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

A project has a single initial outlay followed only by positive cash inflows. It is appraised at a positive effective discount rate of 8% per annum. Which statement is necessarily true?

The discounted payback period, where it exists, is never shorter than the simple payback period. Discounting at a positive rate shrinks each inflow, so cumulative discounted inflows lag cumulative undiscounted inflows and take at least as long to reach the initial outlay.

  1. AThe discounted payback period, where it exists, is never shorter than the simple payback period.Correct
  2. BThe discounted payback period is always shorter than the simple payback period.
  3. CA discounted payback period exists whenever a simple payback period exists.
  4. DA project that has a discounted payback within its life must have a negative NPV at 8%.
  5. The discounted payback period does not depend on the discount rate used.

Explanation

Discounting at a positive rate reduces every inflow, so the cumulative discounted inflows never exceed the cumulative undiscounted ones. Recovery of the outlay therefore takes at least as long. A project can have a simple payback but no discounted payback if the discounted inflows never reach the outlay. Recovery within the project's life means NPV is non-negative, not negative.

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