PART II: VALUATION AND CAPITAL BUDGETING

Discounted Cash Flow Valuation

The signing of big-name athletes is often accompanied by great fanfare, but the numbers are often misleading. For example, in late 2010, catcher Victor Martinez reached a deal with the Detroit Tigers, signing a contract with a reported value of $50 million. Not bad, especially for someone who makes a living using the “tools of ignorance” (jock jargon for a catcher’s equipment). Another example is the contract signed by Jayson Werth of the Washington Nationals, which had a stated value of $126 million. It looks like Victor and Jayson did pretty well, but then there was Carl Crawford, who signed to play in front of Boston’s Red Sox nation. Carl’s contract has a stated value of $142 million, but this amount was actually payable over several years. The contract consisted of a $6 million signing bonus, along with $14 million in the first year plus $122 million in future salary to be paid in the years 2011 through 2017. Victor’s and Jayson’s payments were similarly spread over time. Because all three contracts called for payments that are made at future dates, we must consider the time value of money, which means none of these players received the quoted amounts. How much did they really get? This chapter gives you the “tools of knowledge” to answer this question. For updates on the latest happenings in finance, visit www .rwjcorporatefinance .blogspot.com

4.1 Valuation: The One-Period Case

Keith Vaughn is trying to sell a piece of raw land in Alaska. Yesterday he was offered $10,000 for the property. He was about ready to accept the offer when another individual offered him $11,424. However, the second offer was to be paid a year from now. Keith has satisfied himself that both buyers are honest and financially solvent, so he has no fear that the offer he selects will fall through. These two offers are pictured as cash flows in Figure 4.1. Which offer should Keith choose? Mike Tuttle, Keith’s financial adviser, points out that if Keith takes the first offer, he could invest the $10,000 in the bank at an insured rate of 12 percent. At the end of one year, he would have: $10,000 1 (.12 3 $10,000) 5 $10,000 3 1.12 5 $11,200 Return of Interest principal Because this is less than the $11,424 Keith could receive from the second offer, Mike recommends that he take the latter. This analysis uses the concept of future value (FV) or compound value, which is the value of a sum after investing over one or more periods. The compound or future value of $10,000 at 12 percent is $11,200. 87

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Part II Valuation and Capital Budgeting

Figure 4.1

Cash Flow for Keith Vaughn’s Sale Alternative sale prices $10,000 $11,424

Year:

0

1

An alternative method employs the concept of present value (PV). One can determine present value by asking the following question: How much money must Keith put in the bank today so that he will have $11,424 next year? We can write this algebraically as: PV 3 1.12 5 $11,424 We want to solve for PV, the amount of money that yields $11,424 if invested at 12 percent today. Solving for PV, we have: $11,424 PV 5 _______ 5 $10,200 1.12 The formula for PV can be written as follows: Present Value of Investment: C1 PV 5 _____ 11r

(4.1)

where C1 is cash flow at date 1 and r is the rate of return that Keith Vaughn requires on his land sale. It is sometimes referred to as the discount rate. Present value analysis tells us that a payment of $11,424 to be received next year has a present value of $10,200 today. In other words, at a 12 percent interest rate, Keith is indifferent between $10,200 today or $11,424 next year. If you gave him $10,200 today, he could put it in the bank and receive $11,424 next year. Because the second offer has a present value of $10,200, whereas the first offer is for only $10,000, present value analysis also indicates that Keith should take the second offer. In other words, both future value...