Cost-benefit analysis and the environment

### Basics:

- 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

*IMPORTANT*:

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)

### Payback

### 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:

### 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 | Given |

Single-payment, present worth | Present worth | Future worth | |

Single-payment, compound amount | Future worth | Present worth | |

Uniform-series, present worth | Present worth | Annualised worth | |

Capital-recovery | 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.