Assume a corporation has earnings before depreciation and taxes of $123,000 depreciation of $41,000 and is in a 35 percent tax bracket.

(a)

How much would cash flow be if there were only $21,000 in depreciation? All other factors are the same.(Omit the “$” sign in your response.)

  Cash flow

$   

B

C

D

E

[removed]  

Sensor Technology wishes to determine its coefficient of variation as a company over time. The firm projects the following data (in millions of dollars):

Year

Profits:
Expected value

Standard
deviation

1

$

93

$

34

3

157

65

6

206

98

9

226

120

(a)

Compute the coefficient of variation (V) for each time period. (Round your answers to 2 decimal places.)

Year

Coefficient of
variation

1

[removed]  

3

[removed]  

6

[removed]  

9

[removed]  

(b)

Does the risk (V) appear to be increasing over a period of time?

Kyle’s Shoe Stores, Inc., is considering opening an additional suburban outlet. An aftertax expected cash flow of $100 per week is anticipated from two stores that are being evaluated. Both stores have positive net present values.

  Site A

Probability

Cash flows

.20

50

.40

100

.25

110

.15

150

  Site B

Probability

Cash flows

.10

20

.20

50

.40

100

.20

150

.10

180

(a)

Compute the coefficient of variation for each site. (Do not round intermediate calculations. Round your answers to 4 decimal places.)

Coefficient of
variation

  Site A

[removed]  

  Site B

[removed]  

(b)

Which store site would you select based on the distribution of these cash flows? Use the coefficient of variation as your measure of risk.

Micro Systems is evaluating a $59,100 project with the following cash flows.

Years

Cash flows

1

$

9,180

2

13,100

3

21,700

4

19,400

5

25,600

The coefficient of variation for the project is .654.

Coefficient of variation

Discount rate

0

−

.25

7

%

.26

−

.50

11

.51

−

.75

15

.76

−

1.00

17

1.01

− 

1.25

20

(a-1)

Select the appropriate discount rate.

(a-2)

Compute the net present value. Use Appendix B. (Round “PV Factor” to 3 decimal places, intermediate and final answers to the nearest dollar amount. Negative amount should be indicated by a minus sign.  Omit the “$” sign in your response.)

  Net present value

$ [removed]  

(b) 

Based on the net present value should the project be undertaken?

(a)

Fill in the table below from Appendix B. (Round your answers to 3 decimal places.)

Discount rate

Years

10%

18%

1

[removed]  

[removed]  

10

[removed]  

  [removed]  

20

[removed]  

[removed]  

(b)

What is the impact of a high discount rate on long-term inflows?

Debby’s Dance Studios is considering the purchase of new sound equipment that will enhance the popularity of its aerobics dancing. The equipment will cost $22,400. Debby is not sure how many members the new equipment will attract, but she estimates that her increased annual cash flows for each of the next five years will have the following probability distribution. Debby’s cost of capital is 12 percent.

Cash flow

Probability

$

3,890

.3  

5,330

.2  

8,390

.2  

9,880

.3  

(a)

What is the expected value of the cash flow? (Omit the “$” sign in your response.)

  Expected cash flow

$ [removed]  

(b)

What is the expected net present value? Use Appendix D. (Round “PV Factor” to 3 decimal places, intermediate and final answers to the nearest dollar amount. Negative amount should be indicated by a minus sign. Omit the “$” sign in your response.)

  Net present value

 $ [removed]  

(c)

Should Debby buy the new equipment?

Highland Mining and Minerals Co. is considering the purchase of two gold mines. Only one investment will be made. The Australian gold mine will cost $1,630,000 and will produce $306,000 per year in years 5 through 15 and $572,000 per year in years 16 through 25. The U.S. gold mine will cost $2,012,000 and will produce $270,000 per year for the next 25 years. The cost of capital is 10 percent.

(a-1)

Calculate the net present value for each project. (Round “PV Factor” to 3 decimal places, intermediate and final answers to the nearest dollar amount. Omit the “$” sign in your response.)

Net present value

  The Australian Mine

$ [removed]  

  The U.S. Mine

 $ [removed]  

(a-2)

Which investment should be made?

(b-1)

If the Australian Mine justifies an extra 1 percent premium over the normal cost of capital because of its riskiness and the relative uncertainty of cash flows, recalculate the net present value of the mine.(Round “PV Factor” to 3 decimal places, intermediate and final answers to the nearest dollar amount. Negative amount should be indicated by a minus sign. Omit the “$” sign in your response.)

Net present value

  The Australian Mine

$ [removed]  

(b-2)

Does the investment decision change?

Mr. Sam Golff desires to invest a portion of his assets in rental property. He has narrowed his choices down to two apartment complexes, Palmer Heights and Crenshaw Village. After conferring with the present owners, Mr. Golff has developed the following estimates of the cash flows for these properties.

  Palmer Heights

Yearly aftertax
cash inflow
(in thousands)

Probability

$ 90

.2

95

.2

110

.2

125

.2

130

.2

  Crenshaw Village

Yearly aftertax
cash inflow
(in thousands)

Probability

$ 95

.2

100

.3

110

.4

120

.1

Mr. Golff is likely to hold the complex of his choice for 30 years, and he will use this time period for decision-making purposes. Either apartment complex can be acquired for $206,000. Mr. Golff uses a risk-adjusted discount rate when considering investments. His scale is related to the coefficient of variation.

Coefficient of variation

Discount rate

0

–

0.20

5  

%

0.21

–

0.40

8  

(cost of capital)

0.41

–

0.60

12  

    Over 0.60

16  

(a) 

Compute the risk-adjusted net present values for Palmer Heights and Crenshaw Village. (Omit the “$” sign in your response.)

Net present value

  Palmer Heights

$ [removed]  

  Crenshaw Village

$ [removed]  

(b-1)

Which investment should Mr. Golff accept if the two investments are mutually exclusive?

(b-2)

Which investment should Mr. Golff accept If the investments are not mutually exclusive and no capital rationing is involved?

Allison’s Dresswear Manufacturers is preparing a strategy for the fall season. One alternative is to expand its traditional ensemble of wool sweaters. A second option would be to enter the cashmere sweater market with a new line of high-quality designer label products. The marketing department has determined that the wool and cashmere sweater lines offer the following probability of outcomes and related cash flows.

EXPAND WOOL SWEATERS LINE

ENTER CASHMERE SWEATERS LINE

Expected sales

Probability

Present value
of cash flows
from sales

Probability

Present value
of cash flows
from sales

  Fantastic

.3

$

262,000

.3

$

378,000

  Moderate

.3

194,000

.3

239,000

  Low

.4

88,100

.4

0

The initial cost to expand the wool sweater line is $161,000. To enter the cashmere sweater line the initial cost in designs, inventory, and equipment is $136,000.

(a)

Calculate Net present value. (Negative amounts should be indicated by a minus sign. Omit the “$” sign in your response.)

Net present value

  Expand wool sweaters line

$ [removed]  

  Enter cashmere sweaters line

$ [removed]  

When returns from a project can be assumed to be normally distributed (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 (     ± 1σ). Similarly 95.44 percent will fall within two standard deviations (      ± 2σ), and so on. An abbreviated table of areas under the normal curve is shown here.

Number of σ’s
from expected
value

+ or –

+ and –

.50  

.1915  

.3830  

1.00  

.3413  

.6826  

1.50  

.4332  

.8664  

1.75  

.4599  

.9198  

2.00  

.4772  

.9544  

Assume Project A has an expected value of $34,000 and a standard deviation ( σ ) of $6,800.

(a)

What is the probability that the outcome will be between $23,800 and $44,200? (Round your answer to 4 decimal places.)

  Probability

[removed]  

(b)

What is the probability that the outcome will be between $20,400 and $47,600? (Round your answer to 4 decimal places.)

  Probability

[removed]  

(c)

What is the probability that the outcome will be at least $20,400? (Round your answer to 4 decimal places.)

  Probability

[removed]  

(d)

What is the probability that the outcome will be less than $45,920? (Round your answer to 4 decimal places.)

  Probability

[removed]  

(e)

What is the probability that the outcome will be less than $30,600 or greater than $40,800? (Round your answer to 4 decimal places.)

  Probability

[removed]  

The Oklahoma Pipeline Company projects the following pattern of inflows from an investment. The inflows are spread over time to reflect delayed benefits. Each year is independent of the others.

Year 1

Year 5

Year 10

Cash inflow

Probability

Cash inflow

Probability

Cash inflow

Probability

35

.40  

20

.35  

50

.40  

60

.20  

60

.30  

60

.40  

85

.40  

100

.35  

110

.20  

The expected value for all three years is $60.

(a)

Compute the standard deviation for each of the three years. (Round your answers to 2 decimal places.)

Standard deviation

  Year 1

[removed]  

  Year 5

[removed]  

  Year 10

[removed]  

Treynor Pie Co. is a food company specializing in high-calorie snack foods. It is seeking to diversify its food business and lower its risks. It is examining three companies—a gourmet restaurant chain, a baby food company, and a nutritional products firm. Each of these companies can be bought at the same multiple of earnings. The following represents information about the companies.

Company

Correlation with
Treynor Pie
company

Sales
($ millions)

Expected earnings($ millions)

Standard deviation
in earnings
($ millions)

  Treynor Pie Company

+

1.0

$

182

$

9

$

3.0

  Gourmet restaurant

+

.5

63

9

1.2

  Baby food company

+

.3

54

6

1.7

  Nutritional products company

−

-.6

75

7

3.8

(a-1)

Compute the coefficient of variation for each of the four companies. (Round your answers to 2 decimal places.)

Coefficient of
variation

  Treynor Pie Company

[removed]  

  Gourmet restaurant

[removed]  

  Baby food company

[removed]  

  Nutritional products company

[removed]  

(a-2)

Which company is the least risky?

(a-3)

Which company is the most risky?

(b) 

Which of the acquisition candidates is most likely to reduce Treynor Pie Company’s risk?

Transoceanic Airlines is examining a resort motel chain to add to its operation. Prior to the acquisition, the normal expected outcomes for the firm are as follows:

Outcomes
($ millions)

Probability

  Recession

$

35

.40

  Normal economy

55

.20

  Strong economy

75

.40

(a)

Compute the expected value, standard deviation, and coefficient of variation. (Enter your answer in millions. Round Standard deviation to 2 decimal places and final answer to 3 decimal places.Omit the “$” sign in your response.)

  Expected value

$ [removed]  

  Standard deviation

$ [removed]  

  Coefficient of variation

[removed]  

Sheila Goodman recently received her MBA from the Harvard Business School. She has joined the family business, Goodman Software Products, Inc., as vice president of finance.

     She believes in adjusting projects for risk. Her father is somewhat skeptical but agrees to go along with her. Her approach is somewhat different than the risk-adjusted discount rate approach, but achieves the same objective.

     She suggests that the inflows for each year of a project be adjusted downward for lack of certainty and then be discounted back at a risk-free rate. The theory is that the adjustment penalty makes the inflows the equivalent of riskless inflows, and therefore a risk-free rate is justified.

     A table showing the possible coefficient of variation for an inflow and the associated adjustment factor is shown below:

Coefficient of
variation

Adjustment
factor

0

–

.25

.90

.26

–

.50

.80

.51

–

.75

.70

.76

–

1.00

.60

1.01

–

1.25

.50

    Assume a $180,000 project provides the following inflows with the associated coefficients of variation for each year.

Year

Inflow

Coefficient of variation

1

$

31,800

.15  

2

53,200

.23  

3

77,000

.52  

4

59,100

.71  

5

66,100

1.10  

(a) 

Fill in the table below (Round “Adjustment factor” to 2 decimal places. Omit the “$” sign in your response):

Year

Adjustment factor

Adjusted Inflow

1

[removed]  

$ [removed]  

2

[removed]  

[removed]  

3

[removed]  

[removed]  

4

[removed]  

[removed]  

5

[removed]  

[removed]  

(b-1)

If the risk-free rate is 5 percent, compute the net present value of the adjusted inflows. Use Appendix B. (Round “PV Factor” to 3 decimal places, intermediate and final answers to the nearest whole dollar amount. Negative amount should be indicated by a minus sign. Omit the “$” sign in your response.)

  Net present value

$ [removed]  

(b-2)

Should this project be accepted?