Question

Tanaka Machine Shop is considering a four-year project to improve its production efficiency. Buying a new machine press for $405,000 is estimated to result in $157,000 in annual pretax cost savings. The press falls in the MACRS five-year class, and it will have a salvage value at the end of the project of $57,000. (MACRS schedule) The press also requires an initial investment in spare parts inventory of $24,000, along with an additional $3,300 in inventory for each succeeding year of the project. The shop’s tax rate is 24 percent and its discount rate is 11 percent. Calculate the NPV of this project. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Should the company buy and install the machine press?

Answer 1

The NPV of this project is $62,997.60. The company should buy and install the machine press.

Step-by-step explanation:

To calculate the NPV of the project, we need to determine the cash flows, discount them to the present value, and then subtract the initial investment. The cash flows consist of the annual pretax cost savings and the salvage value at the end of the project. To calculate the annual pretax cost savings, we subtract the annual inventory costs from the savings. The annual inventory costs are the initial inventory cost plus the additional inventory costs for each succeeding year. We can then calculate the net cash flow for each year by multiplying the annual pretax cost savings by (1-tax rate). After determining the net cash flows, we discount them to the present value using the discount rate. Finally, we subtract the initial investment to get the NPV.

Net Cash Flow = [(Annual Pretax Cost Savings - Annual Inventory Costs) - (Annual Pretax Cost Savings - Annual Inventory Costs) * Tax Rate]

Discounted Cash Flow = Net Cash Flow / (1 + Discount Rate)^(Year - 1)

NPV = Sum of Discounted Cash Flows - Initial Investment

Calculating the NPV of the project:

1. Year 1: Net Cash Flow = [($157,000 - $24,000) - ($157,000 - $27,300) * 0.24] = $126,870, Discounted Cash Flow = $126,870 / (1 + 0.11)^(1 - 1) = $126,870, NPV = $126,870 - $405,000 = $-278,130
2. Year 2: Net Cash Flow = [($157,000 - $27,300) - ($157,000 - $30,600) * 0.24] = $126,750, Discounted Cash Flow = $126,750 / (1 + 0.11)^(2 - 1) = $114,148.65, NPV = $114,148.65 - $0 = $114,148.65
3. Year 3: Net Cash Flow = [($157,000 - $30,600) - ($157,000 - $33,900) * 0.24] = $126,630, Discounted Cash Flow = $126,630 / (1 + 0.11)^(3 - 1) = $99,341.57, NPV = $99,341.57 - $0 = $99,341.57
4. Year 4: Net Cash Flow = [($157,000 - $33,900) - ($157,000 - $37,200) * 0.24] = $126,510, Discounted Cash Flow = $126,510 / (1 + 0.11)^(4 - 1) = $86,247.20, NPV = $86,247.20 - $0 = $86,247.20
5. Salvage Value: Net Cash Flow = $57,000 * (1 - 0.24) = $43,320, Discounted Cash Flow = $43,320 / (1 + 0.11)^(4 - 1) = $31,390.18, NPV = $31,390.18 - $0 = $31,390.18
6. NPV = Sum of Discounted Cash Flows - Initial Investment = ($126,870 + $114,148.65 + $99,341.57 + $86,247.20 + $31,390.18) - $405,000 = $62,997.60

The NPV of this project is $62,997.60. Since the NPV is greater than zero, the company should buy and install the machine press.