Question
In: Finance
Your company is deciding whether to invest in a new machine. The new machine will increase...
Your company is deciding whether to invest in a new machine. The
new machine will increase cash flow by $330,000 per year. You
believe the technology used in the machine has a 10-year life; in
other words, no matter when you purchase the machine, it will be
obsolete 10 years from today. The machine is currently priced at
$1,850,000. The cost of the machine will decline by $120,000 per
year until it reaches $1,250,000, where it will remain.
If your required return is 12 percent, calculate the NPV if you
purchase the machine today. (Do not round intermediate
calculations and round your answer to 2 decimal
places, e.g., 32.16.)
NPV $
If your required return is 12 percent, calculate the NPV if you
wait to purchase the machine until the indicated year. (A
negative answer should be indicated by a minus sign. Do not round
intermediate calculations and round your answers to 2 decimal
places, e.g., 32.16.)
| NPV | |
| Year 1 | $ |
| Year 2 | $ |
| Year 3 | $ |
| Year 4 | $ |
| Year 5 | $ |
| Year 6 | $ |
Should you purchase the machine?
Yes
No
If so, when should you purchase it?
Today
One year from now
Two years from now
Solutions
Expert Solution
| NPV | $ 14,573.60 | ||||
| Explanation | |||||
| Year | Investment | Increase cash flow | Total Cash flow | Discount factor @ 12% | Present value |
| 0 | $ (1,850,000.00) | $ (1,850,000.00) | 1.0000 | $ (1,850,000.00) | |
| 1 | $ 330,000.00 | $ 330,000.00 | 0.8929 | $ 294,642.86 | |
| 2 | $ 330,000.00 | $ 330,000.00 | 0.7972 | $ 263,073.98 | |
| 3 | $ 330,000.00 | $ 330,000.00 | 0.7118 | $ 234,887.48 | |
| 4 | $ 330,000.00 | $ 330,000.00 | 0.6355 | $ 209,720.97 | |
| 5 | $ 330,000.00 | $ 330,000.00 | 0.5674 | $ 187,250.86 | |
| 6 | $ 330,000.00 | $ 330,000.00 | 0.5066 | $ 167,188.27 | |
| 7 | $ 330,000.00 | $ 330,000.00 | 0.4523 | $ 149,275.24 | |
| 8 | $ 330,000.00 | $ 330,000.00 | 0.4039 | $ 133,281.47 | |
| 9 | $ 330,000.00 | $ 330,000.00 | 0.3606 | $ 119,001.31 | |
| 10 | $ 330,000.00 | $ 330,000.00 | 0.3220 | $ 106,251.17 | |
| NPV | $ 14,573.60 | ||||
| Year | NPV | ||||
| 1 | $ 14,573.60 | ||||
| 2 | $ 28,322.43 | ||||
| 3 | $ 29,321.12 | ||||
| 4 | $ 16,039.66 | ||||
| 5 | $ (13,235.58) | ||||
| 6 | $ (60,423.85) | ||||
| No, machine should not be purchased as NPV is negative. | |||||
| Today, machine should be purhcased two years from now. | |||||
| (if machine purchased after one year) | |||||
| Year | Investment | Increase cash flow | Total Cash flow | Discount factor @ 12% | Present value |
| 0 | $ (1,730,000.00) | $ (1,730,000.00) | 1.0000 | $ (1,730,000.00) | |
| 1 | $ 330,000.00 | $ 330,000.00 | 0.8929 | $ 294,642.86 | |
| 2 | $ 330,000.00 | $ 330,000.00 | 0.7972 | $ 263,073.98 | |
| 3 | $ 330,000.00 | $ 330,000.00 | 0.7118 | $ 234,887.48 | |
| 4 | $ 330,000.00 | $ 330,000.00 | 0.6355 | $ 209,720.97 | |
| 5 | $ 330,000.00 | $ 330,000.00 | 0.5674 | $ 187,250.86 | |
| 6 | $ 330,000.00 | $ 330,000.00 | 0.5066 | $ 167,188.27 | |
| 7 | $ 330,000.00 | $ 330,000.00 | 0.4523 | $ 149,275.24 | |
| 8 | $ 330,000.00 | $ 330,000.00 | 0.4039 | $ 133,281.47 | |
| 9 | $ 330,000.00 | $ 330,000.00 | 0.3606 | $ 119,001.31 | |
| NPV | $ 28,322.43 | ||||
| (if machine purchased after two years) | |||||
| Year | Investment | Increase cash flow | Total Cash flow | Discount factor @ 12% | Present value |
| 0 | $ (1,610,000.00) | $ (1,610,000.00) | 1.0000 | $ (1,610,000.00) | |
| 1 | $ 330,000.00 | $ 330,000.00 | 0.8929 | $ 294,642.86 | |
| 2 | $ 330,000.00 | $ 330,000.00 | 0.7972 | $ 263,073.98 | |
| 3 | $ 330,000.00 | $ 330,000.00 | 0.7118 | $ 234,887.48 | |
| 4 | $ 330,000.00 | $ 330,000.00 | 0.6355 | $ 209,720.97 | |
| 5 | $ 330,000.00 | $ 330,000.00 | 0.5674 | $ 187,250.86 | |
| 6 | $ 330,000.00 | $ 330,000.00 | 0.5066 | $ 167,188.27 | |
| 7 | $ 330,000.00 | $ 330,000.00 | 0.4523 | $ 149,275.24 | |
| 8 | $ 330,000.00 | $ 330,000.00 | 0.4039 | $ 133,281.47 | |
| NPV | $ 29,321.12 | ||||
| (if machine purchased after two years) | |||||
| Year | Investment | Increase cash flow | Total Cash flow | Discount factor @ 12% | Present value |
| 0 | $ (1,490,000.00) | $ (1,490,000.00) | 1.0000 | $ (1,490,000.00) | |
| 1 | $ 330,000.00 | $ 330,000.00 | 0.8929 | $ 294,642.86 | |
| 2 | $ 330,000.00 | $ 330,000.00 | 0.7972 | $ 263,073.98 | |
| 3 | $ 330,000.00 | $ 330,000.00 | 0.7118 | $ 234,887.48 | |
| 4 | $ 330,000.00 | $ 330,000.00 | 0.6355 | $ 209,720.97 | |
| 5 | $ 330,000.00 | $ 330,000.00 | 0.5674 | $ 187,250.86 | |
| 6 | $ 330,000.00 | $ 330,000.00 | 0.5066 | $ 167,188.27 | |
| 7 | $ 330,000.00 | $ 330,000.00 | 0.4523 | $ 149,275.24 | |
| NPV | $ 16,039.66 | ||||
| (if machine purchased after three years) | |||||
| Year | Investment | Increase cash flow | Total Cash flow | Discount factor @ 12% | Present value |
| 0 | $ (1,370,000.00) | $ (1,370,000.00) | 1.0000 | $ (1,370,000.00) | |
| 1 | $ 330,000.00 | $ 330,000.00 | 0.8929 | $ 294,642.86 | |
| 2 | $ 330,000.00 | $ 330,000.00 | 0.7972 | $ 263,073.98 | |
| 3 | $ 330,000.00 | $ 330,000.00 | 0.7118 | $ 234,887.48 | |
| 4 | $ 330,000.00 | $ 330,000.00 | 0.6355 | $ 209,720.97 | |
| 5 | $ 330,000.00 | $ 330,000.00 | 0.5674 | $ 187,250.86 | |
| 6 | $ 330,000.00 | $ 330,000.00 | 0.5066 | $ 167,188.27 | |
| NPV | $ (13,235.58) | ||||
| (if machine purchased after fourth years) | |||||
| Year | Investment | Increase cash flow | Total Cash flow | Discount factor @ 12% | Present value |
| 0 | $ (1,250,000.00) | $ (1,250,000.00) | 1.0000 | $ (1,250,000.00) | |
| 1 | $ 330,000.00 | $ 330,000.00 | 0.8929 | $ 294,642.86 | |
| 2 | $ 330,000.00 | $ 330,000.00 | 0.7972 | $ 263,073.98 | |
| 3 | $ 330,000.00 | $ 330,000.00 | 0.7118 | $ 234,887.48 | |
| 4 | $ 330,000.00 | $ 330,000.00 | 0.6355 | $ 209,720.97 | |
| 5 | $ 330,000.00 | $ 330,000.00 | 0.5674 | $ 187,250.86 | |
| NPV | $ (60,423.85) | ||||
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