Question

Swift manufacturing must choose between two asset purchases. The annual rate of return and the related probabilities given in the following table summarises the firms analysis to this point

Rate of return	Probability	Rate of return	Probability
-10%	.01	10%	.05
10	.04	15	.010
20	.05	20	.10
30	.10	25	.15
40	.015	30	.20
45	.30	35	.15
50	.15	40	.10
60	.10	45	.10
70	.05	50
80	.04
100	.01

For each project compute and construct a bar chart for each distribution of rates of return, which project would you consider less risky – why?

• Range of possible rates of return
• The expected value of return
• Standard deviation of the return
• Coefficient of variation of the return

Answer 1

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Answer:

Project 257 ((Ri - 0.450)^2) X Pi (Ri - 0.30)^2 (Ri - 0.30)^2 x Pi 0.01) 0.003025 0.0049 0.003125 0.002251 0.000375 Project 432 Weighted Rate of Return (RI) Probability (Pi) Value = (RIX (Ri - 0.30) Pi) 10% 0.05 0.005 -20.00% 15% 0.11 0.015 - 15.00% 20% 0.1 0.02 -10.00% 25% 0.15) 0.0375 -5.00% 30% 0.06 0.00% 35% 0.0525 5.00% 40% 10.00% 45% 0.11 0.045) 15.00% 50% 0.05 0.025 20.00% Rate of Return (Ri) Weighted Value Probability (Pi) (Ri - 0.450) (Ri - 0.450)^2 = (Ri X Pi) -10% -0.001 - 55.00% 0.3025 10% 0.04 0.004 - 35.00% 0.1225 20% 0.05 0.01 -25.00% 0.0625 30% 0.03 -15.00% 0.0225 40% 0.06 -5.00% 0.0025 45% 0.135 0.00% 01 50% 0.0751 0.0025) 60% 0.1 0.06 15.00% 0.0225 70% 25.00% 0.0625 80% 0.04 0.032 3 5.00% 0.1225 100% 0.01 55.00% 0.3025 Sum of weighted value 0.45 Sum of ((Ri - 0.450)^2) X Pi 0.0225 0.01 0.0025 0.00 0.0022 0.00 0.00037 0.15 5.0096 0.04 0.0025 0.01 0.0225 0.04 0.00037 0.00 0.0022 0.00 0.051 0.0003751 0.00225 0.003125 0.0049 0.003025 0.02735 Sum of weighted value 0.300 Sum of ((Ri - 0.30)^2) X Pi 0.0112 Range = 100%- (-10%) = 110% Range = 50% - (10%) = 40.0% Expected Return = Sum of Weighted Value Expected Return (Er) = 0.45 Expected Return = Sum of Weighted Value Expected Return (Er) = 0.3 Variance = Sum of ((Ri - 0.450)^2) X Pi = Variance = 0.02735 Variance = Sum of ((Ri - 0.30)^2) X Pi = Variance = 0.01125 Standard Deviation = (Variance)^(1/2) Standard Deviation = =0.02735^(1/2) Standard Deviation = 0.1654 Standard Deviation = (Variance)^(1/2) Standard Deviation = =0.01125^(1/2) Standard Deviation = 0.1061 Coeficient of Variation of the Reutrns = Standard Deviaton/Expected Return (ET) Standard Deviaton/Expected Return (Er) Coeficient of Variation of the Reutrns = Coeficient of Variation of the Reutrns = Coeficient of Variation of 0.16537/0.45 = the Reutrns = 0.3675 =0.1061/0.30 = 0.3536 0.25 Probability Probability 10% 15% 20% 25% 30% 35% 40% 45% 50% -10% 10% 20% 30% 40% 45% 50% 60% 70% 80% 100%

Since Project 432 has lower coeficient of variation than Project 257, this implies the Project 432 has lower risk.