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A college friend of mine just filed for a patent for a new product – the...
A college friend of mine just filed for a patent for a new product – the “bowling buddy” bowlers’ training aid. The bowling buddy sells for $55 and the variable cost per unit is $26. They rent production space for $25,000 annually. The initial investment is $250,000 and the project life is 5 years. Assume appropriate discount rate is 10% and ignore taxes. Assuming my friend can sell 4,000 bowling buddies per year, what is the IRR of the project?
B) Assuming my friend can sell 3,000 bowling buddies per year, what is the discounted payback period of the project?
Solutions
Expert Solution
Part A:
| Calculation of annual operating cash flow | ||||||
| Year-1 | Year-2 | Year-3 | Year-4 | Year-5 | ||
| No of units | 4,000 | 4,000 | 4,000 | 4,000 | 4,000 | |
| Selling price | $ 55 | $ 55 | $ 55 | $ 55 | $ 55 | |
| Operating cost | $ 26 | $ 26 | $ 26 | $ 26 | $ 26 | |
| Sale | $ 220,000 | $ 220,000 | $ 220,000 | $ 220,000 | $ 220,000 | |
| Less: Operating Cost | $ 104,000 | $ 104,000 | $ 104,000 | $ 104,000 | $ 104,000 | |
| Contribution | $ 116,000 | $ 116,000 | $ 116,000 | $ 116,000 | $ 116,000 | |
| Less: Marketting cost | $ 25,000 | $ 25,000 | $ 25,000 | $ 25,000 | $ 25,000 | |
| Cash flow | $ 91,000 | $ 91,000 | $ 91,000 | $ 91,000 | $ 91,000 | |
| Calculation of IRR | ||||||
| 23.00% | 24.00% | |||||
| Year | Total cash flow | PV factor @ 23% | Present values | PV factor @ 24% | Present values | |
| 0 | $ (250,000) | 1.000 | $ (250,000) | 1.000 | $ (250,000) | |
| 1 | $ 91,000 | 0.813 | $ 73,984 | 0.806 | $ 73,387 | |
| 2 | $ 91,000 | 0.661 | $ 60,149 | 0.650 | $ 59,183 | |
| 3 | $ 91,000 | 0.537 | $ 48,902 | 0.524 | $ 47,728 | |
| 4 | $ 91,000 | 0.437 | $ 39,758 | 0.423 | $ 38,491 | |
| 5 | $ 91,000 | 0.355 | $ 32,323 | 0.341 | $ 31,041 | |
| $ 5,116 | $ (170) | |||||
| IRR | =Lower rate + Difference in rates*(NPV at lower rate)/(Lower rate NPV-Higher rate NPV) | |||||
| IRR | '=23%+ (24%-23%)*(5116.04/(5116.04-(-170.01) | |||||
| 23.97% |
Part B:
| Calculation of annual operating cash flow | ||||||||
| Year-1 | Year-2 | Year-3 | Year-4 | Year-5 | ||||
| No of units | 3,000 | 3,000 | 3,000 | 3,000 | 3,000 | |||
| Selling price | $ 55 | $ 55 | $ 55 | $ 55 | $ 55 | |||
| Operating cost | $ 26 | $ 26 | $ 26 | $ 26 | $ 26 | |||
| Sale | $ 165,000 | $ 165,000 | $ 165,000 | $ 165,000 | $ 165,000 | |||
| Less: Operating Cost | $ 78,000 | $ 78,000 | $ 78,000 | $ 78,000 | $ 78,000 | |||
| Contribution | $ 87,000 | $ 87,000 | $ 87,000 | $ 87,000 | $ 87,000 | |||
| Less: Marketting cost | $ 25,000 | $ 25,000 | $ 25,000 | $ 25,000 | $ 25,000 | |||
| Cash flow | $ 62,000 | $ 62,000 | $ 62,000 | $ 62,000 | $ 62,000 | |||
| Calculation of Discounted payback period | ||||||||
| Year | Annual Cash flow | PV factor @ 10% | Present values | Cumulative PV | ||||
| 0 | $ (250,000) | 1.000 | $ (250,000) | $ (250,000) | ||||
| 1 | $ 91,000 | 0.909 | $ 82,727 | $ (167,273) | ||||
| 2 | $ 91,000 | 0.826 | $ 75,207 | $ (92,066) | ||||
| 3 | $ 91,000 | 0.751 | $ 68,370 | $ (23,696) | ||||
| 4 | $ 91,000 | 0.683 | $ 62,154 | $ 38,458 | ||||
| 5 | $ 91,000 | 0.621 | $ 56,504 | $ 94,962 | ||||
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