# Coefficient of variation, NPV, Normal Distribution

I need help with solving the attached problems numbers 2, 6, 9, and 17 only.

(See attached file for full problem description)

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Chapter 11

2. Monarck King Size Beds, Inc., is evaluating a new promotional campaign that could increase sales. Possible outcomes and probabilities of the outcomes are shown below. Compute the coefficient of variation.

Additional

Possible Outcomes Sales in Units Probabilities

Ineffective campaign . . . . . . . . 20 .20

Normal response . . . . . . . . . . . 30 .50

Extremely effective . . . . . . . . . 70 .30

5. Five investment alternatives have the following returns and standard deviations

of returns.

Returns- Standard

Alternative Expected Value Deviation

A. . . . . . . . . . . $ 5,000 $1,200

B. . . . . . . . . . . 4,000 600

C. . . . . . . . . . . 4,000 800

D. . . . . . . . . . . 8,000 3,200

E. . . . . . . . . . . 10,000 900

Using the coefficient of variation, rank the five alternatives from lowest risk to highest risk

6. In problem 5, if you were to choose between Alternatives B and C only, would you need to use the coefficient of variation? Why?

9. Waste Industries is evaluating a $70,000 project with the following cash flows.

Year Cash Flows

1 . . . . . . . . . . . . . $11,000

2 . . . . . . . . . . . . . 16,000

3 . . . . . . . . . . . . . 21,000

4 . . . . . . . . . . . . . 24,000

5 . . . . . . . . . . . . . 30,000

The coefficient of variation for the project is .847.

Based on the following table of risk-adjusted discount rates, should the project be undertaken? Select the appropriate discount rate and then compute the net present value.

Coefficient Discount

of Variation Rate

0-.25 . . . . . . . . 6%

.26-.50 . . . . . . . . 8

.51-.75 . . . . . . . . 10

. 76-1.00 . . . . . . . 14

1.01-1.25 . . . . . . . 20

17. When returns from a project can be assumed to be normally distributed, such as those shown in Figure 13-6 (represented by a symmetrical, bell-shaped curve), the areas under the curve can be determined from statistical tables based on standard deviations. For example, 68.26 percent of the distribution will fall within one standard deviation of the expected value (D 1_). Similarly 95.44 (Please see attached file for complete description)

a) What is the probability that the outcome would be between $32,000 and $48,000?

b) What is the probability that the outcome would be between $28,000 and $52,000?

c) What is the probability that the outcome would be greater than $32,000 ?

d) What is the probability that the outcome would be less than $55,680?

e) What is the probability that the outcome would be less than $32,000 or greater than $52,000?

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#### Solution Summary

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