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CA Intermediate · Financial Management and Strategic Management · Investment Decisions

Aarav Ltd must choose between two mutually exclusive projects, X and Y, with unequal lives. Project X: NPV Rs 1,20,000 over 3 years. Project Y: NPV Rs 1,60,000 over 5 years. Cost of capital is 10%. PV annuity factors at 10%: 3 years 2.487, 5 years 3.791. Using the equivalent annual annuity (EAA) approach, which project should be selected and what is its EAA (rounded to nearest rupee)?

Project X should be selected with an EAA of Rs 48,251. Dividing each NPV by its annuity factor gives X 48,251 and Y 42,205. The higher annual equivalent wins, even though Y has the larger total NPV, because the lives differ.

  1. AProject X, EAA Rs 48,251Correct
  2. BProject Y, EAA Rs 42,205
  3. CProject X, EAA Rs 42,205
  4. DProject Y, EAA Rs 48,251

Explanation

EAA of X = 1,20,000/2.487 = Rs 48,251. EAA of Y = 1,60,000/3.791 = Rs 42,205. X has the higher EAA, so X is selected. Choosing Y by higher raw NPV ignores the unequal lives.

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