Let’s analyze the problem and calculate the Equivalent Uniform Annual Cost (EUAC) for both alternatives:

Step 1: Key Information

For keeping the vehicle:

• Initial upgrade cost: $5,300
• Operating cost: $1,500/year (for 6 years)
• Salvage value at the end of 6 years: $3,900
• MARR: 12%
• Time period: 6 years

For leasing a vehicle:

• Trade-in value: $9,400
• Lease cost due at signing: $4,600
• Operating and leasing cost: $3,100/year (for 6 years)
• No salvage value is mentioned.
• MARR: 12%
• Time period: 6 years

We will compute the EUAC for each option separately, using the formula:

$EUAC = \text{Capital Recovery Cost} + \text{Annual Operating Cost}$

Where:

1. Capital Recovery Cost (CRC) accounts for initial costs and salvage value: $CRC = P \cdot (A/P, i, n) - F \cdot (A/F, i, n)$
   • $P$: Initial cost
   • $F$: Salvage value
   • $i$: MARR (12% = 0.12)
   • $n$: Time period (6 years)
2. $A/P$, $A/F$ are the Present Worth (P) and Future Worth (F) factors, respectively.

Step 2: EUAC for Keeping the Vehicle

Capital Recovery Cost for keeping:

1. $P = 5,300$, $F = 3,900$, $i = 0.12$, $n = 6$
2. Use $A/P$ and $A/F$ factors from the TVM table for $i = 12\%$, $n = 6$:
   • $A/P = 0.243225$
   • $A/F = 0.112166$

$CRC_{\text{keep}} = 5,300 \cdot 0.243225 - 3,900 \cdot 0.112166$

$CRC_{\text{keep}} = 1,289.09 - 437.45 = 851.64$

Annual Operating Cost:

• Operating cost = $1,500/year$

$EUAC_{\text{keep}} = 851.64 + 1,500 = 2,351.64$

Step 3: EUAC for Leasing the Vehicle

Capital Recovery Cost for leasing:

1. $P = 4,600$, $F = 0$, $i = 0.12$, $n = 6$
2. Use $A/P$ factor for $i = 12\%$, $n = 6$:
   • $A/P = 0.243225$

$CRC_{\text{lease}} = 4,600 \cdot 0.243225$

$CRC_{\text{lease}} = 1,118.83$

Annual Operating Cost:

• Operating cost = $3,100/year$

$EUAC_{\text{lease}} = 1,118.83 + 3,100 = 4,218.83$

Step 4: Final Recommendation

• EUAC(keep): $2,352
• EUAC(lease): $4,219

Since the EUAC for keeping the vehicle is significantly lower, the independent contractor should keep the vehicle.

Would you like detailed explanations or additional clarifications?

Here are five related questions to expand your understanding:

1. How are time value of money factors like $A/P$ and $A/F$ derived mathematically?
2. What is the significance of the MARR in project evaluation?
3. Can this method be used for longer-term decisions, such as 10 or 15 years?
4. How do changes in MARR affect the EUAC values for both alternatives?
5. What other metrics (besides EUAC) could be used to compare alternatives?

Tip: Always double-check TVM factor values from a reliable source, as rounding can slightly influence results.