## Saturday, 3 June 2017

### Flexibility: The inclusion of flexibility into the analysis is generally more relevant in the valuation of individual businesses and projects.

Net present values (NPVs) calculated from single cash flow projections may be inadequate because they do not take into account the ability to expand or scale back.

Here is a simple example.

A firm can scale back by eliminating a negative cash flow project after the first period.

There is a 60% probability of \$20 per year forever or 40% probability of -\$6 per year forever.

The discount rate is 10%.

Without an option to cancel

If the initial cost today is \$100, then without an option to cancel, the NPV would be:

-\$100 + 0.6 x (\$20/0.10) + 0.4 x (-\$6/0.10) = -\$4

With an option to cancel after the first year

With the option to abandon after the first year, the NPV would be:

-\$100 + 0.6 x (\$20/0.10) + 0.4 x (-\$6/1.10) = \$17.82

The value of the option to cancel the project is the difference, or \$21.82

Conclusion:

The inclusion of flexibility into the analysis is generally more relevant in the valuation of individual businesses and projects.

The real-option valuation (ROV) and decision tree analysis (DTA) are the two primary methods of valuation.

• Both depend on forecasting based on contingent states of the world.
• Although ROV is often a better methodology to use than DTA, it is not the right approach in every case.