Chapter 10, Problem 17PROB

Summary Introduction

Scenario Analysis is a technique used to identify the project’s risk and compare the bad and good circumstances with the base case scenario. It considers both the 1) sensitivity of the project’s NPV to its key variables and 2) the change in values of these variables considering their probability distribution.

To carry out the scenario analysis, it is required to calculate the NPV of worst case, best case and base case, followed by the calculation of its standard deviation and co-efficient of variation. If the co-efficient of variation is higher than the average project of the company, the project should be rejected.

Expected NPV, Standard deviation of NPVs and co-efficient of variation of NPVs are calculated as below:

$\begin{array}{c}\text{Expected NPV}={\displaystyle \sum _{i=1}^n{\mathrm{Pr}}_i\left(NP{V}_i\right)}\\ {\mathrm{\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\sigma }}_{NPV}=\sqrt{{\displaystyle \sum _{i=1}^n{\mathrm{Pr}}_i{\left({\text{NPV}}_i-\text{Expected NPV}\right)}^2}}\\ \mathrm{\hspace{1em}\hspace{1em}C}{V}_{NPV}=\frac{{\sigma }_{NPV}}{\text{Expected NPV}}\end{array}$

Here,

Probabilities of the occurrence is “${\mathrm{Pr}}_i$”

NPV for each probability is “$NP{V}_i$”

Standard deviation of NPVs is “${\sigma }_{NPV}$”

Co-efficient of Variation of NPVs is “$C{V}_{NPV}$”

After conducting a scenario analysis, it is estimated, that the NPV of the project for all the three scenarios is as follows. Determine whether the project should be accepted or rejected if the maximum allowable co-efficient of variation is 0.8.

Scenario	Probability	NPV
Best Case	20%	$31,500
Base Case	70%	$19,800
Worst Case	10%	-$20,100