A firm is considering an investment in a new machine with a price of $23 mill to replace its existing machine. The current machine has a book value of $6 mill, and a market value of $10.5 mill. The new machine is expected to have a four-year life, and the old machine has four year left in which it can be be used. If the firm replaced the old machine with the new machine, it expects to save $5mill in operating costs each year over the next four years. Both machines will have no salvage value in four years. It the firm purchases the new machine, it will also need an investment of $400,000 in net working capital. The required return on the investment is 10 %, and the tax rate is 40 %. 1) What is the npv and irr of the decicision to replace old machine? 2) ignoring the time value of money, the new machine saves only 20mill over the next four years and has a cost of 23mill. How is it possible that the decision to replace the old machine has a positive NPV?

a)

Initial Investment

Buy new machine / Keep old machine / Incremental analysis
Purchase new machine / –$23,000,000 / –$23,000,000
Net working capital / –400,000 / –400,000
Sell (buy) old machine / –$10,500,000 / 10,500,000
Taxes on old machine / 1,800,000 / –1,800,000
Total / –$23,400,000 / –$8,700,000 / –$14,700,000

OCF

Buy new machine / Keep old machine / Incremental analysis
Operating expense / $5,000,000 / $5,000,000
Depreciation / 5,750,000 / $1,500,000 / 4,250,000
EBT / –$750,000 / –$1,500,000 / $750,000
Taxes / –300,000 / –600,000 / 300,000
Net income / –$450,000 / –$900,000 / $450,000
OCF / $5,300,000 / $600,000 / $4,700,000

NPV/IRR Calculation

Buy new machine / Keep old machine / Incremental analysis
Year / Cash flow / Cash flow / Cash flow
0 / –$23,400,000 / –$8,700,000 / –$14,700,000
1 / 5,300,000 / 600,000 / 4,700,000
2 / 5,300,000 / 600,000 / 4,700,000
3 / 5,300,000 / 600,000 / 4,700,000
4 / 5,700,000 / 600,000 / 5,100,000
NPV / –$6,326,507.75 / –$6,798,080.73 / $471,572.98
IRR / -3.09% / -37.07% / 11.46%

b)

The purchase of a new machine can have a positive NPV because of the depreciation tax

shield. Without the depreciation tax shield, the new machine would have a negative NPV

since the saved expenses from the machine do not exceed the cost of the machine when

we consider the time value of money.