[ vuZs.net ] MGT201 GDB Solution 27 May,2011 By Saqib Samin

Answers

The expected Rate of Return = 39.7% The standard deviation of the returns=23.5989 % The coefficient of variation of the returns =0.5944 Comment about the riskiness of the new investment = New project with CV=0.5 is less riskier than the CV =0.5944, so new investment should be preferred

 

 

Solution:

a) Expected rate of return

Expected ROR = < r > = pi ri

      = p1 (r1) + p2 (r2) + p3 (r3) + p4(r4) + p5(r5)

     = 0.010 ( -10%) + 0.450 ( 20%) + 0.320 ( 45%) + 0.140(60%) + 0.080 (100%)

      = - 0.1% + 9% + 14.4% + 8.4% + 8 %

     = 39.7%

b) The standard deviation of the returns

Risk = Std Dev = ( r i - < r i > )2 p i

                        = Std Dev = δ = √ Σ (r i - < r i >)² p i.

= √{[(-10-39.7)2 (0.010)] + [(20-39.7)2 (0.0.450)] + [(45-39.7)2 (0.320)] + [(60-39.7)2(0.140) + [(100-39.7)2(.080) }

=√ (24.7009 + 174.6405 + 8.9888 + 57.6926 + 290.8872)

= √ (556.91)

=√557

Standard Deviation, δ = 23.5989

c) Coefficient of variation , CV = Standard Deviation  = 23.5989 / 39.7

    Expected Return

= 0.5944

d) Coefficient of Variation tells us about the Risk per unit Return. The project which offers lowest per unit risk is the best investment. 0.5944 > 0.5. The new investment offer the CV of 0.50 which is lower than calculated CV in part (iii) is 0.5944. Choose the Project with the Lowest CV i-e CV=0.5. As it carries the lowest Risk per unit Return than 0.5944.

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