Question
In: Finance
a) Calculate the dynamic payback period for the project A b) Calculate the return on investment...
a) Calculate the dynamic payback period for the project A
b) Calculate the return on investment of the project A
c) Determine the appropriate selling price which will ensure the NPV of project A and B are the same
d) Determine if the NPV of the project A is more sensitive to interest rate than the selling price. Use appropriate diagrams and appropriate parameter
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Solutions
Expert Solution
a)
| Year | Investment | Revenue | Costs | Net cashflow | Cumulative |
| 0 | $ (25,000) | $ (25,000) | |||
| 1 | $ 10,000 | $ 6,250 | $ 3,750 | $ 3,750 | |
| 2 | $ 10,000 | $ 6,250 | $ 3,750 | $ 7,500 | |
| 3 | $ 10,000 | $ 6,250 | $ 3,750 | $ 11,250 | |
| 4 | $ 10,000 | $ 6,250 | $ 3,750 | $ 15,000 | |
| 5 | $ 10,000 | $ 6,250 | $ 3,750 | $ 18,750 | |
| 6 | $ 10,000 | $ 6,250 | $ 3,750 | $ 22,500 | |
| 7 | $ 10,000 | $ 6,250 | $ 3,750 | $ 26,250 | |
| 8 | $ 10,000 | $ 6,250 | $ 3,750 | $ 30,000 | |
| 9 | $ 10,000 | $ 6,250 | $ 3,750 | $ 33,750 | |
| 10 | $ 10,000 | $ 6,250 | $ 3,750 | $ 37,500 | |
| 11 | $ 10,000 | $ 6,250 | $ 3,750 | $ 41,250 | |
| 12 | $ 10,000 | $ 6,250 | $ 3,750 | $ 45,000 | |
| 13 | $ 10,000 | $ 6,250 | $ 3,750 | $ 48,750 | |
| 14 | $ 10,000 | $ 6,250 | $ 3,750 | $ 52,500 | |
| 15 | $ 10,000 | $ 6,250 | $ 3,750 | $ 56,250 | |
| 16 | $ 10,000 | $ 6,250 | $ 3,750 | $ 60,000 | |
| 17 | $ 10,000 | $ 6,250 | $ 3,750 | $ 63,750 | |
| 18 | $ 10,000 | $ 6,250 | $ 3,750 | $ 67,500 | |
| 19 | $ 10,000 | $ 6,250 | $ 3,750 | $ 71,250 | |
| 20 | $ 10,000 | $ 6,250 | $ 3,750 | $ 75,000 |
The investment is recovered after the 6th year and before 7th year, to find out the exact time we can use the formula
(cumulative cashfow-initial investment)/cashfow per period
=(26,250-25,000)/3,750 =0.33 years or 4 months
Therefore payback is 6years and 4 months
,b) Total net cashflow is $75,000, Initial investment = $25,000
Therefore ROI = 75,000/25,000 = 3 times
c) Selling price for B should be $0.36
d) Project A is more sensitive to Price change that interest rate, below are the calculations by reducing the selling price and interest rate by 20%
| Year | Investment | Revenue | Costs | Net cashflow | Cumulative | Discounting factor | Discounted cashflow |
| 0 | $ (25,000) | $ (25,000) | $ (25,000) | 1.000 | $ (25,000) | ||
| 1 | $ 8,000 | $ 6,250 | $ 1,750 | $ 1,750 | 0.909 | $ 1,591 | |
| 2 | $ 8,000 | $ 6,250 | $ 1,750 | $ 3,500 | 0.826 | $ 2,893 | |
| 3 | $ 8,000 | $ 6,250 | $ 1,750 | $ 5,250 | 0.751 | $ 3,944 | |
| 4 | $ 8,000 | $ 6,250 | $ 1,750 | $ 7,000 | 0.683 | $ 4,781 | |
| 5 | $ 8,000 | $ 6,250 | $ 1,750 | $ 8,750 | 0.621 | $ 5,433 | |
| 6 | $ 8,000 | $ 6,250 | $ 1,750 | $ 10,500 | 0.564 | $ 5,927 | |
| 7 | $ 8,000 | $ 6,250 | $ 1,750 | $ 12,250 | 0.513 | $ 6,286 | |
| 8 | $ 8,000 | $ 6,250 | $ 1,750 | $ 14,000 | 0.467 | $ 6,531 | |
| 9 | $ 8,000 | $ 6,250 | $ 1,750 | $ 15,750 | 0.424 | $ 6,680 | |
| 10 | $ 8,000 | $ 6,250 | $ 1,750 | $ 17,500 | 0.386 | $ 6,747 | |
| 11 | $ 8,000 | $ 6,250 | $ 1,750 | $ 19,250 | 0.350 | $ 6,747 | |
| 12 | $ 8,000 | $ 6,250 | $ 1,750 | $ 21,000 | 0.319 | $ 6,691 | |
| 13 | $ 8,000 | $ 6,250 | $ 1,750 | $ 22,750 | 0.290 | $ 6,590 | |
| 14 | $ 8,000 | $ 6,250 | $ 1,750 | $ 24,500 | 0.263 | $ 6,452 | |
| 15 | $ 8,000 | $ 6,250 | $ 1,750 | $ 26,250 | 0.239 | $ 6,284 | |
| 16 | $ 8,000 | $ 6,250 | $ 1,750 | $ 28,000 | 0.218 | $ 6,094 | |
| 17 | $ 8,000 | $ 6,250 | $ 1,750 | $ 29,750 | 0.198 | $ 5,886 | |
| 18 | $ 8,000 | $ 6,250 | $ 1,750 | $ 31,500 | 0.180 | $ 5,666 | |
| 19 | $ 8,000 | $ 6,250 | $ 1,750 | $ 33,250 | 0.164 | $ 5,437 | |
| 20 | $ 8,000 | $ 6,250 | $ 1,750 | $ 35,000 | 0.149 | $ 5,203 | |
| NPV | $ 86,861 | ||||||
| Year | Investment | Revenue | Costs | Net cashflow | Cumulative | Discounting factor | Discounted cashflow |
| 0 | $ (25,000) | $ (25,000) | $ (25,000) | 1.000 | $ (25,000) | ||
| 1 | $ 10,000 | $ 6,250 | $ 3,750 | $ 3,750 | 0.926 | $ 3,472 | |
| 2 | $ 10,000 | $ 6,250 | $ 3,750 | $ 7,500 | 0.857 | $ 6,430 | |
| 3 | $ 10,000 | $ 6,250 | $ 3,750 | $ 11,250 | 0.794 | $ 8,931 | |
| 4 | $ 10,000 | $ 6,250 | $ 3,750 | $ 15,000 | 0.735 | $ 11,025 | |
| 5 | $ 10,000 | $ 6,250 | $ 3,750 | $ 18,750 | 0.681 | $ 12,761 | |
| 6 | $ 10,000 | $ 6,250 | $ 3,750 | $ 22,500 | 0.630 | $ 14,179 | |
| 7 | $ 10,000 | $ 6,250 | $ 3,750 | $ 26,250 | 0.583 | $ 15,317 | |
| 8 | $ 10,000 | $ 6,250 | $ 3,750 | $ 30,000 | 0.540 | $ 16,208 | |
| 9 | $ 10,000 | $ 6,250 | $ 3,750 | $ 33,750 | 0.500 | $ 16,883 | |
| 10 | $ 10,000 | $ 6,250 | $ 3,750 | $ 37,500 | 0.463 | $ 17,370 | |
| 11 | $ 10,000 | $ 6,250 | $ 3,750 | $ 41,250 | 0.429 | $ 17,691 | |
| 12 | $ 10,000 | $ 6,250 | $ 3,750 | $ 45,000 | 0.397 | $ 17,870 | |
| 13 | $ 10,000 | $ 6,250 | $ 3,750 | $ 48,750 | 0.368 | $ 17,925 | |
| 14 | $ 10,000 | $ 6,250 | $ 3,750 | $ 52,500 | 0.340 | $ 17,874 | |
| 15 | $ 10,000 | $ 6,250 | $ 3,750 | $ 56,250 | 0.315 | $ 17,732 | |
| 16 | $ 10,000 | $ 6,250 | $ 3,750 | $ 60,000 | 0.292 | $ 17,513 | |
| 17 | $ 10,000 | $ 6,250 | $ 3,750 | $ 63,750 | 0.270 | $ 17,230 | |
| 18 | $ 10,000 | $ 6,250 | $ 3,750 | $ 67,500 | 0.250 | $ 16,892 | |
| 19 | $ 10,000 | $ 6,250 | $ 3,750 | $ 71,250 | 0.232 | $ 16,509 | |
| 20 | $ 10,000 | $ 6,250 | $ 3,750 | $ 75,000 | 0.215 | $ 16,091 | |
| NPV | $ 270,905 |
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