Confusing NPV Problem

  • Creator
    Topic
  • October 8, 2015 at 3:40 pm #197420
    Anonymous
    Inactive

    This problem is really confusing me. How was the $34,000 calculated for the tax savings in year 1-3? Thanks for your help.

    McLean, Inc., is considering the purchase of a new machine that will cost $150,000. The machine has an estimated useful life of three years. Assume for simplicity that the equipment will be fully depreciated 30, 40, and 30% in each of the three years, respectively. The new machine will have a $10,000 resale value at the end of its estimated useful life. The machine is expected to save the company $85,000 per year in operating expenses. McLean uses a 40% estimated income tax rate and a 16% hurdle rate to evaluate capital projects.

    Discount rates for a 16% rate are as follows.

    Present Value of $1 Ordinary Annuity of $1

    Year 1 0.8621 0.8621

    Year 2 0.7432 1.6052

    Year 3 0.6407 2.2459

    What is the net present value of this project?

    A.

    $15,842

    B.

    $13,278

    C.

    $9,432

    D.

    $(35,454)

    You did not answer the question. The correct answer is B.

    To determine the net present value of this project, set up an analysis of cash flows as follows:

    Annual Annual Annual Annual

    Before Tax Tax Aftertax Aftertax

    Cash Flows Savings Cash Flow Net Income

    Investment Year 0 (150,000) 0 (150,000) 0

    Annual cash savings Year 1-3 85,000 (34,000) 51,000 51,000

    Depreciation effect Year 1 18,000 18,000 (27,000)*

    Year 2 24,000 24,000 (36,000)**

    Year 3 18,000 18,000 (27,000)*

    Gain on Disposal Year 3 10,000 (4,000) 6,000 6,000

    These depreciation effects are calculated as follows:

    Yr1 150,000 x .30 (depreciation) x .40 (tax rate) = 18,000

    Yr2 150,000 x .40 (depreciation) x .40 (tax rate) = 24,000

    Yr3 150,000 x .30 (depreciation) x .40 (tax rate) = 18,000

    * 18,000 – (150,000 x .30 depreciation) = (27,000)

    ** 24,000 – (150,000 x .40 depreciation) = (36,000)

    Now determine the Net Present Value of Annual Aftertax Cash Flow by year.

    Annual Present Net

    Aftertax Value Present

    Cash Flow x of $1 = Value

    Yrly Total: Yr 0 (150,000) x 1.0000 = (150,000)

    Yr 1 (51,000 + 18,000) x 0.8621 = 59,485

    Yr 2 (51,000 + 24,000) x 0.7432 = 55,740

    Yr 3 (51,000 + 18,000 + 6,000) x 0.6407 = 48,053

    Total 13,278

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