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: A firm is considering an investment in a new machine with a price of $18...

: A firm is considering an investment in a new machine with a price of $18 million to replace its existing machine. The current machine has a book value of $6 million and a market value of $4.5 million. The new machine is expected to have a four-year life, and the old machine has four years left in which it can be used. If the firm replaces the old machine with the new machine, it expects to save $6.7 million in operating costs each year over the next four years. Both machines will have no salvage value in four years. If the firm purchases the new machine, it will also need an investment of $250,000 in net working capital. The required rate of return on the investment is 10 percent, and the tax rate is 39 percent. What are the NPV and IRR of the decision to replace the old machine? Show formulas in Excel please

Solutions

Expert Solution

NPV: $3.67 million (rounded) as demonstrated below:

  • Year Cash Flows in millions
    0 $         -13.16
    1 $             5.26
    2 $             5.26
    3 $             5.26
    4 $             5.51
    NPV $             3.67

    [See Notes towards the end, to see calculations and formulae]

IRR: 22.25% (rounded) as demonstrated below:

  • Year Cash Flows in millions
    0 $         -13.16
    1 $             5.26
    2 $             5.26
    3 $             5.26
    4 $             5.51
    IRR 22.25%

Notes:

  • (in millions)
    Depreciation of new machine $            4.50 [=18/4]
    Depreciation of old machine $            1.50 [=6/4]
    Incremental Depreciation p.a. $            3.00
    Tax savings @ 39% $            1.17 Treated as Cash Flow for years 1-4
    Savings in Operating Cost $            6.70
    Tax on such savings @39% $            2.61
    Balance $            4.09 Treated as Cash Flow for years 1-4
    Salvage value of old machine $            4.50 Treated as Cash Flow in year 1
    Book value of old machine $            6.00
    Loss $            1.50
    Tax savings on such loss $            0.59 Treated as Cash Flow in year 1

    Note: Some teachers and authors [not all of them] ignore the loss on sale of old machine, and the tax savings on such loss, but logically it should be considered.

    Calculation of Yearly Cash Flows
  • Year Particulars Cash Flows in milliions Total
    0 Salvage value of old machine $          4.500
    0 Tax savings on such loss $          0.590
    0 Working capital $        -0.250
    0 Cost of new machine $      -18.000 $              -13.160
    1 Savings on Op. costs and tax on dep. $          5.257 $                  5.257
    2 Savings on Op. costs and tax on dep. $          5.257 $                  5.257
    3 Savings on Op. costs and tax on dep. $          5.257 $                  5.257
    4 Savings on Op. costs and tax on dep. $          5.257
    4 Working capital released $          0.250 $                  5.507

  • NPV Excel Formulae:

  • IRR Excel Formulae:

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