• Description of the profitability index approach to ranking capital projects.
  • Computing the profitability index for given projects. 
  • Ranking of projects by using profitability index. 
  • Describing the equivalent annual annuity approach to ranking capital projects.
  • Describing the step in applying the equivalent annual annuity approach. 
  • Describing and applying certain approaches to overcome and deal with uncertainty in the evaluation of capital projects. 

Once an entity finds the economic projects that can be effectively executed, acceptable projects need to be ranked in terms of desirability. While the NPV and Internal Rate of Return approaches provide a measure of relativity, neither can take into account the relative cost of executing each project. This topic sheds light on the profitability index, a measure designed to rank projects in terms of how desirable they are to the economy. Other topics discussed here are the equivalent annual annuity approach to ranking capital projects and certain approaches to dealing with uncertainty in capital project evaluation. 

Profitability Index - The profitability index (PI), also called the cost/benefit ratio or PV index. It provides a way of ranking projects by taking into account both the cash flow benefit expected from each project and the cost of each project. 

  1. The PI determines the benefit-to-cost ratio of a project (or other investment) by computing the value provided per unit (dollar) of investment in a project. 
  2. The PI for each project may be computed using either the PV of the future cash inflows or the net present value (NPV) (Net Present Value = Net Cash Inflows and Outflows, Including the initial project cost) of a project, with either of these values divided by the initial project cost. 
    • When the PV of future cash inflows is used, the PI for each project would be computed as:
      • PI=PV of Cash Inflows/Project Cost 
      • A project would be economically feasible and logically accepted only if the PI > or equal to 1; otherwise, the present value of cash inflows would be less than the cost of the project. 
      • The resulting percentage index (> or equal to 1) for each project can be used to rank several projects. The higher the percentage, the higher the rank of the project. 
  • When the NPV is used, the PI for each project would be computed as PI = NPV/Project Cost
    • A project would be economically acceptable if the NPV is zero or positive (PV of expected cash inflows is equal to or greater than the PV of expected cash outflows). Thus, the resulting PI would be greater than or equal to 0, which means the project is providing value at least equal to the discount rate used. (e.g. WACC). 
    • The resulting percentage index (>or=0) for each project can be used to rank projects. The higher percentage determines the high rank of the project. 

II. Example -

A. The following shows the determination of the profitability index (PI) for two projects being considered using assumed values for PV (or alternatively, NPV):

Project A = PV (or NPV) = $60,000 / Initial cost = $50,000 = 1.20 Pl

Project B = PV (or NPV) = $110,000 / Initial cost = $100,000 = 1.10 Pl

  1. Based solely on present values or NPV, Project B which is worth $110,000 would be ranked higher than Project A which is $60,000. However, when the amount of the initial investment is taken into account, project A has a higher profitability index (PI=1.20) than Project B (PI=1.10). That result comes about because of the much lower initial investment cost of Project A. 

III. Equivalent Annual Annuity Approach - 

The equal annual annuity approach (EAA) provides a means of comparing projects, especially those with unequal lives. 

A. The EAA calculates the constant annual cash flow generated by a project over its entire life as if it were an annuity and uses the PV of that cash flow as a basis for comparing projects. 

B. The EAA is calculated for each project in the following manner: 

  1. The NPV for each project is determined. 
  2. For each project, the annual cash flows that when discounted (at the cost of capital or another discount rate) for the life of the project exactly equals the NPV of the project; the dollar amount so determined is the EAA for the project. 

The formula used to compute the EAA would be:


In this equation, r is the discount rate, NPV is net present value and n is the number of periods. Luckily, the formula for the above calculation can be found on most financial calculators and computer applications. The outcome and the result would depend on which equation calculates the highest EAA. The project with the highest EAA is the most desirable project to pursue. 

IV. Capital Budgeting Risks -

Capital budgeting analysis uses projections and assumptions. There is a risk that the actual outcomes might vary from the results of the analysis. A number of techniques have been developed to incorporate uncertainty and to measure risks in a project analysis. Those techniques include:

  • Probability Assignment - 
    • In this approach, probabilities are assigned to possible outcomes. These probabilities may be assigned based on past experience, industry-wide measures, forecasts, simulation or other bases. Once possible outcomes have been identified and probabilities have been assigned, an expected value can be determined. 

For Example:

  • Assigning probabilities to cash inflows:
    • PV of Possible Cash Inflows                      Probability of Each Cash Flow                      Expected Value (EV)
    • $125,000 (Pessimistic)                                             .20                                                         $25,000
    • 150,000 (most likely)                                                 .60                                                        $90,000
    • 200,000 (optimistic)                                                   .20                                                        $40,000
    •                                                                                    1.00                                                      $155,000

The computed $155,000 is a probability-adjusted estimate of the cash inflows to be received from the project. Note: It is $5000 more than the most likely value estimate. 

Using expected value data, management also can determine the standard deviation (an estimate of how each expected outcome differs from the mean) and the coefficient of correlation (which provides a measure of risk that is normalized for the size [amount] of the investment). 

  • Risk-Adjusted Discount Rates - 
    • In this approach of addressing uncertainty in project assessment, different discount rates are used for projects with different levels of risk. For a project with a higher or lower level of risk, a higher or lower discount rate would be used. 
  • Time-Adjusted Discount Rates -
    • In this approach, cash flows associated with the later years of a long-term project are discounted at a higher rate than cash flows of the earlier years. The use of a higher discount rate for upcoming years reflects the increased uncertainty in making longer-term projections. 
  • Sensitivity Analysis -
    • This approach entails that the most likely set of assumptions are used to compute the most likely set of an outcome. Then one of the assumptions is changed, and the resulting outcome is determined. This process of changing one assumption at a time is repeated until the effect of changing each major assumption separately on the final outcome is known. This process allows management to consider how sensitive the outcome is to each major assumption. 
  • Scenario Analysis -
    • This approach is similar to sensitivity analysis except that rather than changing one assumption (variable) at a time, many related assumptions are changed simultaneously. This enables management to determine the range of possible outcomes that may occur. 
  • Other Risk Consideration Approaches -
    • ​​​​​​​In addition to the foregoing approaches for recognizing and measuring risk inherent in project analysis, firms might also employ:
      • Simulation
      • Decision-tree analysis

Conclusion -

When ranking acceptable capital projects, methods based on discounted values are much better than methods that do not incorporate the time value of money. The NPV method and, especially the profitability index derived using NPV and the initial project cost, generally are preferred more than the other methods. The final analysis displays some degree of subjectivity which will affect which projects get implemented. 

  • Once capital budgeting (project investments) decisions have been made, the impact of these plans must be built into other affected budgets. For example, a planned new project might have implications for sales revenue, production costs and cash inflows with asset acquisition. 
  • Since the beginning, a project should be monitored frequently to ensure that it continues to meet the entity’s requirements for acceptability.