Calculating Future Values Go to and follow the "Savings Calculator" link. If you currently have $10,000 and invest this money at 9 percent, how much will you have in 30 years? Assume you will not make any additional contributions. How much will you have if you can earn 11 percent? Calculating the Number of Periods Go to and follow the "Cool Million" link. You want to be a millionaire. You can earn 11.5 percent per year. Using your current age, at what age will you become a millionaire if you have $25,000 to invest, assuming you make no other deposits (ignore inflation)? Calculating the Number of Periods Cigna has a financial calculator available at To get to the calculator, follow the "Calculator & Tools" link, then the "Present/Future Value Calculator" link. You want to buy a Lamborghini Diablo VTTT. The current market price of the car is $330,000 and you have $33,000. If you can earn an 11 percent return, how many years until you can buy this car (assuming the price stays the same)?

Calculating Rates of Return Use the Cigna financial calculator to solve the following problem. You still want to buy the Lamborghini VTTT, but you have $50,000 to deposit and want to buy the car in 15 years. What interest rate do you have to earn to accomplish this (assuming the price stays the same)? Future Values and Taxes Taxes can greatly affect the future value of your investment. The Financial Calculators web site at has a financial calculator that adjusts your return for taxes. Follow the "Projected Savings" link on this page to find this calculator. Suppose you have $50,000 to invest today. If you can earn a 12 percent return and no additional annual savings, how much will you have in 20 years? (Enter 0 percent as the tax rate.) Now, assume that your marginal tax rate is 27.5 percent. How much will you have at this tax rate?

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Ross et al.: Fundamentals I III. Valuation of Future I 6. Discounted Cash Flow I I © The McGraw-Hill of Corporate Finance, Sixth Cash Flows Valuation Companies, 2002

Edition, Alternate Edition

Ross et al.: Fundamentals I III. Valuation of Future I 6. Discounted Cash Flow I I © The McGraw-Hill of Corporate Finance, Sixth Cash Flows Valuation Companies, 2002

Edition, Alternate Edition

The signing of big-name athletes is often accompanied by great fanfare, but the numbers are sometimes misleading. For example, in October 1998, the New York Mets signed catcher Mike Piazza to a $91 million contract, the richest deal in baseball history. Not bad, especially for someone who makes a living using the "tools of ignorance" (jock jargon for a catcher's equipment). That record didn't last long. In late 2000, the Texas Rangers offered 25-year-old Alexander Rodriguez, or "A-Rod" as his fans call him, a contract with a stated value of $250 million!

A closer look at the number shows that both Piazza and A-Rod did pretty well, but nothing like the quoted figures. Using Piazza's contract as an example, the value was reported to be $91 million, but the total was actually payable over several years. It consisted of a signing bonus of $7.5 million ($4 million payable in 1999, $3.5 million in 2002) plus a salary of $83.5 million. The salary was to be distributed as $6 million in 1999, $11 million in 2000, $12.5 million in 2001, $9.5 million in 2002, $14.5 million in 2003, and $15 million in both 2004 and 2005. A-Rod's deal was spread out over an even longer period of 10 years. So, once we consider the time value of money, neither player received the quoted amounts. How much did they really get? This chapter gives you the "tools of knowledge" to answer this question.

In our previous chapter, we covered the basics of discounted cash flow valuation. However, so far, we have only dealt with single cash flows. In reality, most investments have multiple cash flows. For example, if Sears is thinking of opening a new department store, there will be a large cash outlay in the beginning and then cash inflows for many years. In this chapter, we begin to explore how to value such investments.

When you finish this chapter, you should have some very practical skills. For example, you will know how to calculate your own car payments or student loan payments. You will also be able to determine how long it will take to pay off a credit card if you make the minimum payment each month (a practice we do not recommend). We will show you how to compare interest rates to determine which are the highest and which are the lowest, and we will also show you how interest rates can be quoted in different, and at times deceptive, ways.

Ross et al.: Fundamentals of Corporate Finance, Sixth Edition, Alternate Edition

III. Valuation of Future Cash Flows

6. Discounted Cash Flow Valuation

© The McGraw-Hill Companies, 2002

PART THREE Valuation of Future Cash Flows

Money Attraction Secrets

Money Attraction Secrets

Discovering The Laws Of The Right Financial Blueprint. I bet you're scared, angry and maybe even confused. These are perfectly rational and appropriate reactions to the worldwide credit crisis that erupted in 2008 and sends shudders through every home in the United States.

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