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

A project has net cashflows of −₹100 at time 0, +₹230 at time 1 and −₹132 at time 2. Which statement about its IRR is correct?

There are two IRRs, 10% and 20%. The cashflow signs change twice (negative, positive, negative), so the equation of value is a quadratic in v with two positive roots. Both rates give a zero net present value, so the IRR is not unique.

  1. AThere is a unique IRR of 10%
  2. BThere are two IRRs, 10% and 20%Correct
  3. CThere is no real IRR
  4. DThere is a unique IRR of 15%, the average of the interest rates tried
  5. There is a unique IRR of 20%

Explanation

The equation −100 + 230v − 132v² = 0 has two positive roots because the cashflow signs change twice. At 10%: −100 + 209.09 − 109.09 = 0. At 20%: −100 + 191.67 − 91.67 = 0. Both rates satisfy the equation, so the IRR is not unique and cannot be used alone for decisions.

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