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

A company has a one-period capital constraint, and projects X, Y and Z are divisible. A linear programming formulation gives a shadow price of $0.28 on the capital constraint. What does this figure most appropriately indicate?

A shadow price of $0.28 means that each additional dollar of capital in the constrained period would raise total NPV by about 28 cents, within the range over which the current solution stays optimal. It is a marginal NPV value, not a discount rate or IRR.

  1. AThe company's cost of capital is 28%
  2. BThe NPV increases by about $0.28 for each extra $1 of capital available now, within the relevant rangeCorrect
  3. CThe profitability index of the best project is 0.28
  4. DThe internal rate of return of the marginal project is 28%

Explanation

A shadow price (dual value) measures the marginal increase in the objective, here total NPV, from relaxing the constraint by one unit, valid over a limited range. It is not a discount rate or an IRR. It equals the profitability index of the marginal project in a simple single-period case but is not interpreted as a return rate.

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