Question

Possible outcomes for three investment alternatives and their probabilities of occurrence are given next.      

	Alternative 1							Alternative 2							Alternative 3
	Outcomes			Probability				Outcomes			Probability				Outcomes			Probability
Failure		60			0.40				80			0.20				70			0.30
Acceptable		85			0.40				150			0.40				275			0.60
Successful		140			0.20				220			0.40				410			0.10

Using the coefficient of variation, rank the three alternatives in terms of risk from lowest to highest. (Do not round intermediate calculations. Round your answers to 3 decimal places.)

	Coefficient of Variation	Rank
Alternative 1
Alternative 2
Alternative 3

Answer 1

Answer :

	Coefficient of Variation	Rank
Alternative 1	0.340	2
Alternative 2	0.319	1
Alternative 3	0.485	3

Calculation :

Calculation of Coefficient of Variation for Alternative 1

Coefficient of Variation = Standard Deviation / Mean

Calculation of Mean

Mean = Sum of (Outcomes * Probabilities)

= (60 * 0.40) + (85 * 0.40) + (140 * 0.20)

= 24 + 34 + 28

= 86

Calculation of Standard Deviation

Standard Deviation = (Sum of Square of Variation from Mean )^(1/2)

Below is the table showing Calculation of Standard Deviation

Possible Outcomes	Outcomes	Probabilities	(d=Outcomes - Mean)	d^2	p*(d^2)
Failure	60	0.40	-26 (60 - 86)	676	270.40 (676 * 0.40)
Acceptable	85	0.40	-1 (85 - 86)	1	0.40 (1 * 0.40)
Successful	140	0.20	54 (140 - 86)	2916	583.20 (2916 * 0.20)
				Total	854

Standard Deviation = [Sum of (p * d^2 ]^(1/2)

= (854)^(1/2)

= 29.2233

Coefficient of Variation = 29.2233 / 86

= 0.3398 or 0.340

Calculation of Coefficient of Variation for Alternative 2

Coefficient of Variation = Standard Deviation / Mean

Calculation of Mean

Mean = Sum of (Outcomes * Probabilities)

= (80 * 0.20) + (150 * 0.40) + (220 * 0.40)

= 16 + 60 + 88

= 164

Calculation of Standard Deviation

Standard Deviation = (Sum of Square of Variation from Mean )^(1/2)

Below is the table showing Calculation of Standard Deviation

Possible Outcomes	Outcomes	Probabilities	(d=Outcomes - Mean)	d^2	p*(d^2)
Failure	80	0.20	-84 (80 - 164)	7056	1411.20 (7056 * 0.20)
Acceptable	150	0.40	-14 (150 - 164)	196	78.40 (196 * 0.40)
Successful	220	0.40	56 (220 - 164)	3136	1254.4 (3136 * 0.40)
				Total	2744

Standard Deviation = [Sum of (p * d^2 ]^(1/2)

= (2744)^(1/2)

= 52.3832

Coefficient of Variation = 52.3832 / 164

= 0.3194 or 0.319

Calculation of Coefficient of Variation for Alternative 3

Coefficient of Variation = Standard Deviation / Mean

Calculation of Mean

Mean = Sum of (Outcomes * Probabilities)

= (70 * 0.30) + (275 * 0.60) + (410 * 0.10)

= 21 + 165 + 41

= 227

Calculation of Standard Deviation

Standard Deviation = (Sum of Square of Variation from Mean )^(1/2)

Below is the table showing Calculation of Standard Deviation

Possible Outcomes	Outcomes	Probabilities	(d=Outcomes - Mean)	d^2	p*(d^2)
Failure	70	0.30	-157 (70 - 227)	24649	7394.70 (24649 * 0.30)
Acceptable	275	0.60	48 (275 - 227)	2304	1382.40 (2304 * 0.60)
Successful	410	0.10	183 (410 - 227)	33489	3348.90 (33489 * 0.10)
				Total	12126

Standard Deviation = [Sum of (p * d^2 ]^(1/2)

= (12126)^(1/2)

= 110.1181

Coefficient of Variation = 110.1181 / 227

= 0.4851 or 0.485