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ACCA Strategic Professional · Advanced Financial Management · Discounted cash flow techniques

A company faces capital constraints at time 0 and again at time 1, and its projects are divisible. Why is ranking projects by a single profitability index unsuitable here?

A single profitability index fails because each project consumes scarce funds in more than one period, and no single ratio captures this. The optimal mix must be found with linear programming, maximising NPV subject to a funds constraint for each period, which also gives shadow prices.

  1. ABecause NPV cannot be calculated when funds are limited in more than one period
  2. BBecause projects use different amounts of each period's scarce funds, so no single ratio ranks them, and linear programming is needed to find the optimal mixCorrect
  3. CBecause the profitability index is only valid when projects are indivisible
  4. DBecause multi-period rationing means the cost of capital no longer applies, so IRR must be used instead

Explanation

With two binding constraints, a project's efficiency depends on how it uses funds in both periods, so one ratio cannot rank projects. The optimum is found by formulating an LP that maximises NPV subject to a constraint for each period, which also yields shadow prices. NPV remains the objective, and divisibility is the usual assumption for the LP.

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