formulas. Let’s calculate for each machine.

Machine D (4 years life)

Given:

• First cost: −84,000
• AOC: −18,000
• Salvage value: 8,000
• Life: 4 years

1. First cost: $\text{FW of First Cost} = -84,000 \times (F/P, 15\%, 4)$
2. AOC (Annual Operating Cost): $\text{FW of AOC} = -18,000 \times (F/A, 15\%, 4)$
3. Salvage value: $\text{FW of Salvage Value} = 8,000 \times (F/F, 15\%, 4)$

Machine E (6 years life)

Given:

• First cost: −94,000
• AOC: −21,000
• Salvage value: 10,000
• Life: 6 years

1. First cost: $\text{FW of First Cost} = -94,000 \times (F/P, 15\%, 6)$
2. AOC (Annual Operating Cost): $\text{FW of AOC} = -21,000 \times (F/A, 15\%, 6)$
3. Salvage value: $\text{FW of Salvage Value} = 10,000 \times (F/F, 15\%, 6)$

Let me now calculate these values based on the future worth factors.The future worth (FW) values for the two machines are:

• Future worth of Machine D: $−228,797.27
• Future worth of Machine E: $−391,256.22

Based on the future worth analysis, Machine D has a higher (less negative) future worth, making it the better choice financially compared to Machine E.

Would you like to explore further details or have any questions?

Here are 5 related questions you could explore:

1. How does changing the MARR affect the future worth analysis?
2. What is the impact of increasing the salvage value on future worth?
3. How would a shorter or longer machine life affect future worth?
4. How would inflation impact these future worth calculations?
5. What are the advantages of using future worth analysis over present worth analysis?

Tip: Always compare machines over the same time frame; use equivalent annual cost (EAC) for machines with different lives.