Assessing return and risk
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Assessing return and risk. Swift Manufacturing must choose between two asset purchases. The annual rate of return and the related probabilities given in the following table summarize the firm’s analysis to this point. Project 257 Project 432 Rate of return Probability Rate of return Probability -10% 0.01 10% 0.05 10 0.04 15 0.10 20 0.05 20 0.10 30 0.10 25 0.15 40 0.15 30 0.20 45 0.30 35 0.15 50 0.15 40 0.10 60 0.10 45 0.10 70 0.05 50 0.05 80 0.04 100 0.01 A) For each project, compute: (1) The range of possible rate of return. (2) The expected return. (3) The standard deviation of the returns. (4) The coefficient of variation. b) Construct a bar chart of each distribution of rates of return. c) Which project would you consider less risky? Why?
1. Range: 1.00 - (-.10) = 1.10
2. Expected return: [pic]
Rate of Return Probability Weighted Value Expected Return
ki Pri ki x Pri [pic]
-.10 .01 -.001
.10 .04 .004
.20 .05 .010
.30 .10 .030
.40 .15 .060
.45 .30 .135
.50 .15 .075
.60 .10 .060
.70 .05 .035
.80 .04 .032
1.00 .01 .010
1.00 .450
3. Standard Deviation: [pic]2 x Pri
ki [pic] [pic] [pic]2 Pri [pic]2 x Pri
-.10 .450 -.550 .3025 .01 .003025
.10 .450 -.350 .1225 .04 .004900
.20 .450 -.250 .0625 .05 .003125
.30 .450 -.150 .0225 .10 .002250
.40 .450 -.050 .0025 .15 .000375
.45 .450 .000 .0000 .30 .000000
.50 .450 .050 .0025 .15 .000375
.60 .450 .150 .0225 .10 .002250
.70 .450 .250 .0625 .05 .003125
.80 .450 .350 .1225 .04 .004900
1.00 .450 .550 .3025 .01 .003025.
.027350
(Project 257 = [pic] = .165378
4. [pic]
Project 432
1. Range: .50 - .10 = .40
2. Expected return: [pic]
Rate of Return Probability Weighted Value Expected Return
ki Pri ki x Pri [pic]
.10 .05 .0050
.15 .10 .0150
.20 .10 .0200
.25 .15 .0375
.30 .20 .0600
.35 .15 .0525
.40 .10 .0400
.45 .10 .0450
.50 .05 .0250
1.00 .300
3. Standard Deviation: [pic]2 x Pri
ki [pic] [pic] [pic]2 Pri [pic]2 x Pri
.10 .300 -.20 .0400 .05 .002000
.15 .300 -.15 .0225 .10 .002250
.20 .300 -.10 .0100 .10 .001000
.25 .300 -.05 .0025 .15 .000375
.30 .300 .00 .0000 .20 .000000
.35 .300 .05 .0025 .15 .000375
.40 .300 .10 .0100 .10 .001000
.45 .300 .15 .0225 .10 .002250
.50 .300 .20 .0400 .05 .002000
.011250
(Project 432 = [pic] = .106066
4. [pic]
b. Bar Charts
Project 257
Probability
[pic]
Rate of Return
Project 432
[pic]
Probability
Rate of Return
c. Summary Statistics
Project 257 Project 432
Range 1.100 .400
Expected Return ([pic]) 0.450 .300
Standard Deviation ([pic]) 0.165 .106
Coefficient of Variation (CV) 0.3675 .3536
Since Projects 257 and 432 have differing expected values, the coefficient of variation should be the criterion by which the risk of the asset is judged. Since Project 432 has a smaller CV, it is the opportunity with lower risk.
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