Christina Company will purchase a van for $40,000.It will have a depreciable life of 5 years and a terminal salvage value of $10,000.Assume a tax rate of 20% and a required after-tax rate of return of 12%.The company uses straight-line depreciation for tax purposes.The annual cash operating savings at the end of each year,exclusive of depreciation,are $10,000 for five years.The present value of one for five periods at 12% is 0.5674.The present value of an ordinary annuity of one for five periods at 12% is 3.6048.What is the net present value of the van?

Question

Quizplus · Accepted Answer

The net present value (NPV) of the van can be calculated by considering the initial investment, the annual cash flows (adjusted for taxes), the tax shield from depreciation, and the salvage value. The calculation is as follows:1. Initial investment: -$40,0002. Annual cash operating savings: $10,000 for five years. These savings are before tax, so they need to be adjusted for the tax rate of 20%. The after-tax savings are $10,000 * (1 - 0.20) = $8,000.3. Present value of the after-tax savings: $8,000 * 3.6048 (present value of an ordinary annuity of one for five periods at 12%) = $28,838.44. Depreciation expense per year: ($40,000 - $10,000) / 5 = $6,000. The tax shield from depreciation is $6,000 * 0.20 (tax rate) = $1,200 per year.5. Present value of the tax shield from depreciation: $1,200 * 3.6048 = $4,325.766. Salvage value after 5 years is $10,000, which needs to be adjusted for taxes since it will reduce the depreciation base. However, for simplicity and because the question does not specify otherwise, we'll consider its present value directly without tax adjustment. Present value of the salvage value: $10,000 * 0.5674 = $5,6747. NPV = Initial investment + Present value of after-tax savings + Present value of tax shield from depreciation + Present value of salvage value = -$40,000 + $28,838.4 + $4,325.76 + $5,674 = -$1,161.84Rounding to the nearest dollar, the NPV is approximately -$1,162, which corresponds to choice B.

Christina Company Will Purchase a Van for $40,000