Pace University
Fin 647 Advanced Topics in Financial Management
Prof. P.V. Viswanath

Fall 2005
Exam 2


  1. If your answers are not legible or are otherwise difficult to follow, I reserve the right not to give you any points.
  2. If you cheat in any way, I reserve the right to give you no points for the exam, and to give you a failing grade for the course.
  3. You may bring in sheets with formulas, but no worked-out examples, or definitions, or anything else.
  4. You must explain all your answers.

1. Read the following WSJ article and answer any two of the questions below (15 points each):

  1. The article explains how the amount of the unfunded pension liability depends on the assumptions made regarding the rate of return on pension assets, the discount rate applied to expected payouts on the pension plan, and the size and timing of the payouts. Explain how you would go about determining the correct discount rate to be applied to the expected payouts on GM's pension plan to get the present value of the payouts. Be as specific as possible. Explain using the CAPM.
  2. Your friend thinks that all this discussion of unfunded pension liabilities is unnecessary. "I have studied the CAPM," he says. "The risk involved is completely diversifiable. Hence, it is irrelevant!" How would you respond to him?
  3. The WSJ for Nov. 11 ran an article entitled "FASB Votes to Revise Pension Rules" with the following sentence in it:
    Under the first stage (of the revision), companies would be required for the first time to show on their balance sheets the amounts by which their pension plans are overfunded or underfunded. Essentially, companies would be required to lift this information from the footnotes in their financial statements, where it now is relegated, and place it on their balance sheets as an asset or a liability.
    The initial phase of revisions, if enacted, could force many large manufacturers with significantly underfunded pension obligations to slash their reported shareholder equity. FASB members estimated that the change would affect corporate balance sheets by hundreds of billions of dollars.

    Wwhat would have been the effect on the stock price of the manufacturers referred to in the quote above, when this announcement was made. What will be the effect when these manufacturers, in the future, report weaker balance sheets due to the need to incorporate unfunded pension liabilities? (Assume that security markets are efficient.) Explain your answer.

Pension Inquiry Shines Spotlight On Assumptions
Small Changes in Calculations At Companies Have a Big Effect On Retiree Liability -- and Profit

November 9, 2005; Page C1

Labor unions and the government's Pension Benefit Guaranty Corp. want to make sure big companies' pension funds are healthy enough to pay promised benefits to current and future retirees. The Securities and Exchange Commission, on the other hand, is grappling with another question: Did the companies tweak key financial assumptions of these plans to make the companies themselves look more flush?

The SEC, which refers internally to any such maneuvers as "reverse engineering," is probing whether companies had an eye on their shareholders, not their retirees, when they changed some financial assumptions in recent years, according to people familiar with the matter.

Such assumptions are used, say, in calculating the size of a plan's future pension obligations. The SEC's interest in the pension plans has been known for months, and details about the probe, including the focus on the financial assumptions, continue to surface.

A look at some of the assumptions involved in calculating the funding status of the plans at General Motors Corp., one of the companies under review, shows how small changes -- such as a quarter-point increase or decrease in the interest rate used to calculate the total liability -- can change the size of that obligation by billions of dollars. GM estimates that its plans, with about $100 billion in assets, were slightly overfunded at the end of 2004.

GM, which has said it is cooperating with the SEC's probe, declined to comment for this story. Boeing Co., Delphi Corp., Ford Motor Co., Navistar International Corp. and Northwest Airlines also have disclosed SEC inquiries about their pension plans, with some saying their accounting was proper. The agency hasn't accused any company of wrongdoing.

The SEC also is looking at pension-accounting issues that don't involve assumptions but can help burnish a firm's financial statements, the people said. At the same time, the Financial Accounting Standards Board is scheduled to vote tomorrow on whether to take another look at pension-accounting rules. The FASB's existing rules have been criticized as allowing companies to distort their financial performance, and the board may consider stricter standards.

Many assumptions at issue are disclosed in footnotes of the companies' financial statements. On their face, a company's choices are difficult for outsiders to challenge. While an interest rate may look high or low, a company always could argue it made a good-faith estimate. But the SEC is using its subpoena power to dig into the thought processes, to determine if the estimates were made in good faith -- or were results-driven.

That is, did the companies come up with the desired result first, and then figure out which assumptions would get them there?

"The key to whether or not any of these companies will have a problem with the SEC will depend on how they support their pension assumptions," said David Zion, an analyst who specializes in accounting and taxation for Credit Suisse First Boston.

Here are three areas that SEC investigators are looking at:

Discount rate: Companies use discount rates to figure out the present value of things they need to pay in the future. Think of it this way: $1 million in cash 10 years from now is worth less than $1 million in cash today. How much less? Well, that's where the discount rate comes in.

To place a current value on future pension payments, companies typically look to prevailing interest rates for high-grade corporate bonds. The way the math works, the higher the discount rate, the lower the current value of the future liability -- and the better funded a plan would appear.

"A small change in the discount rate can make a big difference in whether you look well-funded," said Jack Ciesielski, a Baltimore-based expert on pension accounting who provides research to institutional investors. And thanks to the quirky current accounting rules, changes in the rate may have generated accounting gains that boosted net income.

Many auto makers, including GM and Ford, have lowered their discount rates in the past several years, as interest rates have fallen. GM's discount rate in 2004 was 5.75%, down from 7.8% in 1999, in line with a portfolio of bonds rated double-A by Moody's Investors Service Inc., according to GM. Each year the discount rate has decreased, GM's liability and annual pension expense have increased. GM's financial filings note that a 0.25% decrease in its discount rate would increase its annual pretax pension expense by $160 million and raise its pension-benefit obligation by $2.3 billion, according to financial filings.

Scott A. Taub, the SEC's deputy chief accountant, said companies need to be able to justify the chosen discount rate. "What would trouble me in terms of selection of the discount rate is if a company selected or changed its discount rate in an attempt to manage earnings," he said.

Expected rate of return: Under accounting rules, companies use an expected, or assumed, return on pension assets, rather than an actual return, to help smooth the impact of market swings on their pension plans' value in their financial statements. If actual returns turn out to be greater, or lower, than the expected return, the effects are filtered into the annual pension expense over a period of years.

At GM, a 0.25% increase in the expected return on assets lowers the company's pension obligation by $220 million, according to its financial filings.

From 1999 through 2002, GM assumed an expected return of 10%, and it has assumed 9% since then. Actual returns have varied, from 18.1% in 1999 to negative 7.3% in 2003. The company's average rate of return over the past 15 years has been about 9%, according to GM.

The FASB may consider requiring companies each quarter to adjust a plan's assets and liabilities on their balance sheets to "fair value," eliminating the smoothing technique.

Health-care inflation: In estimating a company's liability for health-care benefits to current and future retirees, companies must estimate health-care inflation. Companies are supposed to take into account recent experience and trends, according to SEC officials.

As of December, GM, which is the nation's largest private provider of health care, used 10.5% for its current inflation rate and 5% for a longer-term rate, according to its financial filings. Small changes mean big swings: A one-percentage-point increase in the health-care trend rate would increase GM's liability for these benefits by $8.4 billion and increase the annual expense by $543 million, its filings show. A decrease of similar size would shrink the liability by $7 billion and the expense by $384 million.

SEC investigators want to know if companies at some point in the past may have used an artificially high health-care liability figure, then subsequently reduced it, a reduction that would have had the effect of boosting earnings.

2. (10 points each) Shown below is a regression of the return on GM stock against the return on the NYSE composite, using price data from Moneyline (Note: dividends have not been factored in.) Answer the questions below using the information from the regression analysis:

  1. If, tomorrow evening, you hear that the market has gone up 1% from today's close, what would be your best estimate of the price of GM, assuming that yesterday's closing price for GM was $24.50?
  2. Your friend does not believe the beta estimate from the regression. "Hey, this beta was computed using a limited sample of observations. The true underlying beta could be anything! It could be 3.5, for all I know!," says he. Convince your friend that the true beta is very unlikely to be so high.
  3. What proportion of the variance of returns on GM stock can be explained by movements in the market?
  4. If the average monthly rate on T-bills over this period was 0.50% (not annualized), did GM stock out-perform the market over this period (adjusted for beta risk)?
Regression Statistics
Multiple R 0.5613
R Square 0.3150
Adjusted R Square 0.3032
Standard Error 0.0800
Observations 60.0000
Significance F
Regression 1.0000 0.1706 0.1706 26.6718 0.0000
Residual 58.0000 0.3709 0.0064
Total 59.0000 0.5414      
Standard Error
t Stat
Lower 95%
Upper 95%
Intercept -0.0111 0.0104 -1.0747 0.2870 -0.0318 0.0096
NYSE; ret 1.3801 0.2672 5.1645 0.0000 0.8452 1.9150

3. (10 points each) Answer any three of the following questions:

  1. According to the WSJ for November 12, 2005, "DaimlerChrysler AG Friday said it is selling its entire 12.4% stake in Mitsubishi Motors Corp., an investment that has been a source of friction among DaimlerChrysler executives." According to Moneyline, the beta for Daimler Chrysler is 1.33 (based on historical data). Do you think it would be appropriate for DaimlerChrysler to use this beta to make capital budgeting decisions going forward? Explain your answer. If you did use this beta,
    1. DaimlerChrysler would tend to accept projects that should be rejected
    2. DaimlerChrysler tend to reject projects that should be accepted
    3. It would make no difference
  2. A stock with a higher beta will always have a higher return variance than a stock with a lower beta. True or false? Explain your answer.
  3. You are investing a million dollars in a fund. Fortunately, you won't need the money for another five years; so you don't plan to take the money out before then. This is just as well, because the fund charges a very high penalty for withdrawals before the termination of the fund, which, in this case, is five years. You are trying to figure out what your hurdle rate should be for this investment (i.e. how much should you expect to make per year, for this to be a worthwhile investment)?
  4. The beta of a stock is 1, that is, the same as the market beta. However, over the last five years, the actual variance of returns on this stock has been twice as large as that of the market portfolio. How can this be? If you run a regression of returns on this stock on the market portfolio, what would the R2 of the regression be?


1. a. I would figure out the beta of the payouts, first. That is, I would need to know how the payouts would vary if market conditions changed. For example, if it is true that there would be more people retiring in a down market (maybe fuelled by GM's layoffs in such a situation), the beta of the payouts would be negative. Once I have the beta, I would multiply it by the market risk premium and add the riskfree rate to it. This would give me the correct discount rate to apply to the expected payouts to get the present value of the payouts. As far as the riskfree rate is concerned, since this is a longterm "project," I would use the 10-year Treasury bond yield.

Insofar as estimating the beta, I would use scenario analysis. Alternatively, I could look at the covariance between payouts on GM's pension plan in the past with the return on the market portfolio. See part b. for an alternate approach.

b. There is no reason to believe ex ante that the risk is diversifiable. For example, in the scenario above, the risk would not be diversifiable. The standard approach seems to assume that the promised amounts are fixed ex-ante, and therefore, what we have is essentially a debt obligation of the company. However, since pension payments get priority, they would be compared to a high-grade bond of the company. In this case, however, the risk is not considered diversifiable, since corporate bankruptcy risk is likely to be correlated with market movements.

c. If markets are efficient, there should be no market reaction, since there is really no new information.

2. a. Since the estimated beta is 1.3801, I would expect GM to go up by 1.3801(1%) or 1.3801%. Therefore, the best estimate of GM's price would be 24.5(1.013801) or $24.838

b. The lower and upper 95% confidence intervales are 0.8452 and 1.915; this means that the likelihood that the true beta is beyond these limits is only 5%. Hence it is unlikely that the true beta would be as high as 3.5.

c. The R2 of the regression is 0.3150. Hence 31.5% of the variance of returns on GM stock can be explained by market movements.

d. We have to look at the intercept minus (1-beta)(riskfree rate); if this is positive, it means that the stock outperformed the market, after adjustment for risk. This quantity works out to -0.0111-(1-1.3801)(0.005) = -0.0092, which is less than zero. Hence GM did not outperform the market.

3. a. If Mitsubishi Motors had a different risk/beta profile than the rest of DaimlerChrysler, it would not be appropriate to use a historical beta, which would include the effect of Mitsubishi Motors, for the future. However, one could argue that both are auto companies, and hence the historical estimate can be used.

If the Mitsubishi Motors segment has a higher beta than the rest of DaimlerChrysler, then using the historical beta would mean that we would be using a higher beta estimate for DaimlerChrysler's capital budgeting decisions than would be appropriate. In this case, we would be setting too high a hurdle rate, and we would be rejecting projects that should be accepted.

b. False; a stock with a lower beta could have a higher return variance if it had a lot of diversifiable firm-specific risk.

c. You should take the five year T-bill rate and add to it the beta of hte fund times your estimate of the market risk premium. This is the hurdle rate that you should use.

d. We know that Var(Ri) = beta2Var(Rm) + Var(idiosyncratic risk). Furthermore, R2 = [beta2Var(Rm)]/Var(Ri). Hence, in this case, we have the R2 of the regression equal to 0.5.