Analytical Methods for Lawyers
Prof. Palmiter (Spring 2007)
Finance Unit – Exercise 4
Diversification and CAPM
1.Why diversify? Your client is a widower with three investment choices. Uncertain about the economy, your client wants to be safe. The following table shows how the three different investment choices are expected to behave under different assumptions about the economy.
Effect of diversification / Investments / PortfoliosX / Y / Z / XY (50/50) / XZ (50/50)
Bust (33% chance) / -4% / 4% / 16% / 0% / 6%
Normal (33% chance) / 8% / 8% / 8% / 8% / 8%
Boom (33% chance) / 20% / 12% / 0% / 16% / 10%
Statistics:
Expected return / 8% / 8% / 8% / 8% / 8%
Std deviation / 9.80% / 3.27% / 6.53% / 6.53% / 1.63%
Calculate the expected return and standard deviation for Portfolio YZ and then for Portfolio XYZ. Which of these various portfolios is safest for your client? Can you construct a safer portfolio?
- Prudent man rule? You are trustee for a family trust that is governed by the “prudent man rule.” See Wikipedia. Consider the investment choices in the previous problem. Which investment do you expect will be the most expensive? the least expensive? Historically, what investments did the prudent man rule dictate you make? How has portfolio theory changed your options? Would you violate the prudent man rule by not creating a diversified portfolio?
3.CAPM to find risk-adjusted returns? Your client, a university endowment fund, has been presented with three investment choices. Assume the risk-free rate of return is 2.4%, and the expected return of the market is 9.5%. You can choose between three portfolios (A, B, and C) having the following properties:
Market / A / B / CExpected return / .095 / .05 / .11 / .17
beta / 1.0 / 0.40 / 1.50 / 2.00
Using the CAPM formula [where E(r) = Rf + beta*( Rm - Rf )] which portfolio should the endowment fund choose? Would you advise using CAPM?
- What’s a beta? Your client BuyUp Inc is in the business of identifying closely held family businesses that, after a few years of professional management can be taken public or sold to larger corporations. It has identified two companies, X and Y. BuyUp wants to compare their risks (volatility) to that of the market. You have the following return data:
Return (%)
Year / Market / X / Y
1996 / 22.9 / 45 / 15
1997 / 33.4 / 43 / 26
1998 / 28.6 / 25 / 15
1999 / 21 / 41 / 18
2000 / -9.1 / -13 / -6
2001 / -11.9 / -29 / 7
2002 / -22.1 / -43 / -15
2003 / 28.7 / 27 / 25
2004 / 10.9 / 25 / 18
2005 / 4.9 / -13 / 5
You notice that the returns have been (on average) about the same for the market, as well as X and Y. But you are worried about risk. Compute (or estimate) beta. Draw the characteristic line for each company’s returns compared to the market and estimate the slope for each line. Or use regression analysis to compute the line's slope. Compare the companies’ risks to the market – which is a better buy?
Given each company’s beta, what do you predict will be the return on X and Y next year, assuming either an up market next year of +18.0% or a down market of -7.0%? (Assume a market risk-free rate of 3.2%.)
5.Liquidate or continue? BigAir Construction Inc is a contractor for HVAC systems in high-rise buildings. The company fails to keep up with new high-efficiency systems being used in the industry and is hemorrhaging cash. The company files for relief under the Bankruptcy Act, with management proposing a reorganization plan under which the company will go forward after creditors receive new debt equal to 60 cents on the dollar. PozosBank, the company’s largest creditor, asserts the company is worth more liquidated. Management tells a story of discounted cash value.
After taking evidence, the court determines the company’s 2006 earnings of $1.2 million will grow at an annul rate of 4% for five years and then go flat.
Year / Projected Earnings2007 / $1,248,000
2008 / $1,297,920
2009 / $1,349,837
2010 / $1,403,830
2011 / $1,459,983
2012 and thereafter / $1,518,383
The court also determines that the appropriate discount rate (using CAPM) should be 11.64%, on the assumption the following inputs:
R(c) = R(f) + B(a) × [R(m) – R(f)]R(c) = the CAPM cost of capital
R(f) = the after-tax risk free rate of return
B(a) = the beta, or risk, of the asset
R(m) = the return on the market portfolio
R(m) - R(f) = the market risk premium
After-tax risk free rate of return -- R(f): / 3.8%
Beta coefficient -- B(a): / 0.80
Market risk premium -- R(m) – R(f): / 9.8%
Derived Discount Rate: / 11.64%
Finally, the judge decides that BigAir should be liquidated – and its creditors paid immediately – if its discounted cash flow (net present value) is less than $10 million. Using the figures above, compute BigAir’s discounted cash value. Should the judge order liquidation or approve the reorganization plan?