Question
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Question: Company X uses fermentation to produce a valuable industrial chemical. A startup company approaches X...
Question: Company X uses fermentation to produce a valuable industrial chemical. A startup company approaches X with a novel microbe that will increase the yield of the chemical, so that profits will increase by an estimated $14.0k/mo. The startup company wishes to sell the rights to use the microbe for a seven-year period, at a price of $480k.
Engineers at company X estimate the increased production will entail additional maintenance, costing $12.0k in year 2, $14.0k in year 4, and $17.0k in year 6 of the project.
1. What would a cash flow diagram of the project, from the standpoint of Company X?
2. How can I calculate the present value of the project, assuming a 13.0% annual interest rate?
3. Using Excel, make a well-formatted graph of the project present value vs. interest rate, for interest rates ranging from 0 to 30% APR.
Solutions
Expert Solution
1. Here, the additional maintenance cost is spread throughout the year. For eg., $12,000 in year-2 is spread across 12 months of year 2 at $1,000 per month
| Month | Net-cashflows |
| 0 | -480,000 |
| 1 | 14000 |
| 2 | 14000 |
| 3 | 14000 |
| 4 | 14000 |
| 5 | 14000 |
| 6 | 14000 |
| 7 | 14000 |
| 8 | 14000 |
| 9 | 14000 |
| 10 | 14000 |
| 11 | 14000 |
| 12 | 14000 |
| 13 | 13000 |
| 14 | 13000 |
| 15 | 13000 |
| 16 | 13000 |
| 17 | 13000 |
| 18 | 13000 |
| 19 | 13000 |
| 20 | 13000 |
| 21 | 13000 |
| 22 | 13000 |
| 23 | 13000 |
| 24 | 13000 |
| 25 | 14000 |
| 26 | 14000 |
| 27 | 14000 |
| 28 | 14000 |
| 29 | 14000 |
| 30 | 14000 |
| 31 | 14000 |
| 32 | 14000 |
| 33 | 14000 |
| 34 | 14000 |
| 35 | 14000 |
| 36 | 14000 |
| 37 | 12833.33333 |
| 38 | 12833.33333 |
| 39 | 12833.33333 |
| 40 | 12833.33333 |
| 41 | 12833.33333 |
| 42 | 12833.33333 |
| 43 | 12833.33333 |
| 44 | 12833.33333 |
| 45 | 12833.33333 |
| 46 | 12833.33333 |
| 47 | 12833.33333 |
| 48 | 12833.33333 |
| 49 | 14000 |
| 50 | 14000 |
| 51 | 14000 |
| 52 | 14000 |
| 53 | 14000 |
| 54 | 14000 |
| 55 | 14000 |
| 56 | 14000 |
| 57 | 14000 |
| 58 | 14000 |
| 59 | 14000 |
| 60 | 14000 |
| 61 | 12583.33333 |
| 62 | 12583.33333 |
| 63 | 12583.33333 |
| 64 | 12583.33333 |
| 65 | 12583.33333 |
| 66 | 12583.33333 |
| 67 | 12583.33333 |
| 68 | 12583.33333 |
| 69 | 12583.33333 |
| 70 | 12583.33333 |
| 71 | 12583.33333 |
| 72 | 12583.33333 |
| 73 | 14000 |
| 74 | 14000 |
| 75 | 14000 |
| 76 | 14000 |
| 77 | 14000 |
| 78 | 14000 |
| 79 | 14000 |
| 80 | 14000 |
| 81 | 14000 |
| 82 | 14000 |
| 83 | 14000 |
| 84 | 14000 |
| Year | Yearly cash-flows |
| 0 | -480,000 |
| 1 | 168000 |
| 2 | 156000 |
| 3 | 168000 |
| 4 | 154000 |
| 5 | 168000 |
| 6 | 151000 |
| 7 | 168000 |
2.
We use the NPV function in excel
Discount rate = 13%/12 ( Since there are 12 periods per year and 13% is the annual interest rate.
We get the Net Present Value of the project = $276,561.0098
3. We calculate the NPV for different annual interest rates
| Annual APR | NPV |
| 0% | 667000 |
| 1% | 627913.5744 |
| 2% | 590641.8359 |
| 3% | 555089.1215 |
| 4% | 521165.1996 |
| 5% | 488784.9465 |
| 6% | 457868.0411 |
| 7% | 428338.6801 |
| 8% | 400125.3096 |
| 9% | 373160.3743 |
| 10% | 347380.0814 |
| 11% | 322724.1789 |
| 12% | 299135.7485 |
| 13% | 276561.0098 |
| 14% | 254949.1375 |
| 15% | 234252.0893 |
| 16% | 214424.4441 |
| 17% | 195423.2505 |
| 18% | 177207.8841 |
| 19% | 159739.9133 |
| 20% | 142982.9737 |
| 21% | 126902.6492 |
| 22% | 111466.3613 |
| 23% | 96643.26432 |
| 24% | 82404.14675 |
| 25% | 68721.33897 |
| 26% | 55568.62618 |
| 27% | 42921.16651 |
| 28% | 30755.41396 |
| 29% | 19049.04597 |
| 30% | 7780.895112 |
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