| Question 5 (a): | ||||||
| Step 1: | ||||||
| Calculation of Equivalent Annual Annuity of Projects B and D | ||||||
| Year | Project B | Project D | ||||
| Cash Flows | Discount Rate @10% | Discounted Cash flows | Cash Flows | Discount Rate @10% | Discounted Cash flows | |
| 0 | -1000 | 1 | -1000 | -1000 | 1 | -1000 |
| 1 | 300 | 0.909090909 | 272.7272727 | 600 | 0.909090909 | 545.4545455 |
| 2 | 400 | 0.826446281 | 330.5785124 | 800 | 0.826446281 | 661.1570248 |
| 3 | 500 | 0.751314801 | 375.6574005 | |||
| 4 | 600 | 0.683013455 | 409.8080732 | |||
| NPV | 388.7713 | 206.6116 | ||||
| Equivalent Annual Annuity of Project B = NPV / Annuity Discount Factor | ||||||
| = 388.7713 / 4.16985446 | ||||||
| = 93.23 | ||||||
| Equivalent Annual Annuity of Project D = NPV / Annuity Discount Factor | ||||||
| = 206.6116 /2.73553719 | ||||||
| = 75.53 | ||||||
| Step 2: | ||||||
| Calculation of NPV of Projects B and D using Replacement Chain Method | ||||||
| In this case project B should be repeated 3 times and project D for 5 times | ||||||
| So that projects will have equal life | ||||||
| Year | Project B | Project D | ||||
| Cash Flows | Discount Rate @10% | Discounted Cash flows | Cash Flows | Discount Rate @10% | Discounted Cash flows | |
| 0 | -1000 | 1 | -1000 | -1000 | 1 | -1000 |
| 1 | 300 | 0.909090909 | 272.7272727 | 600 | 0.909090909 | 545.4545455 |
| 2 | 400 | 0.826446281 | 330.5785124 | 800 | 0.826446281 | 661.1570248 |
| 3 | 500 | 0.751314801 | 375.6574005 | -1000 | 0.751314801 | -751.3148009 |
| 4 | 600 | 0.683013455 | 409.8080732 | 600 | 0.683013455 | 409.8080732 |
| 5 | -1000 | 0.620921323 | -620.9213231 | 800 | 0.620921323 | 496.7370584 |
| 6 | 300 | 0.56447393 | 169.342179 | -1000 | 0.56447393 | -564.4739301 |
| 7 | 400 | 0.513158118 | 205.2632473 | 600 | 0.513158118 | 307.8948709 |
| 8 | 500 | 0.46650738 | 233.2536901 | 800 | 0.46650738 | 373.2059042 |
| 9 | 600 | 0.424097618 | 254.458571 | -1000 | 0.424097618 | -424.0976184 |
| 10 | -1000 | 0.385543289 | -385.5432894 | 600 | 0.385543289 | 231.3259737 |
| 11 | 300 | 0.350493899 | 105.1481698 | 800 | 0.350493899 | 280.3951196 |
| 12 | 400 | 0.318630818 | 127.4523271 | -1000 | 0.318630818 | -318.6308177 |
| 13 | 500 | 0.28966438 | 144.8321899 | 600 | 0.28966438 | 173.7986278 |
| 14 | 600 | 0.263331254 | 157.9987526 | 800 | 0.263331254 | 210.6650034 |
| NPV | 780.0557731 | 631.9250345 | ||||
| Step 3: | ||||||
| Project B | Project D | |||||
| WACC | 10% | 10% | ||||
| Equivalent Annual Annuity | 93.23 | 75.53 | ||||
| Replacement Chain (RC) NPV | 780.06 | 631.93 | ||||
Question 5b:
Project B should be selected as Equivalent Annual Annuity and Replacement Chain (RC) NPV for Project B is higher than Project D
| Step 1: | ||||||||||||
| Year | Project A | Project B | Project C | Project D | ||||||||
| Cash Flows | Discount Rate @10% | Discounted Cash flows | Cash Flows | Discount Rate @10% | Discounted Cash flows | Cash Flows | Discount Rate @10% | Discounted Cash flows | Cash Flows | Discount Rate @10% | Discounted Cash flows | |
| 0 | -1000 | 1 | -1000 | -1000 | 1 | -1000 | -1000 | 1 | -1000 | -1000 | 1 | -1000 |
| 1 | 1000 | 0.909090909 | 909.0909091 | 300 | 0.909090909 | 272.7272727 | 550 | 0.909090909 | 500 | 600 | 0.909090909 | 545.4545455 |
| 2 | 0.826446281 | 0 | 400 | 0.826446281 | 330.5785124 | 450 | 0.826446281 | 371.9008264 | 800 | 0.826446281 | 661.1570248 | |
| 3 | 0.751314801 | 0 | 500 | 0.751314801 | 375.6574005 | 350 | 0.751314801 | 262.9601803 | ||||
| 4 | 0.683013455 | 0 | 600 | 0.683013455 | 409.8080732 | 250 | 0.683013455 | 170.7533638 | ||||
| NPV | -90.9091 | 388.7713 | 305.6144 | 206.6116 | ||||||||
| Step 2: | ||||||||||||
| Equivalent Annual Annuity of Project A = NPV / Annuity Discount Factor | ||||||||||||
| = -90.9091 /1.909091 | ||||||||||||
| = -47.14 | ||||||||||||
| Equivalent Annual Annuity of Project B = NPV / Annuity Discount Factor | ||||||||||||
| = 388.7713 / 4.16985446 | ||||||||||||
| = 93.23 | ||||||||||||
| Equivalent Annual Annuity of Project C = NPV / Annuity Discount Factor | ||||||||||||
| = 305.6144 /4.16985446 | ||||||||||||
| = 73.29 | ||||||||||||
| Equivalent Annual Annuity of Project D = NPV / Annuity Discount Factor | ||||||||||||
| = 206.6116 /2.73553719 | ||||||||||||
| = 75.53 | ||||||||||||
| Step 3: | ||||||||||||
| Project B and C has higher NPV hence these should be selected based on NPV rule | ||||||||||||
| Project B and D has higher Equivalent Annual Annuity is higher hence these should be selected based on EAA rule | ||||||||||||
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