Answer: Prject : 3 should be accepted with NPV = $ 48,373.92
Working notes for the above answer is as under
First of all we will find NPV of the project as follow
| Plan -1 | ||||
| Year | Initial Cost |
Annual Benefit |
MARR Factor@10% |
Prasent Value |
| 0 | -220,000 | 1 | -220000 | |
| 1 | 39000 | 0.9090909 | 35454.55 | |
| 2 | 39000 | 0.8264463 | 32231.4 | |
| 3 | 39000 | 0.7513148 | 29301.28 | |
| 4 | 39000 | 0.6830135 | 26637.52 | |
| 5 | 39000 | 0.6209213 | 24215.93 | |
| 6 | 39000 | 0.5644739 | 22014.48 | |
| 7 | 39000 | 0.5131581 | 20013.17 | |
| 8 | 39000 | 0.4665074 | 18193.79 | |
| 9 | 39000 | 0.4240976 | 16539.81 | |
| 10 | 39000 | 0.3855433 | 15036.19 | |
| 19638.12 | ||||
| Plan -2 | ||||
| Year | Initial Cost |
Annual Benefit |
MARR Factor@10% |
Prasent Value |
| 0 | -100,000 | 1 | -100000 | |
| 1 | 15000 | 0.9090909 | 13636.36 | |
| 2 | 15000 | 0.8264463 | 12396.69 | |
| 3 | 15000 | 0.7513148 | 11269.72 | |
| 4 | 15000 | 0.6830135 | 10245.2 | |
| 5 | 15000 | 0.6209213 | 9313.82 | |
| 6 | 15000 | 0.5644739 | 8467.109 | |
| 7 | 15000 | 0.5131581 | 7697.372 | |
| 8 | 15000 | 0.4665074 | 6997.611 | |
| 9 | 15000 | 0.4240976 | 6361.464 | |
| 10 | 15000 | 0.3855433 | 5783.149 | |
| -7831.49 | ||||
| Plan -3 | ||||
| Year | Initial Cost |
Annual Benefit |
MARR Factor@10% |
Prasent Value |
| 0 | -265,000 | 1 | -265000 | |
| 1 | 51000 | 0.9090909 | 46363.64 | |
| 2 | 51000 | 0.8264463 | 42148.76 | |
| 3 | 51000 | 0.7513148 | 38317.05 | |
| 4 | 51000 | 0.6830135 | 34833.69 | |
| 5 | 51000 | 0.6209213 | 31666.99 | |
| 6 | 51000 | 0.5644739 | 28788.17 | |
| 7 | 51000 | 0.5131581 | 26171.06 | |
| 8 | 51000 | 0.4665074 | 23791.88 | |
| 9 | 51000 | 0.4240976 | 21628.98 | |
| 10 | 51000 | 0.3855433 | 19662.71 | |
| 48372.92 | ||||
| Plan -4 | ||||
| Year | Initial Cost |
Annual Benefit |
MARR Factor@10% |
Prasent Value |
| 0 | -180,000 | 1 | -180000 | |
| 1 | 26000 | 0.9090909 | 23636.36 | |
| 2 | 26000 | 0.8264463 | 21487.6 | |
| 3 | 26000 | 0.7513148 | 19534.18 | |
| 4 | 26000 | 0.6830135 | 17758.35 | |
| 5 | 26000 | 0.6209213 | 16143.95 | |
| 6 | 26000 | 0.5644739 | 14676.32 | |
| 7 | 26000 | 0.5131581 | 13342.11 | |
| 8 | 26000 | 0.4665074 | 12129.19 | |
| 9 | 26000 | 0.4240976 | 11026.54 | |
| 10 | 26000 | 0.3855433 | 10024.13 | |
| -20241.3 | ||||
So NPV of all project as per MARR 10% are as follow
| Project | NPV |
| Project -1 | 19638.1171 |
| Project -2 | -7831.4934 |
| Project -3 | 48372.9224 |
| Project -4 | -20241.255 |
From the above calculation we can see that, project -3 has highest NPV so the project-3 will be accepted.
