Industries is considering a proposed project whose estimated NPV is $12 million.
ID: 2776726 • Letter: I
Question
Industries is considering a proposed project whose estimated NPV is $12 million. This estimate assumes that economic conditions will be "average." However the CFO realizes that conditions could be better or worse, so she performed a scenario analysis and obtained these results: Calculate the project's expected NPV, standard deviation, and coefficient of variation. Round you answers to two decimal places. Enter your answers for the project's expected standard deviation in millions. For example an answer of $13,000,000 should be entered as 13.Explanation / Answer
Expected NPV = $ 5.7 million
Standard Deviation npv= $ 20.84 million
Coefficient of Variance CV = 3.66
Economic Scenario
Probability
NPV
Probability * NPV
Recession
0.05
-$ 58 Million
-$2.9 Million
Below Average
0.20
-$18 Million
-$3.6Million
Average
0.50
$12 Million
$ 6 Million
Above Average
0.20
$22 Million
$ 4.4 Million
Boom
0.05
$ 36 Million
$1.8 Million
Expected NPV = Sum (Probability * NPV) = $ 5.7 Million
Variance = Sum (probability * (NPV-Expected NPV)^2)
Variance = 0.05 *(-58-5.7)^2+0.2*(-18-5.7)^2+0.5*(12-5.7)^2+0.2*(22-5.7)^2+0.05*(36-5.7)^2
= 0.05 * 4057.69 + 0.2*561.69+.5*39.69+0.2*265.69+0.05*918.09
= 202.8845+112.338+19.845+53.138+45.9045
= 434.11
Standard Deviation of NPV = Square root (434.11) = (434.11)^1/2 = 20.8353 or 20.84 (rounded off)
Coefficient of Variance = Standard Deviation / Mean (or expected NPV)
= 20.84/5.7 = 3.656 or 3.66
Economic Scenario
Probability
NPV
Probability * NPV
Recession
0.05
-$ 58 Million
-$2.9 Million
Below Average
0.20
-$18 Million
-$3.6Million
Average
0.50
$12 Million
$ 6 Million
Above Average
0.20
$22 Million
$ 4.4 Million
Boom
0.05
$ 36 Million
$1.8 Million