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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Present value and accumulated value of cashflow streams

A project costs Rs 50,000 now and returns Rs 20,000, Rs 25,000 and Rs 18,000 at the end of years 1, 2 and 3 respectively. At an effective annual rate of 8%, what is the net present value?

The net present value is Rs 4,240.97. The three inflows discount to Rs 54,240.97 at 8%, and subtracting the Rs 50,000 initial outlay, which is already at time 0, leaves a positive NPV. Ignoring discounting or the outlay gives wrong values.

  1. ARs 4,240.97Correct
  2. BRs 13,000.00
  3. CRs 54,240.97
  4. DRs 222.19
  5. Rs 4,580.25

Explanation

PV of inflows = 20,000/1.08 + 25,000/1.1664 + 18,000/1.259712 = 18,518.52 + 21,433.47 + 14,288.98 = 54,240.97. NPV = 54,240.97 - 50,000 = 4,240.97. Rs 54,240.97 omits the outlay, and Rs 13,000 ignores discounting.

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