## Determining Present Value of Project Costs and Benefits

Project costs and benefits are incurred at different times during a project’s life. As such, the process of discounting allows the expression of a stream of costs or benefits as one number in present value terms.

## Comparing Costs and Benefits

Benefit and cost streams form the basis of several measures of project viability:

* Net Present Value (NPV):* NPV is the value resulting from subtracting the expected cost from the expected benefits. Projects with a NPV greater than zero are worth undertaking.

* Benefit – Cost Ratio (BCR)*: the BCR is the ratio of the present value of benefits to the present value of costs. The ratio should be greater than 1.0 for a project to be acceptable

^{[1]}. For example, a BCR of 1.25 indicates that for every $1 of cost, the project will return $1.25 of benefit. BCR is a

*relative*measure of viability.

__Internal Rate of Return (IRR)__* :* the IRR is the discount rate at which the present value of costs equals the present value of benefits. Alternatively, IRR is the discount rate at which NPV = 0 and BCR = 1.0. If IRR exceeds the opportunity cost of the capital, the project is considered to be economically sound and worth pursuing. [2]

**Using Excel to calculate cost-benefit**

Value to Calculate |
Excel Function |
Function Help |

PV |
NPV() | Excel help |

Net Present Value | NPV() | Excel help |

Benefit Cost Ratio | n/a | n/a |

Internal Rate of Return | IRR() | Excel help |

**References:**

^{[1]} It is not in any way inconsistent for a project to have a low positive NPV (because it is a small project) at the same time as it has a high BCR.

[2] The IRR* *is a criteria to be used with caution because: (i) it cannot be calculated for all projects (e.g. projects where the stream of net benefits is strictly positive for each year or projects with multiple IRR); and, (ii) “it is a mathematical concept and not an investment criterion for evaluating alternative cash flows. When the cash flows are irregular, with net costs occurring in the later years of the project, it will give unreliable results in the ranking of alternative options”(Treasury Board of Canada 2007).