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Range of Returns

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See the attached file.
a) Explain why the geometric and arithmetic mean returns are not equal and whether one or the other may be more useful for investment decision making.

b) For the time period indicated, rank these investments on a risk-adjusted basis from most to least desirable. Explain your rationale.

c) Assume the returns in these series are normally distributed.

1. Calculate the range of returns that an investor would have expected to achieve 95 percent of the time holding common stocks.

2. Suppose an investor holds real estate for this time period. Determine the probability of at least breaking even on this investment.

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The solution calculates the range of returns.

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1) If Jonathon were risk-indifferent, which investments would he select? If he were risk-averse, which investments would he select? If he were risk-seeking, which investments would he select?

2) Determine the expected value of return for each server. Purchase of which server is riskier?
3) Calculate the expected return over the 4-year period for each of the three alternatives. Calculate the standard deviation of returns over the 4-year period for each of the three alternatives.
4) Find the range of NPVs, and subjectively compare the risks associated with purchasing these computers.

See the file attached for better viewing of word tables.

Problem 1: Jonathon Barrs is a manager for Easy Manufacturing, LLC. He wishes to evaluate three possible investments. These investments are for the purchase of new machine tools from Germany, Japan, and a local US manufacturer. The firm earns 10% on its investments and they have a risk index of 5%. The chart below lays out the expected return and expected risks of the three projects.
Investment Expected Return Expected Risk
German Tools 15.00% 8.00%
Japanese Tools 13.00% 9.00%
Local Manufacturer 11.00% 7.00%

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

Problem 2: Big Bank, Inc., is considering the purchase of one of two high speed servers, R and S. Both should provide benefits over a 10-year period, and each requires an initial investment of $4,000. Management has constructed the table (at the top of the facing page) of estimates of rates of return and probabilities for pessimistic, most likely, and optimistic results.

a. Determine the range for the rate of return for each of the two servers.
b. Determine the expected value of return for each server.
c. Purchase of which server is riskier? Why?

Server R Server S
Amount Probability Amount Probability
Initial Investment $4,000.00 1 $4,000.00 1
Annual rate of
return
Pessimistic 20.00% 0.25 15.00% 0.2
Most likely 25.00% 0.5 25.00% 0.55
Optimistic 30.00% 0.25 35.00% 0.25

Note: Question B use the following format.

Possible
Outcomes Probability Expected Return Expected Return
Server R or S Pessimistic
Most likely
Optimistic
Expected Return

Question 3: You have been given the return data shown in the first table on three countries-China, India, and South Korea-over the period 2007-2010.

Expected return
Year China India South Korea
2009 16% 17% 14%
2010 17% 16% 15%
2011 18% 15% 16%
2012 19% 14% 17%

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

Alternative Investment
1 100% of China
2 50% of China and 50% or India
3 50% of China and 50% of South Korea

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?

Question 4:

James Secretarial Services is considering the purchase of one of two new personal computers, P and Q. Both are expected to provide benefits over a 10-year period, and each has a required investment of $3,000. The firm uses a 10% cost of capital. Management has constructed the following table of estimates of annual cash inflows for pessimistic, most likely, and
optimistic results.

Computer P Computer Q
Initial Investment CFo $3,000.00 $3,000.00
Outcome Annual Cash Flows
Pessimistic $500.00 $400.00
Most Likely $750.00 $750.00
Optimistic $1,000.00 $1,200.00

1. Determine the range of annual cash inflows for each of the two computers.
2. Construct a table similar to this for the NPVs associated with each outcome for both computers.
3. Find the range of NPVs, and subjectively compare the risks associated with purchasing these computers.

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