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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Project appraisal

A machine costs Rs 500,000. It generates net cash flow of Rs 80,000 at the end of each year for 10 years and is then sold for Rs 100,000 at the end of year 10. At an effective annual rate of 9%, what is the net present value?

The NPV is Rs 55,653.69. The annuity of 80,000 for 10 years at 9% is worth 513,412.61, and the resale value of 100,000 at year 10 is worth 42,241.08 today. The total of 555,653.69 less the cost of 500,000 gives the NPV.

  1. ARs 13,412.61
  2. BRs 113,412.61
  3. CRs 55,653.69Correct
  4. DRs 101,860.83
  5. Rs 21,859.05

Explanation

v^10 = 0.422411 and a10 = (1 − 0.422411)/0.09 = 6.417658. PV = 80,000 × 6.417658 + 100,000 × 0.422411 = 513,412.61 + 42,241.08 = 555,653.69. NPV = 55,653.69. Omitting the resale value gives 13,412.61, and leaving the resale undiscounted gives 113,412.61.

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