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# Two business projects: Coefficient, standard deviation, and expected value

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A firm is considering two business projects. Project A will return a loss of \$45 if conditions are poor, a profit of \$35 if conditions are good, and a profit of \$155 if conditions are excellent. Project B will return a loss of \$100 if conditions are poor, a profit of \$60 if conditions are good, and a profit of \$300 if conditions are excellent. The probability distribution of conditions follows:

Conditions : Poor Good Excellent
Probabilities: 40% 50% 10%

(i) Calculate the expected value of each project and identify the preferred project according to this criterion.
(ii) Calculate the standard deviation of each project and identify the project that has the higher level of risk.
(iii) Calculate the coefficient of variation for each project and identify the preferred project according to this criterion.

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Solution:

(i) Calculate the expected value of each project and identify the preferred project according to this criterion.
Project A Project B
P Profit X1 Profit X2 P*X1 P*X2
Poor 0.4 -45 -100 -18 -40
Good 0.5 35 60 17.5 30
Excellent 0.1 155 300 15.5 ...

#### Solution Summary

The solution describes the steps needed for choosing a project from given alternatives based upon expected profit, standard deviation and coefficient of variation.

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## Cost of capital/internal rate of return/standard deviation

Chapter 12 Problems

7. X-treme Vitamin Company is considering two investments, both of which cost \$10,000. The cash flows are as follows:

Year Project A Project B
1 . . . . . . . . . . \$12,000 \$10,000
2 . . . . . . . . . . 8,000 6,000
3 . . . . . . . . . . 6,000 16,000

a. Which of the two projects should be chosen based on the payback method?

b. Which of the two projects should be chosen based on the net present value method? Assume a cost of capital of 10 percent.

c. Should a firm normally have more confidence in answer a or answer b?

15. The Danforth Tire Company is considering the purchase of a new machine that
would increase the speed of manufacturing and save money. The net cost of this
machine is \$66,000. The annual cash flows have the following projections.

Year Cash Flow
1. . . . . . . . . \$21,000
2. . . . . . . . . 29,000
3. . . . . . . . . 36,000
4. . . . . . . . . 16,000
5. . . . . . . . . 8,000

a. If the cost of capital is 10 percent, what is the net present value?
b. What is the internal rate of return?
c. Should the project be accepted? Why?

20. Miller Electronics is considering two new investments. Project C calls for the purchase of a coolant recovery system. Project H represents an investment in a heat recovery system. The firm wishes to use a net present value profile in comparing the projects. The investment and cash flow patterns are as follows:

Project C Project H
(\$25,000 investment) (\$25,000 investment)
Year Cash Flow Year Cash Flow
1 . . . . . . . . . . . . . .\$ 6,000 1 . . . . . . . . . . . . . . .\$20,000
2 . . . . . . . . . . . . . . .7,000 2 . . . . . . . . . . . . . . . . .6,000
3 . . . . . . . . . . . . . . .9,000 3 . . . . . . . . . . . . . . . . .5,000
4 . . . . . . . . . . . . . .13,000

a. Determine the net present value of the projects based on a zero discount rate.

b. Determine the net present value of the projects based on a 9 percent discount rate.

c. The internal rate of return on Project C is 13.01 percent, and the internal rate of return on Project H is 15.68 percent. Graph a net present value profile for the two investments similar to Figure 12-3. (Use a scale up to \$10,000 on the vertical axis, with \$2,000 increments. Use a scale up to 20 percent on the horizontal axis, with 5 percent increments.)

Chapter 13 Problems

1. Myers Business Systems is evaluating the introduction of a new product. The
possible levels of unit sales and the probabilities of their occurrence are given
below:

Possible Sales
Market Reaction in Units Probabilities
Low response . . . . . . . . . . . . . 20 .10
Moderate response . . . . . . . . . 40 .30
High response . . . . . . . . . . . . . 55 .40
Very high response . . . . . . . . . 70 .20

a. What is the expected value of unit sales for the new product?
b. What is the standard deviation of unit sales?

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.

14. Mr. Monty Terry, a real estate investor, is trying to decide between two potential small shopping center purchases. His choices are the Wrigley Village and Crosley Square. The anticipated annual cash inflows from each are as follows:

Wrigley Village Crosley Square
Yearly Aftertax Yearly Aftertax
Cash Inflow Cash Inflow
(in thousands) Probability (in thousands) Probability
\$10 . . . . . . . . . . . .1 \$20 . . . . . . . . . . . .1
30 . . . . . . . . . . . .2 30 . . . . . . . . . . . .3
40 . . . . . . . . . . . .3 35 . . . . . . . . . . . .4
50 . . . . . . . . . . . .3 50 . . . . . . . . . . . .2
60 . . . . . . . . . . . .1

a. Find the expected value of the cash flow from each shopping center.
b. What is the coefficient of variation for each shopping center?
c. Which shopping center has more risk?

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