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Problem 8-22 Calculating NPV and IRR for a Replacement A firm is considering an investment in...
Problem 8-22 Calculating NPV and IRR for a Replacement
A firm is considering
an investment in a new machine with a price of $18.15 million to
replace its existing machine. The current machine has a book value
of $6.15 million and a market value of $4.65 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 $6.85
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
$265,000 in net working capital. The required return on the
investment is 12 percent and the tax rate is 35 percent.
What is the NPV of the decision to purchase a new machine?
(Enter your answer in dollars, not millions of dollars. Do
not round intermediate calculations and round your answer to 2
decimal places, e.g., 1,234,567.89.)
NPV $
What is the IRR of the decision to purchase a new machine?
(Do not round intermediate calculations. Enter your answer
as a percent rounded to 2 decimal places, e.g.,
32.16.)
IRR %
What is the NPV of the decision to purchase the old machine?
(A negative answer should be indicated by a minus sign.
Enter your answer in dollars, not millions of dollars. Do not round
intermediate calculations and round your answer to 2 decimal
places, e.g., 1,234,567.89.)
NPV $
What is the IRR of the decision to purchase the old machine?
(Do not round intermediate calculations. 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.)
IRR %
Solutions
Expert Solution
New Machine Depreciation
|
New machine cost (in Mn $) |
18.15 |
|
New machine cost (in $) |
18,150,000.00 |
|
Useful life (in years) |
4.00 |
|
Depreciation per year |
4,537,500.00 |
|
Working capital infusion which can be revived back at the end of 4 years (in $) |
265,000.00 |
We can see that no specific cashflows are identified for the old machine, we cna compute the NPV and IRR for new machine.
Cashflow table
|
Year |
0 |
1 |
2 |
3 |
4 |
|
Initial cashflow |
|||||
|
New machine cost - A |
(18,150,000.00) |
||||
|
Working capital infusion (in Mn) - B |
(265,000.00) |
||||
|
Sale value of old machine |
4,650,000.00 |
||||
|
Less : Book value of machine |
6,150,000.00 |
||||
|
Loss on sale of machine |
(1,500,000.00) |
||||
|
Less : Tax @35% |
(525,000.00) |
||||
|
Loss after tax |
(975,000.00) |
||||
|
Add : Book value of machine |
6,150,000.00 |
||||
|
Cashflow from sale of old machine - C |
5,175,000.00 |
||||
|
Total Initial cashflows (A+B+C) |
(13,240,000.00) |
||||
|
Intermediate cashflows |
|||||
|
Savings in operating cost |
6,850,000.00 |
6,850,000.00 |
6,850,000.00 |
6,850,000.00 |
|
|
Less : depreciation |
4,537,500.00 |
4,537,500.00 |
4,537,500.00 |
4,537,500.00 |
|
|
Profit before tax |
2,312,500.00 |
2,312,500.00 |
2,312,500.00 |
2,312,500.00 |
|
|
Less : Tax @ 35% |
809,375.00 |
809,375.00 |
809,375.00 |
809,375.00 |
|
|
Profit after tax |
1,503,125.00 |
1,503,125.00 |
1,503,125.00 |
1,503,125.00 |
|
|
Add : Depreciation |
4,537,500.00 |
4,537,500.00 |
4,537,500.00 |
4,537,500.00 |
|
|
Cashflow after tax |
6,040,625.00 |
6,040,625.00 |
6,040,625.00 |
6,040,625.00 |
|
|
Terminal cashflows |
|||||
|
Claw back of working capital |
265,000.00 |
||||
|
Net cashflows |
(13,240,000.00) |
6,040,625.00 |
6,040,625.00 |
6,040,625.00 |
6,305,625.00 |
|
PV factor @ 12% -->Formula --> 1/(1+12%)^nth year |
1.0000 |
0.8929 |
0.7972 |
0.7118 |
0.6355 |
|
PV of cashflows |
(13,240,000.00) |
5,393,415.18 |
4,815,549.27 |
4,299,597.56 |
4,007,338.68 |
|
NPV |
5,275,900.69 |
IRR computation
IRR can be computed using the interpolation method. This would give an approximate value of IRR.
NPV @ 30%
|
Year |
0 |
1 |
2 |
3 |
4 |
|
Initial cashflow |
|||||
|
New machine cost - A |
(18,150,000.00) |
||||
|
Working capital infusion (in Mn) - B |
(265,000.00) |
||||
|
Sale value of old machine |
4,650,000.00 |
||||
|
Less : Book value of machine |
6,150,000.00 |
||||
|
Loss on sale of machine |
(1,500,000.00) |
||||
|
Less : Tax @35% |
(525,000.00) |
||||
|
Loss after tax |
(975,000.00) |
||||
|
Add : Book value of machine |
6,150,000.00 |
||||
|
Cashflow from sale of old machine - C |
5,175,000.00 |
||||
|
Total Initial cashflows (A+B+C) |
(13,240,000.00) |
||||
|
Intermediate cashflows |
|||||
|
Savings in operating cost |
6,850,000.00 |
6,850,000.00 |
6,850,000.00 |
6,850,000.00 |
|
|
Less : depreciation |
4,537,500.00 |
4,537,500.00 |
4,537,500.00 |
4,537,500.00 |
|
|
Profit before tax |
2,312,500.00 |
2,312,500.00 |
2,312,500.00 |
2,312,500.00 |
|
|
Less : Tax @ 35% |
809,375.00 |
809,375.00 |
809,375.00 |
809,375.00 |
|
|
Profit after tax |
1,503,125.00 |
1,503,125.00 |
1,503,125.00 |
1,503,125.00 |
|
|
Add : Depreciation |
4,537,500.00 |
4,537,500.00 |
4,537,500.00 |
4,537,500.00 |
|
|
Cashflow after tax |
6,040,625.00 |
6,040,625.00 |
6,040,625.00 |
6,040,625.00 |
|
|
Terminal cashflows |
|||||
|
Claw back of working capital |
265,000.00 |
||||
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