Blog: Mgt201 GDB solution

“Discussion Question”

The annual expected returns and related probabilities associated with a new investment opportunity analyzed by a local firm are here as under:

Rate of Return (%)

-10

20

45

60

100

Probability of Returns

0.010

0.450

0.320

0.140

0.080

You are required to calculate the following:

a.The expected Rate of Return

b.The standard deviation of the returns

c.The coefficient of variation of the returns

d.If another investment of similar risk bears CV of 0.50. Then compare the CV calculated in No. (iii), and guide about the riskiness of the new investment.


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Solution:


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.