Question

10.1 Consider the following probability distribution of returns estimated for a proposed project that involves a new ultrasound machine: State of the Economy Very poor Poor Average Good Very good Probability of Occurrence 0.10 0.20 Rate of Return -10.0% 0.0 0.40 10.0 0.20 20.0 0.10 30.0 a. What is the expected rate of return on the project? b. What is the project's standard deviation of returns? What is the project's co- efficient of variation (CV) of returns? (Hint: CV is defined as the standard deviation of returns divided by the expected rate of return. It measures the amount of risk per unit of return.) c. What type of risk do the standard deviation and CV measure?

Answer 1

Calculation of Standard Deviation of the Project:

• Cumulative Return = Probability of Economy * Return in each State

• Expected Return = Sum of Cumulative Return

• Return Deviation from Expected Return =   Return in each State - Expected Return

• Square Return Deviation from Expected Return = ( Return Deviation from Expected Return) ^2

• Cumulative Square Return Deviation from Expected Return = Probability of Economy * Square Return Deviation from Expected Return

• Variance = Sum of Cumulative Square Return Deviation from Expected Return

• Standard Deviation = Sqrt of ( Variance )

• Co efficient of Variance = Standard Deviation / Expected Return

Ans a :Expected Return = 10.00%

Ans b :Co efficient of Variance = 1.095

Ans c : Standard Deviation and Cv measure total risk related to the project. Total risk issum of systematic and unsystematic risk. As Standard deviation/ coefficient of variance describe variation in final cash flow related to change in any project parameter it measure Total Risk of theproject


  

Calculation :

A B D E F G H 1 Return Cumulative Return 2 3 4 5 6 7 8 State of Economy Probability Very Poor 0.10 Poor 0.20 0.40 0.20 Very Good 0.10 -10.00% 0.00% 10.00% 20.00% 30.00% Return Deviation from Expected Return -20.000% -10.000% 0.000% 10.000% 20.000% -1.000% 0.000% 4.000% 4.000% 3.000% Square Return Deviation from Expected Return 0.0400 0.0100 0.0000 0.0100 0.0400 Average Good Cumulative Square Return Deviation from Expected Return 0.0040 0.0020 0.0000 0.0020 0.0040 9 expected return 10.000% 10 11 12 13 14 Variance Standard Deviation Co efficient of Variance 0.0120 10.95% 1.09544511501033

А B C D E F G H 1 2 Return Cumulative Return State of Economy Probability Very Poor 0.10 Poor 0.20 Average 0.40 Good 0.20 Very Good 0.10 -10.00% 0.00% 10.00% 20.00% 30.00% =C4D4 =C5 D5 =C6*D6 =C7*D7 =C8*D8 Return Deviation from Expected Return =D4-$E$11 =D5-$E$11 =D6-$E$11 =D7-$E$11 =D8-$E$11 Square Return Deviation from Expected Return =F412 =F542 =F642 =F712 =F82 Cumulative Square Return Deviation from Expected Return =G4*C4 =G5*C5 =G6 C6 =G7 C7 =G8 C8 3 4 5 6 7 8 9 10 11 12 13 14 15 expected return =SUM(E4:E8) Variance Standard Deviation Co efficient of Variance =SUM(H4:48) =SQRT (H11) =H12/E11