Net Present Value of Purchasing Equipment | CFA Level 1 Exam | Test Prep

Net Present Value of Purchasing Equipment

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Pierce Products is deciding whether it makes sense to purchase a new piece of equipment. The equipment costs $100,000 (payable at t = 0). The equipment will provide before-tax cash inflows of $45,000 a year at the end of each of the next four years (t = 1, 2, 3, 4). The equipment can be depreciated according to the following schedule: t = 1: 0.33 t = 2: 0.45 t = 3: 0.15 t = 4: 0.07 At the end of four years the company expects to be able to sell the equipment for a salvage value of $10,000 (after-tax). The company is in the 40 percent tax bracket. The company has an after-tax cost of capital of 11 percent. Since there is more uncertainty about the salvage value, the company has chosen to discount the salvage value at 12 percent. What is the net present value of purchasing the equipment?

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A

First, find the after-tax CFs associated with the project. This is accomplished by subtracting the depreciation expense from the raw CF, reducing this net CF by taxes and then adding back the depreciation expense.

For t = 1: ($45,000 - $33,000)(1 - 0.4) + $33,000 = $40,200.

Similarly, the after-tax CFs for t = 2, t = 3, and t = 4 are $45,000, $33,000, and $29,800, respectively.

Now, enter these CFs along with the cost of the equipment to find the pre-salvage NPV (note that the salvage value is not yet accounted for in these CFs). The appropriate discount rate for these CFs is 11%. This yields a pre-salvage NPV of $16,498.72. Finally, the salvage value must be discounted. The PV of the salvage value is: N = 4, I = 12, PMT = 0, FV = -10,000, and PV = $6,355.18. Adding the PV of the salvage amount to the pre-salvage NPV yields the project NPV of $22,853.90.

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