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

A project requires an outlay of Rs 50,000 now and pays Rs 20,000 at the end of each half-year for 18 months (three payments). The cost of capital is 12% per annum nominal, convertible half-yearly. Given a(3) at 6% = 2.673012, what is the NPV?

The NPV is Rs 3,460.24. The nominal 12% convertible half-yearly means 6% per half-year, so the three payments of Rs 20,000 have a present value of Rs 53,460.24, which exceeds the Rs 50,000 outlay by that amount.

  1. ARs 6,667.85
  2. BRs 3,460.24Correct
  3. C-Rs 1,963.38
  4. DRs 10,000.00
  5. Rs 53,460.24

Explanation

The half-yearly rate is 12%/2 = 6%. PV of inflows = 20,000 x 2.673012 = 53,460.24. NPV = 53,460.24 - 50,000 = 3,460.24. Using 12% per half-year gives -1,963.38, which wrongly applies the nominal rate to each period. Rs 53,460.24 is the PV of inflows, not the NPV.

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