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CA Intermediate · Financial Management and Strategic Management · Investment Decisions

Vistara Foods must choose one of two mutually exclusive machines, each replaceable with an identical machine at the end of its life. Machine X has a 2-year life and NPV of ₹86,775 at 10%. Machine Y has a 3-year life and NPV of ₹1,12,000 at 10%. Annuity factors at 10% are 1.7355 for 2 years and 2.4869 for 3 years. Which machine should be chosen and why?

Machine X should be chosen. With unequal lives, projects are compared by equivalent annual annuity, which is NPV divided by the annuity factor. X gives about ₹50,000 a year while Y gives about ₹45,036, so X is better even though Y has the higher total NPV.

  1. AMachine Y, because its NPV of ₹1,12,000 is higher
  2. BMachine X, because its equivalent annual annuity is about ₹50,000 against about ₹45,036 for YCorrect
  3. CMachine Y, because its equivalent annual annuity is about ₹45,036, which is higher
  4. DMachine X, because its equivalent annual annuity is about ₹43,388

Explanation

With unequal lives and replacement, compare equivalent annual annuity (NPV / annuity factor). X = 86,775 / 1.7355 = 50,000. Y = 1,12,000 / 2.4869 = 45,036. X has the higher annual benefit, so choose X. Comparing raw NPVs ignores the different lives, and 43,388 is just NPV/2, which ignores discounting.

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