Questions: Ridgley Custom Metal Products (RCMP) must purchase a new tube bender. RCMP's MARR is 12 percent. The company is considering three models: Model First Cost Economic Life Yearly Net Savings Salvage Value T 100,000 7 years 55,000 15,000 A 100,000 6 years 40,000 2,000 X 160,000 6 years 65,000 80,000 Using the annual worth method, which of the three tube benders should RCMP buy? The annual worth of Model T is . The annual worth of Model A is . The annual worth of Model X is . So, the Model is the better choice to buy. (Round to the nearest cent as needed.)

Solution Steps

To determine which tube bender RCMP should purchase, we will calculate the annual worth (AW) for each model. The annual worth is calculated using the formula:

\[ \text{AW} = \text{Yearly Net Savings} - \left(\text{First Cost} - \text{Salvage Value} \times \text{P/F factor}\right) \times \text{A/P factor} \]

Where:

• The P/F factor is the present worth factor for the salvage value at the end of the economic life.
• The A/P factor is the capital recovery factor for the first cost over the economic life.

We will use the given MARR of 12% to find these factors from the compound interest table.

The annual worth (AW) for Model T is calculated using the formula:

\[ \text{AW}_T = \text{Yearly Net Savings}_T - \left(\text{First Cost}_T - \text{Salvage Value}_T \times \text{P/F factor}\right) \times \text{A/P factor} \]

Substituting the values:

• First Cost \( = 100,000 \)
• Economic Life \( = 7 \)
• Yearly Net Savings \( = 55,000 \)
• Salvage Value \( = 15,000 \)

The calculated annual worth for Model T is:

\[ \text{AW}_T \approx 34,574.99 \]

The annual worth for Model A is calculated similarly:

\[ \text{AW}_A = \text{Yearly Net Savings}_A - \left(\text{First Cost}_A - \text{Salvage Value}_A \times \text{P/F factor}\right) \times \text{A/P factor} \]

Substituting the values:

• First Cost \( = 100,000 \)
• Economic Life \( = 6 \)
• Yearly Net Savings \( = 40,000 \)
• Salvage Value \( = 2,000 \)

The calculated annual worth for Model A is:

\[ \text{AW}_A \approx 15,923.88 \]

The annual worth for Model X is calculated as follows:

\[ \text{AW}_X = \text{Yearly Net Savings}_X - \left(\text{First Cost}_X - \text{Salvage Value}_X \times \text{P/F factor}\right) \times \text{A/P factor} \]

Substituting the values:

• First Cost \( = 160,000 \)
• Economic Life \( = 6 \)
• Yearly Net Savings \( = 65,000 \)
• Salvage Value \( = 80,000 \)

The calculated annual worth for Model X is:

\[ \text{AW}_X \approx 35,941.94 \]

Comparing the annual worths:

• \( \text{AW}_T \approx 34,574.99 \)
• \( \text{AW}_A \approx 15,923.88 \)
• \( \text{AW}_X \approx 35,941.94 \)

The model with the highest annual worth is Model X.

Final Answer