Fin 320 Advanced Financial Analysis
Homework Assignments
Spring 2000
Prof. P.V. Viswanath

Assignments must be typed and submitted before the start of class on the due date.

Assignment 1: Objective Function of the Firm

Read the article below and answer the following questions:

  1. What are the sources of the different conflicts that you perceive in the pension conversion issue?

  2. How would you solve the conflict between employers and employees that is inherent in the pension conversion issue?

  3. Since both employees and employers would be interested in maximizing the value of the company, why is there any need for third party intervention, such as IRS?  Is this intervention unnecessary?  

US Employers Argue Pension Conversions Aren't Unfair

Wall Street Journal, January 20, 2000
By Fowler W. Martin

WASHINGTON -- Two major employer organizations told the Internal Revenue Service Thursday that conversions of defined benefit pension plans to cash balance arrangements don't violate U.S. age discrimination laws.

The groups, in written submissions to the agency in response to an IRS request for comment, said that certain aspects of conversions that appear to treat some employees differently than others are based on length of service and the extent to which benefits have accrued under an old plan rather than on the age of an employee.

The submissions were made by the Association of Private Pension and Welfare Plans (APPWP), which represents both plan sponsors and the professionals that service them, and the ERISA Industry Committee (ERIC), which represents primarily large employers.

ERISA stands for the Employee Retirement Income Security Act of 1974, a landmark law aimed at protecting retiree benefits.

The IRS, the Department of Labor, the Equal Employment Opportunity Commission and the Pension Benefit Guaranty Corp. (PBGC) are currently conducting a wide-ranging review of hybrid plans, of which cash balance plans are one type, and the issues that arise when conventional defined benefit plans are converted to such arrangements.

The agencies are looking into a number of issues including possible age discrimination and whether companies have deliberately misled employees as to the nature and intent of plan changes.

The IRS, which grants tax-favored status to pension plans, has suspended approving conversions pending the outcome of the review.

Companies have argued that conversions are necessary to satisfy the requirements of a more mobile work force and a unstable business environment in the fast-moving, high-tech economy. Some employee groups and other critics maintain that the cost-savings, aimed at driving up share prices for the benefit of investors and senior management, are the main motivation.

Several members of Congress have introduced bills aimed at curbing perceived conversion abuses and further legislative activity is expected during the course of this year. There is widespread agreement, among plan sponsors as well as the Clinton administration and legislators of both political parties, that companies need to make to make more information available to their employees when conversions take place, but there is little agreement on the nature of any additional reforms.

"Specific changes and clarification in some rules may be appropriate, especially with respect to ensuring adequate disclosure of the terms of cash balance conversions," the APPWP told the IRS.

But the notion that conversions are age discriminatory is "erroneous," said James Delaplane, the organization's vice president for retirement policy.

The APPWP argued both that hybrid plans are neither discriminatory in and of themselves and that illegal age discrimination doesn't take place when conversions are carried out.

The discrimination argument typically arises in situations where some employee are subject to a "wear away" period when an old plan is converted to a new one. That occurs when their accrued benefits under an old plan, which are protected by law, are higher than their starting balance under a new plan. In such situations, beneficiaries are often required to work for a number of years before accruing any new benefits, but they don't lose their old ones.

In some cases, another issue arises: expected future benefits, which aren't protected by law, are lower under the new plan than under the old arrangement -- sometimes substantially lower.

Benefits typically accrue slowly for most of an employee's career under a traditional defined benefit plan and then rise very sharply in the last few years before retirement. In a cash balance plan, benefits typically accue evenly over an employee's years of service.

An advisory panel to the Labor Department, consisting of private-sector experts, recently urged companies to protect long-serving employees who would otherwise be adversely impacted by wear-away periods. But the group stopped short of recommending any new mandates and it didn't offer any opinion of the age discrimination question.

Older employees typically experience the longest wear-away periods in conversion situations, but that isn't because of their age, the APPWP said. Rather, it's a function of an employee's pay history and length of service, the association said.

"It is completely clear under the law that a benefit plateau based on one or more factors -- such as length of service -- that generally correlate with age does not constitute age discrimination," the APPWP said. It also argued that "motive" has to be present for age discrimination to occur under U.S. law.

ERIC, which advanced a similar argument, said that cash balance plans are playing a "vital role" in encouraging companies to start and maintain pension plans "in an otherwise oppressive regulatory environment."

Defined benefit plans, which have been falling out of favor in recent years, have a number of advantages over the currently more popular defined contributions plans, such as 401(k) arrangements. The funding and investment risk is born by the plan sponsor rather than the beneficiary, accrued benefits are protected by the PBGC, and retirees can receive a guaranteed lifetime benefit.

On the other hand, companies often "integrate" benefits with Social Security payments, meaning retirees get less income than expected, and they generally don't adjust retirement annuity payments for inflation. Moreover, in recent years, as the stock market has boomed, many defined benefit plans have become overfunded, prompting companies to attempt to recapture the surpluses in ways that allow them to report higher earnings.

In contrast, investment gains accruing in defined contribution accounts belong to the beneficiaries. But such individual accounts typically aren't protected against market declines.

In its submission to the IRS, the APPWP asked the agency to provide new guidance, or clarify existing rules, on a variety of issues affecting the design and operation of cash balance plans.

In particular, the association urged the IRS to consider something known as back-loading rules, how the term "accrued benefit" is applied in certain circumstances and how interest rates should be applied to augment annual balances. Regulators should also consider the beneficial role cash balance plans play in easing pension plan administration during corporate mergers and acquisitions and the harm that would come from the retroactive application of any new rulings, the APPWP said.

Assignment 2: Present Value

1. You are an investment advisor who has been approached by a client for help on his financial strategy.  He has $250,000 in savings in the bank.  He is 55 years old and expects to work for 15 more years, making $80,000 a year.  (He expects to make a return of 8% on his investments for the foreseeable future.  You can ignore taxes.)

  1. Once he retires 15 years from now, he would like to be able to withdraw $60,000 a year for the following 25 years.  (His actuary tells him he will live to be 95 years old.)  How much would be need in the bank 15 years from now to be able to do this?

  2. Because of family demands, your client does not expect to be able to save more than $2,000 a year for the next five years.  Assuming that he keeps to this savings schedule, how much would he have to save over the following ten years in order to be able to afford to withdraw $60,000 a year during retirement, as planned?

  3. Assume that it is now five years from the events described in the initial paragraph.  Contrary to the expected return of 8% on investments, the stock market has crashed and expected returns are only 5%.  In order to be able to continue to withdraw $60,000 a year during retirement, how much more will your client have to save over the next ten years?

  4. If your client insists on saving no more than was originally planned (in part b.), how much would he be able to withdraw each year during retirement?

2. Go to  Pick any stock that you are interested in, that has positive earnings per share, and that pays dividends.   Pick any one analyst, and use his/her earnings estimates.  Assume that the EPS estimate for the coming year is correct, and that the estimated 5-year growth rate is correct.   If the estimated 5-year growth rate is greater than 6%, assume that growth will taper off to 6% per year after 5 years.  If not, assume that growth will continue at the estimated rate forever.

Go to Yahoo or another similar site, and find out the dividends paid on the stock last year.  Compute the ratio of dividends per share to earnings per share last year (this is called the dividend payout ratio).  Assume that this payout ratio will remain constant forever.  

Go to Yahoo or another site and find the stock's beta.  Go to Bloomberg or another similar site, and find the yield on 1 year Treasury bills.  Use the following formula to compute the required rate of return on your stock:

Required rate of return (in % p.a.) = 1 year T-bill yield + 5.5 (Stock beta)

Using your computed dividend estimates and required rate of return, compute the price of the stock.  (Keep in mind when dividends will be paid.)  Is your estimate too high or too low?  Can you explain the difference?  Document all the web sources that you used to obtain your information.

Assignment 3: Understanding Financial Statements

An excellent source for financial statement information is the Library home page; this location is very useful  because you can download the information in Excel format, and you can get up to 10 years worth of information.  In order to obtain the data, go to; click on Databases; choose the Disclosure database from the bottom option (Please choose a database).  Enter the ticker name for AT&T (T) and choose either the Global 10-K history or the U.S. 10-K history options to download the data in Excel format.  (You can also find the information at; however, it is not downloadable.)

  1. Compute the debt-equity ratio for the last five years, and plot this ratio over time.  What decisions/judgments do you have to make in order to compute the ratio?
  2. Compare the latest debt-equity ratio from your computations with the reported debt-equity ratio from another source, such as  Can you explain the difference?

Assignment 4: Risk and Return

1. Get stock price data from for the period from February 1995 to February 2000 for Sun Microsystems (ticker symbol SUNW), US West (USW) and Wal-Mart Stores, Inc. (WMT) in a spreadsheet format. Use the last column of the data (titled Adj. Close) to compute monthly returns. Then compute the expected returns and standard deviations of returns for different portfolio proportions of SUNW and USW, then USW and WMT; and then SUNW and WMT. Also compute the portfolio proportions of the absolute minimum variance portfolio for each of the three pairs of stocks. Next, plot on a single graph, the (E(R), s) combinations for all three pairs of assets. Show the minimum variance portfolios on your graph.

Answer the following questions:

  1. If you had not yet computed the portfolio variances for different portfolio combinations, and you wanted to minimize portfolio variance to the greatest extent, which of the three pairs of stocks would you choose? Why? Note: I am looking for an answer that relates to the characteristics of the assets. An answer that chooses one of the two pairs because its minimum portfolio variance is lower is insufficient.
  2. Can you decrease the standard deviation of returns of a portfolio consisting of two stocks below the standard deviations of returns of either stock by itself? If so, how? Can you increase portfolio standard deviation of return above the standard deviations of returns of either stock by itself? If so, how?

(You can find an file containing an example of portfolio construction with two assets on my webpages.)

2. Download stock price data from for IBM (ticker symbol IBM) for the period December 1978 to December 1983 in a spreadsheet format. Use the last column of the data (titled Adj. Close) to compute monthly returns. Download index data for the S&P 500 from Economagic for the same period. Use regression to compute the beta for IBM (in Excel). Now use data for the period December 1993 to December 1998 to compute IBM's beta again. Then look up the beta number provided for IBM on Yahoo. Answer the following questions:

  1. Show the results of your regression and interpret the coefficients.
  2. How confident are you regarding your beta estimate? (Answer this question with respect to the beta that you computed using the 1993-1998 data.
  3. Can you think of ways to improve your beta estimate (for the 1993-1998 period)?
  4. Is your beta estimate for the 1993-1998 period different from the beta number provided by Yahoo? Why?
  5. Is your beta estimate for the 1978-1983 period different from the estimate for the 1993-1998 period? Explain any differences.
  6. What do you infer about IBM from your results?

(Old stocks for Q. 1: ROCK, IPS and FDY; Time period: August 1994 to August 1999; use new stocks unless you're specifically okayed to use old stocks.)

Assignment 5: Capital Structure

Answer the questions posed on the final exam for Fall 1999.

Suggested Solutions

Assignment 1

1. The main conflict seems to be due to the fact that employee interests and firm interests, as articulated by management are not the same. Firm interests are twofold: one, that cash balance plans are better for the purpose of attracting younger employees that might not stay in the firm for a long period; two, conversions might be advantageous to the firm in that the total payout might be lower for some employees under the cash balance plan.
2. As far as the first issue is concerned, the firm might just allow existing employees to be grandfathered, or make them whole in some other way. If the purpose of the management is actually to save money by taking away expected benefits that were promised, but not explicitly contracted for, it may be difficult to reach a compromise.
However, there are reputation issues for the firm to take into account. And, if these are factored in, as well, the firm might well decide that the potential savings due to the conversion are not worth it, in the interests of a more contented and productive workforce.
3. Ex-ante this is true; ex-post it might not be true, as we have seen in this case. However, to the extent that the company is in it for the long-haul, ex-post and ex-ante interests could well coincide.
The other problem is that there may information asymmetry, so that even ex-ante firms may be able to take advantage of unsuspecting prospective employees (or customers). However, this is relevant, only if "good" firms cannot inexpensively signal their quality to the employees.

Assignment 2

Problem 1. 
Year Cashflow (at year end) (in thousands) Present Value (at 8%) Value at the end of year 15 (at 8%)
0 250 250 25 x 3.172 = 793.042
1-15 80 80 x 8.559 = 684.758 684.758 x 3.172 = 2172.1682
16-40 60 60 x 10.6748/(1.08)15 = 201.9081 201.9081 x 3.172 = 640.4866

Present values of annuities are computed using the annuity formula (for example in the last two rows of the table; column 3); 3.172 is simply equal to (1.08)15

a. The answer from the above table is 640.4866.

b. The already available $250 will grow to $793.042; so no more additional saving is necessary.  From part (a), we know that on ly $640.4866 is required at the end of yr. 15 (when he is 70).  He can even dissave.  How much can he dissave (or consume in excess of his salary) during the fifteen years?  Suppose he chooses to dissave $x per year.  Then, we need PV(annuity of x per year for 15 years at 8%) = (793.042-640.4866)/(1.08)15.  Solving, we find x = $5.6185

c. It's five years from the beginning of the events described.  The $2 that the client saved each year would have amounted to PV(annuity of 2 per year for 5 years at 8%) x (1.08)5 = 11.7332 and the initial 250 would have grown to 367.332, for a total of 379.065.  From this point on, the monies will grow at 5%.  So these already accumulated funds will grow to 379.065(1.05)10 = 617.457 by the time the client retires.  Now, he will need $60 per year for the next 25 years.  It's value at the time of retirement can be computed as PV(annuity of 60 per year for 25 years at 5%).  This works out to 845.63667, which is greater than the 617.457, which the client has accumulated.  Hence, he needs to plan to save $y every year for the next ten years, such that PV($y per year for 10 years at 5%)(1.05)10 = (845.63667 - 617.457).  Solving, we find 18.141328 a year.

d. If, on the other hand, the client only wants to save $2 per year for the next 10 years, he would have 617.457 + PV(annuity of $2 for 10 years at 5%)(1.05)10 = 617.457 + 25.15579.  Equating this to the present value of an annuity of $x for 25 years at 5%, we find $x = $45.595 a year.

Problem 2:

Suppose we pick GE.  Go to and pick the first Institutional Broker, who has EPS estimates of $3.70 for 2000.  The estimated five-year growth rate is 15%. 

From,  we see that dividends last year were $1.64, with earnings of $3.22 for a payout ratio of  approximately 50%.  (Keep in mind that earnings are year-to-date, while dividends seem to be for the last fiscal year (somewhat unclear from the information provided on the site.)  The stock beta is given as 1.16.  The return on 1 year T-bills ( as of Feb. 8, 2000 is 6.19%.

Using this payout ratio, dividends next year would be 3.70/2 = 1.85 next year and is expected to grow at 15% for the next five years, with growth tapering off to 6%, as provided for in the question.

The required rate of return is given by 6.19 + 1.16(5.5) = 12.57%

Discounting the dividends for the next 5 years using the information generated, we have a present value of 8.5796.  Dividends at the end of the sixth year would be 1.85(1.15)4(1.06) = 3.4298.  Discounting the value (at the end of year 5) of the dividends from the future that would be expected to grow at 6% p.a., we get 3.4298/(.1257 - 0.06) = 52.204.  Discounting the value to the beginning of year 1, we have 52.204(1.1257)5 = 28.8795.  Adding in the 8.5796, we get an estimated stock price of $37.46.  The actual stock price at 11 am on Feb. 8, 2000 was $138!

We assumed that all dividends on a yearly basis, starting one year from now, i.e. as of Feb. 8, 2001.  In practice, GE pays dividends four times a year starting in March.  We would need to adjust our computations for this.  However, the estimated price and the actual price are far apart!  How are we to explain this?

Assignment 3

Solution to Assignment 3

Assignment 4

Solution to Assignment 4

Assignment 5

Solution to Assignment 5

Go to the FIN 320 Home Page

Go to Prof. P.V. Viswanath's Home Page