A firm is considering an investment in a new machine with a price of $18 million
ID: 2724107 • Letter: A
Question
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 6million and a market value of $4.5 million. The new machine 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 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?
Explanation / Answer
1
Calculation of NPV of the decision to replace the old machine:
Year 0
Year 1
Year 2
Year 3
Year 4
Investment in new machine
$(18,000,000.00)
Investment in net working capital
$ (250,000.00)
Sale Value of old Machine
$ 4,500,000.00
Increase in Tax Saving on depreciation:
Annual Depreciation on old machine (6,000,000 / 4) = 1,500,000
Annual Depreciation on new machine (18,000,000 / 4) = 4,500,000
Incremental Depreciation = 4,500,000-1,500,000 = 3,000,000
Increase in Tax Saving on depreciation = 3,000,000 *39% =
$1,170,000.00
$1,170,000.00
$1,170,000.00
$1,170,000.00
Saving in operating cost (Net of Tax) = $6,700,000 * (1-39%) =
$4,087,000.00
$4,087,000.00
$4,087,000.00
$4,087,000.00
Net Cash Flows (CF)
$(13,750,000.00)
$5,257,000.00
$5,257,000.00
$5,257,000.00
$5,257,000.00
Present value of $ 1 (PVF) (Year, 10%)
1.00000
0.90909
0.82645
0.75131
0.68301
1 / (1+10%)^0
1 / (1+10%)^1
1 / (1+10%)^2
1 / (1+10%)^3
1 / (1+10%)^4
PV = CF * PVF
$(13,750,000.00)
$4,779,090.91
$4,344,628.10
$3,949,661.91
$3,590,601.73
NPV = Sum of PVs
$ 2,913,982.65
2
Calculation of IRR of the decision to replace the old machine:
Year 0
Year 1
Year 2
Year 3
Year 4
Investment in new machine
$(18,000,000.00)
Investment in net working capital
$ (250,000.00)
Sale Value of old Machine
$ 4,500,000.00
Increase in Tax Saving on depreciation:
Annual Depreciation on old machine (6,000,000 / 4) = 1,500,000
Annual Depreciation on new machine (18,000,000 / 4) = 4,500,000
Incremental Depreciation = 4,500,000-1,500,000 = 3,000,000
Increase in Tax Saving on depreciation = 3,000,000 *39% =
$1,170,000.00
$1,170,000.00
$1,170,000.00
$1,170,000.00
Saving in operating cost (Net of Tax) = $6,700,000 * (1-39%) =
$4,087,000.00
$4,087,000.00
$4,087,000.00
$4,087,000.00
Net Cash Flows (CF)
$(13,750,000.00)
$5,257,000.00
$5,257,000.00
$5,257,000.00
$5,257,000.00
IRR =
19.46%
(Using IRR excel formula "=IRR()"
1
Calculation of NPV of the decision to replace the old machine:
Year 0
Year 1
Year 2
Year 3
Year 4
Investment in new machine
$(18,000,000.00)
Investment in net working capital
$ (250,000.00)
Sale Value of old Machine
$ 4,500,000.00
Increase in Tax Saving on depreciation:
Annual Depreciation on old machine (6,000,000 / 4) = 1,500,000
Annual Depreciation on new machine (18,000,000 / 4) = 4,500,000
Incremental Depreciation = 4,500,000-1,500,000 = 3,000,000
Increase in Tax Saving on depreciation = 3,000,000 *39% =
$1,170,000.00
$1,170,000.00
$1,170,000.00
$1,170,000.00
Saving in operating cost (Net of Tax) = $6,700,000 * (1-39%) =
$4,087,000.00
$4,087,000.00
$4,087,000.00
$4,087,000.00
Net Cash Flows (CF)
$(13,750,000.00)
$5,257,000.00
$5,257,000.00
$5,257,000.00
$5,257,000.00
Present value of $ 1 (PVF) (Year, 10%)
1.00000
0.90909
0.82645
0.75131
0.68301
1 / (1+10%)^0
1 / (1+10%)^1
1 / (1+10%)^2
1 / (1+10%)^3
1 / (1+10%)^4
PV = CF * PVF
$(13,750,000.00)
$4,779,090.91
$4,344,628.10
$3,949,661.91
$3,590,601.73
NPV = Sum of PVs
$ 2,913,982.65
2
Calculation of IRR of the decision to replace the old machine:
Year 0
Year 1
Year 2
Year 3
Year 4
Investment in new machine
$(18,000,000.00)
Investment in net working capital
$ (250,000.00)
Sale Value of old Machine
$ 4,500,000.00
Increase in Tax Saving on depreciation:
Annual Depreciation on old machine (6,000,000 / 4) = 1,500,000
Annual Depreciation on new machine (18,000,000 / 4) = 4,500,000
Incremental Depreciation = 4,500,000-1,500,000 = 3,000,000
Increase in Tax Saving on depreciation = 3,000,000 *39% =
$1,170,000.00
$1,170,000.00
$1,170,000.00
$1,170,000.00
Saving in operating cost (Net of Tax) = $6,700,000 * (1-39%) =
$4,087,000.00
$4,087,000.00
$4,087,000.00
$4,087,000.00
Net Cash Flows (CF)
$(13,750,000.00)
$5,257,000.00
$5,257,000.00
$5,257,000.00
$5,257,000.00
IRR =
19.46%
(Using IRR excel formula "=IRR()"
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