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Calculating Mean, Standard Deviation & CV of Sales

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The demand for MICHTEC's products is related to the state of the economy. If the economy is expanding next year (an above-normal growth in GDP), the company expects sales to be $90 million. If a recession occurs next year (a decline in GDP), sales are expected to be $75 million. If next year is normal (a moderate growth in GDP), sales are expected to be $85 million. MICHTEC's economists estimate the chances that the economy will be either expanding, normal, or in a recession next year at 0.2, 0.5, and 0.3, respectively.

a. Compute expected annual sales.
b. Compute the standard deviation of annual sales.
c. Compute the coefficient of variation of annual sales.

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Please refer to the attached file for better clarity of tables and missing formulas


a. Compute expected annual sales.
State of economy Probability (P) Sales (S) P*S
Expansion 0.2 90 18.00
Recession 0.3 75 ...

Solution Summary

This solution describes the steps to calculate expected sales, standard deviation of annual sales and coefficient of variation of annual sales.

See Also This Related BrainMass Solution

Calculate the expected rate of return and standard deviation of expected returns of stocks when the probability distribution of expected return are given.

1. Stocks X and Y have the following probability distributions of expected future returns:

PROBABILITY X Y Rate of return Y Rate of return X
10% -10% -35% -4% -1%
20% 20% 0% 0% 4%
40% 12% 20% 8% 5%
20% 20% 25% 5% 4%
10% 38% 45% 5% 4%

a. Calculate the expected rate of return, khat, for Stock Y (expected return for Stock X, Kx hat, equals 12%).

b. Calculate the standard deviation of expected returns for Stock X. (that for Stock Y is 20.35%). Now Calculate the
coefficient of variation for Stock Y. Is it possible that most investors might regard Stock Y as being less risky than
Stock X? Explain.

2. Shalit Corporation's 2002 sales were $12 million. Sales were $6 million 5 years earlier (in 1997).

a. To the nearest percentage point, at what rate have sales been growing?
b. Suppose someone calculated the sales growth for Shalit Corporation in part a as follows:
"Sales doubled in 5 years. This represents a growth of 100 percent in 5 years, so dividing 100 percent by 5, we find the growth rate
to be 20 percent per year". Explain what is wrong with this calculation.

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