The time value of money is perhaps the most critical tool we learn in finance. We need a firm handle on all aspects of present value and future value in order to apply the time value concept to valuation. Perhaps when we relate these topics to situations that we encounter in our daily lives, these concepts will become easier to grasp. Go to the directbanking.com Web site and play with the monthly payment calculator. Plug in the price of your dream vehicle and some financing terms and see what the payment will be.

1. What factors determine monthly payments when you purchase a big-ticket item?
   
   
2. What happens to the payment, all else equal, when the term is increased?
   
   
3. Plug in $10,000, a five- percent interest rate and 4 years term. How much is the monthly payment?
   
   
4. Now what happens when you increase the term to 5 years? How much is the new payment?
   
   
5. What happens to the payment, all else equal, when the interest rate is increased?
   
   
6. Plug in $20,000, an 8 percent interest rate and 6 years term. How much is the monthly payment?
   
   
7. Now what happens when you increase the interest rate to 9 percent? How much is the new payment?

LEAD STORY-DATELINE: Business Week, December 3, 2001.

On October 31, 2001, the U.S. Treasury announced that it would no longer issue 30-year bonds. Since long bonds have been in short supply for months, the announcement pushed up prices for existing 30-year Treasury bonds. That's great, as long as you happen to own long Treasuries. But the announcement had some unintended effects for firms with defined benefit pension plans.

In a nutshell, the impact is quite costly and may be devastating to many firms, given the current economic recession. Pension consultants Watson Wyatt & Co. estimate that businesses may need to make additional deposits to pension plans of $40 billion.

IRS regulations require that firms calculate pension plan funding requirements on an annual basis. The regulations force firms to determine the current value of future pension obligations using a four-year average of 30-year Treasury bond yields, regardless of how the funds are actually invested. Compared to corporate bonds, the long Treasury bond yields are a full percentage point too low. Thus, the current value of future obligations gets overstated by as much as 12 to 15 percent.

TALKING IT OVER AND THINKING IT THROUGH!

1. Suppose your firm employs Joan Reed. Your pension plan promises to pay Joan a lump sum benefit in the amount of $100,000 when she retires in seven years. Draw the pension plan's cash flow time line.
   
   
2. Find the present value of the firm's promise to Joan assuming the pension fund investments earn 5 percent annual rate of interest.
   
   
3. Find the present value of the firm's promise to Joan assuming the pension fund investments earn 4 percent annual rate of interest.
   
   
4. In your own words, explain the relationship between bond yields and valuation.
   
   
5. Suppose the pension fund is actually earning 5 percent on assets, but the IRS requires the firm to determine the funding adequacy of future obligations at 4 percent. How much additional cash would your firm need to deposit to meet the IRS funding requirements?

THINKING ABOUT THE FUTURE!

Once a firm's pension becomes "underfunded" according to the IRS rules, it faces additional negatives. These include being charged higher insurance premiums by the Pension Benefit Guaranty Corporation.

To change the IRS rules requires Congressional action before year-end 2001. What possible political solutions are there to the dilemma caused by the Treasury's October 31 announcement?

SOURCES:

Henry, David. "Pension Plans: $40 Billion Short?," Business Week, December 3, 2001.

The social security system provides retirement benefits to millions of Americans. Contributions to the system are made by payroll deductions throughout a worker's lifetime, and benefits are typically received many years later at retirement. Retirement benefits are paid monthly based on a formula that incorporates a worker's lifetime earnings and retirement age. Critics of the system argue that contributions are too high in relation to the benefits received. Any valid analysis of the social security system must involve consideration of the time value of money both in the determination of the future value of years of contributions and the present value of years of retirement benefits.

Visit the Social Security Administration's Web site, which provides information on the social security system and analysis tools that assist individuals in the determination of their obligations and expected benefits. Begin by reviewing some of the Frequently Asked Questions. In particular, question 11 provides information on the contributions required of each covered worker and his or her employer, and question 14 gives a brief overview of how retirement benefits are determined. Use this information to help you answer question one. Go back to the home page and click on Benefit/Tax Changes for 2002 in the Benefits Payments section. Review the history of automatic cost of living adjustments and use this information to answer question two. Return to the home page and click on Office of the Actuary in the Research and Data section. Select Compute Your Own Benefit and use the Quick Calculator to help answer questions three and four.

Explore the rest of the Social Security Administration Web site to learn more about this massive government program that collects and distributes billions of dollars and affects the vast majority of workers and their families in the United States.

1. Use the Maximum Earnings Taxable amounts for both social security and Medicare to calculate the amount of taxes that would be paid by a worker earning $100,000 in 2001. Calculate the taxes for the same worker earning $100,000 in 2002. What is the change in the effective tax rate caused by the increase in Maximum Earnings Taxable amounts from 2001 to 2002?
   
   
2. Cost of living increases can have a dramatic impact on retirement benefits. Inflation was much higher in the 1970's and 1980's than it has been since then. Compare the increase in the benefit amount from June 1975 to July 1982 for a retiree receiving $10,000 per year in June 1975 with the increase in the benefit amount from December 1994 to January 2002 for a retiree receiving $10,000 in December 1994. Determine your answer using an electronic spreadsheet.
   
   
3. Bill is a 40-year-old worker earning $50,000 per year. Use the Quick Calculator to determine Bill's monthly retirement benefit if he continues to earn $50,000 per year until he retires at age 67. Bill contributes 6.2 percent of his salary to social security and his employer also contributes 6.2 percent. If these contributions were placed in a private investment account each month and not into social security, what effective annual rate of return would Bill need to achieve to get the same expected retirement benefit as he expects to get from social security? Assume that Bill expects to live for 20 years after his retirement in 2029. Also, include the contributions that would have been made in prior years based on the estimated earnings provided on the Social Security Web site. These contributions from prior years can be found by clicking on see the earnings we used.
   
   
4. Recalculate the effective annual return assuming that Bill lives for 10 years after retirement and for 30 years after retirement. Summarize the impact of life expectancy on the relative value of social security benefits.
   
   
5. Click on the breakeven age button on the Quick Calculator page. The analysis indicates that a person who delays retirement to age 67 in order to receive a higher monthly benefit amount would need to live to be 78 years old in order to breakeven compared to a person who retires at age 62 with a lower benefit amount. How is the breakeven age calculated? If Bill retires at age 62 and invests his social security payments in an account that earns 10 percent interest, how much would he have sixteen years later at age 78? Compare this with the amount Bill would have if he retires at age 67 and invests the higher social security payments in an account paying 10 percent interest for eleven years. Do your answers support the breakeven age given by social security? If not, explain.

How many of us would like to accumulate a cool million dollars by the time we retire? Probably all of us, if we were honest with ourselves. Money doesn't buy happiness but it does pay the bills. Go to the Unico Bank Web site and play with the Millionaire calculator.

Alter the values in the table to fit your specific situation and hit the calculate button. The graph will indicate your total accumulation, given your assumptions, by your target retirement age. At the top of the table the heading will indicate the age your current plan will actually make you a millionaire! Play with several of the values like savings per month and expected rate of return and notice how the age changes.

1. What happens to the length of time it takes you to become a millionaire when you increase your savings per month?
2. What happens when you increase the expected rate of return?
3. How do taxes impact your accumulation?
4. Why are marginal tax rates important instead of average?
5. What rate should you use for an expected return?
6. What happens if I want to become a millionaire sooner than the calculator indicates?

Go to The Mortgage Expert Web site and select Mortgage Calculators to answer the questions. For each question, record which of the Web site calculators you used and what you filled in for each blank (i.e., variable). Check the Web calculator's answer by using your financial calculator. Show your financial calculator keystrokes.

1. Assume that you need to borrow $150,000 to buy a home. If the annual interest rate is 7.625 percent, what are the monthly payments for interest and principal? Assume the loan begins today and has a 30-year term.
   
   
2. What balance would you owe at the end of the first year?
   
   
3. Assuming no prepayment, how much interest is paid over the life of the loan? Explain the calculation of your answer.
   
   
4. Use the Web calculator to determine the term of the loan if $50/month is pre-paid.