A firm is considering an investment in a new machine with a price of $18.01 mill

Question

A firm is considering an investment in a new machine with a price of $18.01 million to replace its existing machine. The current machine has a book value of $6.01 million and a market value of $4.51 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 $6.71 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 $251,000 in net working capital. The required return on the investment is 11 percent, and the tax rate is 34 percent. Assume the company uses straight-line depreciation.

What is the NPV of the decision to keep the old machine? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16. Enter your answer in dollars, not millions of dollars, e.g., 1,234,567. A negative answer should be indicated by a minus sign.)

What is the IRR of the decision to keep the old machine? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16. A negative answer should be indicated by a minus sign.)

Explanation / Answer

Formula sheet

A B C D E F G H I 2 3 Input Data (all data in million) 4 Old Machine New Machine 5 Purchase Cost $18.01 6 Salvage Value $0.00 $0.00 7 Current Book Value $6.01 8 Remaining Useful life (Years) 4 4 9 Depreciation per year $1.50 $4.50 10 Current Market Value $4.51 11 Net working Capital $0.00 $0.251 12 Tax Rate 34% 13 Cost of capital 11% 14 Savings in operating Cost 6.71 15 NPV of the decesion to keep machine will be the neagative of NPV to replace the machine. 16 To determine the NPV, incremental cash flow from the replacement needs to be calculated. 17 To calculate the incremental cash flow, cash flow for existing and new Machine needs to be calculated. 18 19 Calculation of Cash flow of old Machine: 20 21 Depreciation schedule of the old Machine can be written as follows assuming the current year is year 0: 22 23 Year 0 1 2 3 4 24 Depreciation $1.50 $1.50 $1.50 $1.50 25 Book Value $6.01 $4.51 $3.01 $1.50 $0.00 26 27 Calculation of opportunity cost: 28 Current market value of the Machine will act as a opportunity cost. 29 Before Tax market value $4.51 30 Book value of old Machine $6.01 31 Gain or loss on sale ($1.50) =D29-D30 32 Tax Expense on gain or loss 0.51 =-D31*D12 33 Net Proceed from sale of old Machine $5.02 34 35 Cash flow for old Machine: 36 Operating cash flow needs to be calculated using the following formula: 37 Operating Cash Flow = EBIT*(1-T)+Depreciation 38 Free cash flow can be calculated using following equation: 39 Free Cash Flow = Operating Cash Flow - Capital Expenditures - Change in working capital 40 41 Year 0 1 2 3 4 42 Opportunity cost ($5.02) 43 Depreciation Expense ($1.50) ($1.50) ($1.50) ($1.50) 44 EBIT ($1.50) ($1.50) ($1.50) ($1.50) 45 Tax expense $0.51 $0.51 $0.51 $0.51 46 EBIT*(1-T) ($0.99) ($0.99) ($0.99) ($0.99) 47 Add Depreciation $1.50 $1.50 $1.50 $1.50 48 Operating Cash Flow $0.51 $0.51 $0.51 $0.51 49 Change in working capital $0.00 50 Recovery of working capital $0.00 51 Salvage Value $0.00 52 Free Cash flow for old Machine ($5.02) $0.51 $0.51 $0.51 $0.51 53 54 Calculation of Cash flow of new Machine: 55 Depreciation schedule of the new Machine can be written as follows: 56 Purchase cost of the new Machine $18.01 57 58 Year 0 1 2 3 4 59 Depreciation $4.50 $4.50 $4.50 $4.50 60 Book Value $18.01 $13.51 $9.01 $4.50 $0.00 61 62 Cash flow for New Machine: 63 Operating cash flow needs to be calculated using the following formula: 64 Operating Cash Flow = EBIT*(1-T)+Depreciation 65 Free cash flow can be calculated using following equation: 66 Free Cash Flow = Operating Cash Flow - Capital Expenditures - Change in working capital 67 68 Year 0 1 2 3 4 69 Investment ($18.01) 70 Savings in Operating Cost $6.71 $6.71 $6.71 $6.71 71 Depreciation Expense ($4.50) ($4.50) ($4.50) ($4.50) 72 EBIT $2.21 $2.21 $2.21 $2.21 73 Tax expense ($0.75) ($0.75) ($0.75) ($0.75) 74 EBIT*(1-T) $1.46 $1.46 $1.46 $1.46 75 Add Depreciation $4.50 $4.50 $4.50 $4.50 76 Operating Cash Flow $5.96 $5.96 $5.96 $5.96 77 Change in working capital ($0.2510) 78 Recovery of working capital $0.25 79 Salvage Value 80 Free Cash flow for new Machine ($18.26) $5.96 $5.96 $5.96 $6.21 81 82 83 Calculation of incremental cash flow for replacing the existing machine 84 Free Cash flow for new Machine ($18.26) $5.96 $5.96 $5.96 $6.21 85 Free Cash flow for old Machine ($5.02) $0.51 $0.51 $0.51 $0.51 86 Incremental Cash flow ($13.24) $5.45 $5.45 $5.45 $5.70 87 88 NPV calculation: 89 NPV of the project is present value of future cash flows discounted at required rate of return less the initial investment. 90 Given the following cash flow and MARR, NPV for the project can be calculated as follows: 91 Year 0 1 2 3 4 92 Free Cash Flow (FCF) ($13.24) $5.45 $5.45 $5.45 $5.70 93 MARR (i) 11.0% 94 (P/F,i,n) for each year 0.90 0.81 0.73 0.66 95 Present Value of cash flows = FCF*(P/F,i,n) $4.91 $4.42 $3.98 $3.75 96 Present value if future cash flows $17.07 =SUM(E95:H95) 97 98 NPV for Replacing the Old machine =Present value fo future cash flows - Initial investment 99 $3.8283 =D96+D92 100 101 Hence NPV of keeping the old machine is ($3,828,327) 102 103 IRR Calculation: 104 105 IRR is the rate at which NPV of the project will be zero. 106 Given the following cash flow IRR can be calculated as below: 107 108 IRR can also be found using IRR function in excel as follows: 109 Year 0 1 2 3 4 110 Cash Flow ($13.24) $5.45 $5.45 $5.45 $5.70 111 IRR 23.85% =IRR(D110:H110) 112 113 Hence IRR keeping the old machine is -23.85% 114

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