Question

A manufacturing firm is considering two models of lathes. Model A will have an initial cost of $29,000, an operating cost of $2750, and a salvage value of $6500 after 6 years. Model B will have an initial cost of $36,500, an operating cost of $2200, and a $7750 resale value after 12 years. At an interest rate of 10% per year, which model should the consulting firm buy? You can use a study period of 12 years.

Answer 1

To determine which lathe model is more cost-effective, we calculate the Present Worth or NPV for both models, considering their respective costs, lifecycle, and 12-year period at an interest rate of 10% per year.

Step-by-step explanation:

The manufacturing firm must decide between two models of lathes to achieve cost-efficiency. Model A and Model B have different initial costs, operating costs, and salvage values to consider, especially with a study period of 12 years and an interest rate of 10% per year. The decision should be based on the calculation of the Present Worth or Net Present Value (NPV) for both options to determine which model results in lower costs over the study period.

To calculate the Present Worth or NPV, the initial cost, annual operating costs, and salvage value at the end of the study period should be considered. For Model A, since it only has a life of 6 years, it would need to be replaced halfway through the 12-year study period, incurring an additional initial cost. In contrast, Model B would last the entire 12 years without replacement. By discounting all costs back to their present values and comparing the totals, it will be clear which model is more cost-effective over 12 years.

Answer 2

To determine which model the consulting firm should buy, calculate the present value of costs and salvage values for each model. Model A has a total cost of $44039.57, while Model B has a total cost of $53709.61. Therefore, the firm should buy Model A.

Step-by-step explanation:

To determine which model the consulting firm should buy, we need to calculate the present value of the costs and salvage values for each model.

For Model A:

1. Calculate the present value of the operating cost using the formula PV = PMT x (1 - (1 + r)⁻ⁿ) / r, where PMT is the annual operating cost, r is the interest rate, and n is the number of years. PV = $2750 x (1 - (1 + 0.10)⁻⁶) / 0.10 = $11637.08.
2. Calculate the present value of the salvage value using the formula PV = FV / (1 + r)ⁿ, where FV is the salvage value, r is the interest rate, and n is the number of years. PV = $6500 / (1 + 0.10)⁶ = $3402.49.
3. Add the initial cost, operating cost present value, and salvage value present value to get the total cost of Model A: $29000 + $11637.08 + $3402.49 = $44039.57.

For Model B:

1. Calculate the present value of the operating cost using the formula PV = PMT x (1 - (1 + r)⁻ⁿ) / r, where PMT is the annual operating cost, r is the interest rate, and n is the number of years. PV = $2200 x (1 - (1 + 0.10)⁻¹²) / 0.10 = $14523.68.
2. Calculate the present value of the salvage value using the formula PV = FV / (1 + r)ⁿ, where FV is the salvage value, r is the interest rate, and n is the number of years. PV = $7750 / (1 + 0.10)¹² = $2685.93.
3. Add the initial cost, operating cost present value, and salvage value present value to get the total cost of Model B: $36500 + $14523.68 + $2685.93 = $53709.61.

Comparing the total costs, the consulting firm should buy Model A as it has a lower total cost of $44039.57 compared to Model B's total cost of $53709.61.