Cost-benefit analysis and the environment 


  • A project is an investment activity where labour and/or capital is spent to create producing asset from which we can expect future benefits. A project is characterised by

    • Specific starting and ending points
    • Its major costs and returns are measurable
    • It should have a specific geographic location
    • It should have a specific clientele group
    • It should have a well defined time sequence of investment and production activities


"Continuous and Discrete Time Discounting" from the Wolfram Demonstrations Project
Explore the effect of discounting by visiting the Wolfram demonstration (click on the graph to the left).

Project budgeting is done by one (or more) of the following methods:

Capital budgeting methods

  • Payback period: which measures the time required for the cash inflows to equal the original outlay. It measures risk, not return.
  • Cost-benefit analysis: which includes issues other than cash, such as time savings.
  • Real option method: which attempts to value managerial flexibility that is assumed away in NPV.
  • Internal rate of return: which calculates the rate of return of a project without making assumptions about the reinvestment of the cash flows (hence internal).
  • modified internal rate of return (MIRR): similar to IRR, but it makes explicit assumptions about the reinvestment of the cash flows. Sometimes it is called Growth Rate of Return.

Three principles

Of the five alternatives above there are really only three different principles of project evaluation:
  • Payback
  • Cost-Benefit (including real option)
  • Internal Rate of Return (including MIRR)


does not include discounting, it purely a matter of time when the initial investment is covered. When a cash amount of C is received every year (t) after an investment I, the payback is (t I)/C. Payback is one (all investment covered) after t years, t = C/I.

Key cost-benefit indicators:

  • PVB (present value of benefits);
  • PVC (present value of costs);
  • NPV (PVB less PVC);
  • NPV/k (where k is the level of funds available) and
  • BCR (benefit cost ratio, PVB divided by PVC).

Internal rate of return (IRR)

IRR is similar to NPV, but solved for the discount rate rather than the present (or future) value. See also the table below.

Economic Evaluation factors

 Name Formula Solves for
 Single-payment, present worth
 Present worth
 Future worth
 Single-payment, compound amount
 Future worth Present worth
 Uniform-series, present worth

 Present worth Annualised worth
Annualised worth 
 Present worth
 Sinking fund
 Annualised worth Future worth 
Uniform-series, compound amount 
 Future worth Annualised worth 

A project overview is often presented by Gantt charts, as in the figure below, where the different activities are planned in time.