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# Risk preference/risk analysis and NPV calculations

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Part one

1. Risk preferences Sharon Smith, the financial manager for Barnett Corporation, wishes to evaluate three prospective investments: X, Y, and Z. Currently, the firm earns 12% on its investments, which have a risk index of 6%. The expected return and expected risk of the investments are as follows:

Investment Expected return Expected risk index
X 14% 7%
y 12 8
z 10 9

a. If Sharon were risk-indifferent, which investments would she select? Explain why.
b. If she were risk-averse, which investments would she select? Why?
c. If she were risk-seeking, which investments would she select? Why?
d. Given the traditional risk preference behavior exhibited by financial managers, which investment would be preferred? Why?

2. Risk analysis Solar Designs is considering an investment in an expanded product line. Two possible types of expansion are being considered. After investigating the possible outcomes, the company made the estimates shown in the following table:

Expansion A Expansion B
Initial investment \$12,000 \$12,000
Annual rate of return
Pessimistic 16% 10%
Most likely 20% 20%
Optimistic 24% 30%

a. Determine the range of the rates of return for each of the two projects.
b. Which project is less risky? Why?
c. If you were making the investment decision, which one would you choose? Why? What does this imply about your feelings toward risk?
d. Assume that expansion B's most likely outcome is 21% per year and that all other facts remain the same. Does this change your answer to part c? Why?

3. Portfolio analysis You have been given the return data shown in the first table on three assets - F, G, and H - over the period 2007-2010.

Expected return
Year Asset F Asset G Asset H
2007 16% 17% 14%
2008 17 16 15
2009 18 15 16
2010 19 14 17

Using these assets, you have isolated the three investment alternatives shown in the following table:

Alternative Investment

1 100% of asset F
2 50% of asset F and 50% of asset G
3 50% of asset F and 50% of asset H

a. Calculate the expected return over the 4-year period for each of the three alternatives.
b. Calculate the standard deviation of returns over the 4-year period for each of the three alternatives.
c. Use your findings in parts a and b to calculate the coefficient of variation for each of the three alternatives.
d. On the basis of your findings, which of the three investment alternatives do you recommend? Why?

4. Basic sensitivity analysis Murdock Paints is in the process of evaluating two mutually exclusive additions to its processing capacity. The firm's financial analysts have developed pessimistic, most likely, and optimistic estimates of the annual cash inflows associated with each project. These estimates are shown in the following table.

Project A Project B
Initial investment (CF0) \$8,000 \$8,000
Outcome Annual cash inflows (CF)
Pessimistic \$200 \$900
Most likely 1,000 1,000
Optimistic 1,800 1,100

a. Determine the range of annual cash inflows for each of the two projects.
b. Assume that the firm' s cost of capital is 10% and that both projects have 20-year lives. Construct a table similar to this for the NPVs for each project. Include the range of NPVs for each project.
c. Do parts a and b provide consistent views of the two projects? Explain.
d. Which project do you recommend? Why?

#### Solution Preview

Part one

1. Risk preferences Sharon Smith, the financial manager for Barnett Corporation, wishes to evaluate three prospective investments: X, Y, and Z. Currently, the firm earns 12% on its investments, which have a risk index of 6%. The expected return and expected risk of the investments are as follows:

Investment Expected return Expected risk index
X 14% 7%
y 12 8
z 10 9

a. If Sharon were risk-indifferent, which investments would she select? Explain why.

Risk indifference implies that risk does not matter and we look for higher returns and so Sharon would select X and Y since these have a higher return than 12% currently.

b. If she were risk-averse, which investments would she select? Why?

A risk averse person would select an investment which provides the highest return per unit of risk. Sharon would select X since that offers a higher return with a small increase in risk.

c. If she were risk-seeking, which investments would she select? Why?

A risk seeking person only looks at risk without looking at return. Sharon would accept Y and Z since that have higher risk.

d. Given the traditional risk preference behavior exhibited by financial managers, which investment would be preferred? Why?

The traditional risk behavior is risk averse and so investment X would be preferred.

2. Risk analysis Solar Designs is considering an investment in an expanded product line. Two possible types of expansion are being considered. After investigating the possible outcomes, the company made the estimates shown in the following table:

Expansion A Expansion B
Initial investment \$12,000 \$12,000
Annual rate of return
Pessimistic 16% 10%
Most likely 20% 20%
Optimistic 24% 30%

a. Determine the range of the ...

#### Solution Summary

The solution explains some questions relating to risk preference, risk analysis and NPV calculations.

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