# Expected Value,Standard Deviation & Coefficient of Variation

A firm has decided to invest in a piece of land. Management has estimated that the land can be sold in 5 years for the following possible prices:

Price Probability

10,000 .20

15,000 .30

20,000 .40

25,000 .10

a. Determine the expected selling price for the land.

b. Determine the standard deviation of the possible sales prices.

c. Determine the coefficient of variation.

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#### Solution Preview

Hello Student,

For section (a), you may note that in general the expected value of a random variable is calculated by assigning a probability to each possible outcome and then taking a probability-weighted average of the outcomes. Therefore, in order to calculate the expected selling price for land, you need to multiply the price of each land (possible outcome) by its probability, and then calculate the sum all results. Hence, the expected selling price for land would be given as:

Price Probability Price x Probability

$10,000 0.2 $2,000

$15,000 0.3 $4,500

$20,000 0.4 $8,000

$25,000 0.1 $2,500

Total 1.0 $17,000 (This total is the expected selling price for land.)

Note that at all times the total of the ...

#### Solution Summary

This solution provides you with step by step explanation as to how to calculate the expected value, standard deviation and coefficient of variation given a set of possible prices. Solution is adequately referenced.

Value, standard deviation, and coefficient of variation of cash flows

A firm is considering two alternative projects. Project A needs an investment of $800,000. Project B needs an investment of $750,000. Relevant annual cash flow data for the two projects over their expected seven-year lives are as follows:

Project A Project B

Pr. Cash Flow Pr. Cash Flow

0.50 $ 0 0.045 $ 0

0.50 500,000 0.910 200,000

0.045 400,000

Calculate the expected value, standard deviation, and coefficient of variation of cash flows for each project.

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