The Xyz Company Has Estimated Expected Cash Flows For 1996 To Be As Fo
The XYZ Company has estimated expected cash flows for 1996 to be as follows: Probability Cash flow .10
$120,000 .15 140,000 .50 150,000 .15 180,000 .10 210,000 Calculate: a. Expected value (5) b. Standard deviation (6) c. Coefficient of variation (4) d. The probability that the cash flow will be less than $100
The analysis of expected cash flows for XYZ Company in 1996 involves calculating key statistical measures to understand the central tendency, variability, and risk associated with these projections. Using the probabilities and cash flow estimates provided, we can systematically perform these calculations to aid in financial decision-making and risk assessment.
The expected value (EV) of the cash flows is the weighted average of all possible outcomes, calculated by multiplying each cash flow by its associated probability and summing these products:
EV = (0.10 * $120,000) + (0.15 * $140,000) + (0.50 * $150,000) + (0.15 * $180,000) + (0.10 * $210,000)
EV = $12,000 + $21,000 + $75,000 + $27,000 + $21,000 = $156,000
Thus, the expected cash flow for 1996 is approximately $156,000.
The standard deviation measures the dispersion of cash flows around the expected value, reflecting the risk or volatility inherent in the estimates. It is computed by first determining the variance, which involves calculating the squared deviations of each cash flow from the EV, weighted by their probabilities.
Variance (σ²) = Σ [P(i) * (Cash Flow(i) - EV)²]
Calculations:
For $120,000: 0.10 * ($120,000 - $156,000)² = 0.10 * (-$36,000)² = 0.10 * 1,296,000,000 = 129,600,000
For $140,000: 0.15 * (-$16,000)² = 0.15 * 256,000,000 = 38,400,000
For $150,000: 0.50 * (-$6,000)² = 0.50 * 36,000,000 = 18,000,000
For $180,000: 0.15 * $24,000² = 0.15 * 576,000,000 = 86,400,000
For $210,000: 0.10 * $54,000² = 0.10 * 2,916,000,000 = 291,600,000
Total Variance = 129,600,000 + 38,400,000 + 18,000,000 + 86,400,000 + 291,600,000 = 564,000,000
Standard deviation (σ) = √Variance = √564,000,000 ≈ $23,755
Coefficient of Variation Calculation
The coefficient of variation (CV) is a normalized measure of risk per unit of return, computed as the ratio of the standard deviation to the expected value:
CV = σ / EV = $23,755 / $156,000 ≈ 0.152
This indicates that about 15.2% of the expected cash flow represents variability, providing insight into the risk level relative to the mean.
To determine the probability that cash flows will be less than $100,000, we examine the possible outcomes:
The lowest cash flow estimate is $120,000, which exceeds $100,000.
Since all possible outcomes are greater than $100,000, the probability that the cash flow will be less than $100,000 is zero.
Therefore, it is virtually impossible for the cash flow in 1996 to fall below $100,000 based on these estimates.
Conclusion
In summary, the expected cash flow for XYZ Company in 1996 stands at approximately $156,000, with a standard deviation of about $23,755 indicating moderate variability. The coefficient of variation suggests a relative risk level of around 15.2%, and the probabilities imply a zero chance of cash flows dropping below $100,000. These statistical insights assist managers in understanding potential financial outcomes and incorporating risk into strategic planning.
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