butler 3e 10 auto 7/24/14 11:05 AM Page 565 Chapter X Principles of Valuation Market prices are often viewed as the best measure of the value of a good or service. Because market prices can be determined objectively and generally cannot be manipulated, they are often relied upon to generate unbiased, independent measures of value. Obviously, market prices are important in many legal contexts, whether they are used for filling gaps in contracts or determining the appropriate compensation for governmental takings of property. However, in many legal situations, adequate market indicators are not available and surrogates for market value must be calculated. This chapter focuses on the concept of the time value of money — that cash flows received at earlier points in time are worth more than cash flows received at later points in time. Among these concepts are prejudgment interest calculations — the methodology for determining the value today of money lost in the past — and present value calcula - tions — the methodology for determining the value today of payments to be received in the future. Section A considers prejudgment interest calculations and explains what the interest rate in the calculations represents. Section B discusses discounting of future payments into present values and demonstrates how those general principles are applied in lawsuits by focusing on the determination of the relevant future stream of dollars and the selection of the proper discount rate. Section C considers two methodologies that courts apply in determining the value of life. Finally, Section D demonstrates how to value close corporations using two different approaches. A. Prejudgment Interest Prejudgment interest is interest accruing on the amount of a legal award from the time of the injury or damage to the time the judgment is entered by the court. It compensates a plaintiff for the loss of the use of funds and the effects of inflation after she suffered a cognizable economic harm caused by the defendant. Prejudgment interest is necessary to fully compensate plaintiffs because of the time value of money. If the plaintiff had never suffered economic damages, she could have instead invested that money and earned income or interest. Prejudgment interest is calculated as a small percentage tacked onto the principal award. For example, if only one year has elapsed between injury and judgment, the economic damages are $1,000,000 and the relevant interest rate is 4%, then the prejudgment 565 butler 3e 10 auto 7/24/14 11:05 AM Page 566 566 X · PRINCIPLES OF VALUATION interest would be $1,000,000 × .04 = $40,000. Thus, the plaintiff’s total award would be $1,040,000. What if four years elapsed between injury and judgment? Courts are split on whether they use simple or compound interest to compute prejudgment interest. Simple interest is interest paid on the original principal award only. Thus, if the prejudgment interest was $40,000 a year and four years elapsed between injury and judgment, the total prejudgment interest award would be $160,000, and the total damage award would be $1,160,000. Compound interest is interest earned not only on the original principal, but also on all interest amounts earned previously. If we assume that interest compounds once per year, then we can use a simple formula for future value calculations to compute the total damage award to the plaintiff: FV = P × (1+I) n where P = the principal award I = the relevant interest rate in the economy (assumed constant) n = the number of years elapsed FV = the future value or total damage award In our example, the plaintiff’s total award would be $1,169,859 ($1,000,000 × 1.04 4) As the amount of damages and length of time between injury and judgment increases, the amount of prejudgment interest increases. Similarly, slight changes in the interest rate can have significant impacts on the prejudgment interest award. If the interest rate in the above calculation had been 8% instead of 4%, the plaintiff’s award would have been $1,360,489 ($1,000,000 × 1.08 4), a difference of over $190,000! Yet despite the importance of prejudgment interest, there is no uniform method for determining it. Many jurisdictions have strict statutory or common law prescriptions on both when prejudgment interest is awarded and the interest rate used in the calculations. Other jurisdictions give courts discretion on whether to award it and how to calculate it. In these jurisdictions, courts have grappled with what the interest rate should represent. Should it reflect the interest that the plaintiff could have earned on her money, or the risk of the defendant’s default? Gorenstein Enterprises, Inc. v. Quality Care-USA, Inc. United States Court of Appeals for the Seventh Circuit 874 F. 2d 431 (1989) POSNER, Circuit Judge. This protracted litigation over a franchise resulted in a resounding defeat for the franchisee and its principals — the Gorenstein brothers. Substantial and experienced busi - nessmen who own and operate several nursing homes in the Chicago area, they had obtained a franchise in 1978 from Quality Care-USA to provide home health care services in the Chicago area under Quality Care’s registered trademark. Home health care services involve the provision of nursing and other medical care in the home rather than in an institution. Licensed home health care providers can provide some services that unlicensed ones cannot; the parties disagree over whether Quality Care undertook as part of its deal with the Gorensteins to obtain a license for the franchised operation. butler 3e 10 auto 7/24/14 11:05 AM Page 567 X · PRINCIPLES OF VALUATION 567 Shortly after obtaining the franchise from Quality Care the Gorensteins defaulted on their royalty obligations, and in 1980 Quality Care terminated the Gorensteins’ franchise and demanded that they cease using the Quality Care trademark forthwith. Ignoring the demand, the Gorensteins instead sued Quality Care in an Illinois state court, seeking rescission of the franchise agreement. ... * * * Quality Care’s case then went to the jury, which found in its favor and awarded damages. The judge trebled the jury’s award of damages for trademark infringement, and also awarded Quality Care attorney’s fees on the entire judgment, plus prejudgment interest, at 9 percent per annum, on the award of trademark damages (untrebled), making a grand total that with postjudgment interest is now approaching $900,000. * * * There is no federal statutory interest rate on prejudgment interest. But as the 9 percent figure used by the district judge was well below the average interest rate for “securities” comparable in riskiness to Quality Care’s cause of action for trademark infringement against the Gorensteins, he can hardly be criticized for setting too high a rate. Surely the rate was too low; there were times while this suit was pending when the prime rate exceeded 20 percent. For the future, we suggest that district judges use the prime rate for fixing prejudgment interest where there is no statutory interest rate. That is a readily ascertainable figure which provides a reasonable although rough estimate of the interest rate necessary to compensate plaintiffs not only for the loss of the use of their money but also for the risk of default. The defendant who has violated the plaintiff’s rights is in effect a debtor of the plaintiff until the judgment is entered and paid or otherwise collected. At any time before actual payment or collection of the judgment the defendant may default and the plaintiff come up empty-handed. The plaintiff is an unsecured, uninsured creditor, and the risk of default must be considered in deciding what a compensatory rate of interest would be. A federal statute, 28 U.S.C. Sec. 1961, fixes the post judgment interest rate for federal cases (including diversity cases) as the rate on 52-week Treasury bills at the last auction of those bills before the judgment was entered. This rate is too low, because there is no default risk with Treasury bills. Of course the courts are bound by that rate so far as post - judgment interest is concerned. But prejudgment interest is governed by federal common law, and the courts are free to adopt a more discriminating approach. We have chosen the prime rate for convenience; a more precise estimate would be the interest rate paid by the defendant for unsecured loans. We do not want to straitjacket the district judges but we do want to caution them against the danger of setting prejudgment interest rates too low by neglecting the risk, often nontrivial, of default. * * * Notes and Questions 1. Posner and Interest Rates: Why does Posner believe the interest rate paid by the defendant for unsecured loans is the precise rate to use? Consider our discussion of risk and market prices in Chapter VI. 2. Back-Door Prejudgment Interest: Suppose a plaintiff had to take out a loan as a result of suffering economic harm caused by the defendant. If the court awards the interest paid on the loan as part of the plaintiff’s damage award, is that different from an award of prejudgment interest? Consider the following opinion: butler 3e 10 auto 7/24/14 11:05 AM Page 568 568 X · PRINCIPLES OF VALUATION United Telecommunications, Inc. v. American Television and Communications Corp. United States Court of Appeals for the Tenth Circuit 536 F.2d 1310 (1976) William E. Doyle, Circuit Judge. Involved here is the exchange of an interest in Jefferson-Carolina Corp., a cable television company, by United Telecommunications, Inc. (“United”) for 175,000 shares of American Television & Communications Corp. (“ATC”). ... The purchase agreement between United and ATC .