WFU Law School
Law & Valuation
2.1 Risk and Return Fundamentals

2.1.1 Returns


What is interest?

Fundamental to valuation is the practice (observed throughout history) that the those who permit another to use their money demand a return—or "interest." What is interest? Simply put, it is the amount charged to use money for a given period.

Why do people charge interest? One answer, though circular, is that everybody does it! Charging interest reflects the reality that those who lend or invest money expect to receive a return—for example, when we put our money in a bank.

But why are others willing to pay you for using your money? Well, money is in short supply, and those who don't have it will pay you to use it. You presumably have other uses for your money and will not give up current use, unless you get something in return. Interest compensates you for the opportunity cost of allowing another to use your money.

How do others pay you for the use of your money? With a promise -- of returning to you more than you gave! If I can get you to part with your money—hoping I can put it to productive (or pleasurable) use and promising I will later pay you more than you gave me—then we both benefit. I get the desirable use of your money, and you a promise of greater wealth.

How much can you charge for use of your money? That depends on how much I and others are willing to pay. For example, if banks are willing to pay you a 6% return to use your money for a year, you might demand a higher return (say 15%) from me since my promise to pay is less convincing than the bank's. So why don't you charge me 25% interest? At that price, your money is too expensive assuming I have others willing to lend to me at 15%. The law does limit the interest rates that can be charged by certain lenders, especially banks. See, e.g., 12 U.S.C. § 85 (establishing usury limits for national banks).

Notice that "interest" can have a wide range of meanings. Normally, interest refers to a return when payment is relatively certain—as in the case of bank interest. But it can also refer to a return with less certainty—as is the case when dividends are paid on corporate stock or profits are paid in a joint venture. Whatever the name, it's still payment for using another's money!

Example

A $1,000 bond pays $10 monthly interest and after 1 year is worth -- $1,050 / $920 / $500. What is its annual return?


Answer: The return for each bond is:

Bond
Return calculation
Return
$1,050
($1,050 - $1,000 + $120)
$1,000
17%
$920
($920 - $1,000 + $120)
$1,000
4%
$500
($500 - $1,000 + $120)
$1,000
-38%

BROWN V. LEGAL FOUNDATION OF WASH. (US Supreme Court 2003 )

Every State uses interest on lawyers' trust accounts (IOLTA) to pay for legal services for the needy. In promulgating Rules establishing Washington's program, the State Supreme Court required that:

(a) all client funds be deposited in interest-bearing trust accounts, (b) funds that cannot earn net interest for the client be deposited in an IOLTA account,(c) lawyers direct banks to pay the net interest on the IOLTA accounts to the Legal Foundation of Washington (Foundation), and (d) the Foundation use all such funds for tax-exempt law-related charitable and educational purposes.

It seems apparent from the court's explanation of its IOLTA Rules that a lawyer who mistakenly uses an IOLTA account for money that could earn interest for the client would violate the Rule. That court subsequently made its IOLTA Rules applicable to Limited Practice Officers (LPOs), nonlawyers who are licensed to act as escrowees in real estate closings.

Petitioners, who have funds that are deposited by LPOs in IOLTA accounts, and others sought to enjoin respondent state official from continuing this requirement, alleging, among other things, that the taking of the interest earned on their funds in IOLTA accounts violates the Just Compensation Clause of the Fifth Amendment, and that the requirement that client funds be placed in such accounts is an illegal taking of the beneficial use of those funds. (More>>)


Calculation of Returns

What are returns? Returns are simply the net gains or losses an asset produces. Often return is stated as a percentage -- the change in value from time zero to a future time. A general formula for a return over any time period is --

RETURNt =
(PRICEt - PRICE0 + CASHFLOWt) / PRICE0
RETURNt
rate of return for period t
PRICEt
value at end of period t
PRICE0
value at beginning of period t
CASHFLOWt
added value during period t

When the value of the beginning and the end of a period are known, the computation is straightforward.

A caution

A famous example of a return calculation gone awry comes from the Beardstown Ladies investment club. The Ladies achieved national fame for supposedly creating portfolio returns that put Wall Street gurus to shame. They sold a book touting average annual returns of 23.4% for the period 1983-1993, during a period when market returns hovered in the low teens. They sold 800,000 copies of their book, published other books, and hit the speakers' circuit.

But an audit by Price Waterhouse revealed the Ladies had averaged annual returns of only 9.1%. The Ladies goofed by incorrectly counting their average annual return for 1991 and 1992 as the average performance for a full decade.

See Karen Hube, “How to Sidestep a ‘Beardstown Blunder’ When Calculating Portfolio Performance,” Wall St. J. (Mar. 25, 1998).

 

 

Example - Begin/end of period

How should you calculate investment returns when there are cashflows during the return period? This is one of the most tricky aspects of return calculation. For example, suppose you began the year with a portfolio worth $50,000 and over the year you added $17,000 in investments, but withdrew $11,000 -- for a net cash flow of $6,000 -- and finished the year with a investment of $60,000. How much did your portfolio return?

One simple calculation is to assume that half the net cash flow was added at the beginning of the investment period (increasing your "beginning value")and that the other was added at the end (decreasing your "ending value").

Beginning value
$50,000
Ending value
$60,000
Net cash flow (NCF) during period
$6,000
Beginning value plus half NCF
$53,000
Ending value minus half NCF
$57,000
Calculate estimated return
($57,000 - $53,000)
$53,000
Estimated return
7.55%

Notice that this result would be misleading if the cash inputs of $17,0000 occurred entirely at the beginning of the investment period, and cash outputs of $11,000 happened at the end. Then, $67,000 (begining value plus inputs) would have produced $71,000 (ending value before outputs) - - a signficantly smaller return of 5.97%.


Internal rate of returns

Sometimes returns are promised - as when a company promises to pay interest and principal on its bonds. But often returns are variable - as when a company promises dividends based on earnings, or an employer promises an employee "hefty" pay increases.

How can past returns be extrapolated to calculate future returns? Predicting returns is an art. There are different methods:

  • Average returns: this assumes that returns will merely be an average of past returns, no growth or decline.
  • Annualized growth rate: this assumes that beginning and ending returns reflect future returns. It reflects assumptions about relevant periods, and that past returns suggest a pattern of growth or contraction.
  • Internal rate of growth: This weighs the returns during a period and attempts to identify a lnear (or other) equation that best describes them. Finding this rate of change depends on a number of assumptions and predictions: which period one looks at, whether the growth/contraction is linear or not, and whether the rate continues indefinitely.

Example

Return to the "Old Man and the Apple Tree." Recall that the earnings/cash flow wass assumed to be be $45 over time. Consider what returns should be in the future if the following were the returns over the last 10 years:

1992
20
1993
-10
1994
50
1995
34
1996
45
1997
43
1998
57
1999
41
2000
46
2001
44
2002
50

See the attached spreadsheet


Returns in legal contexts

Estimating returns—deciding what to include, when it will occur, how long it will continue, and whether to make adjustments—is often at the heart of financial valuations. Remember, however, this process of estimation does not occur in a vacuum—especially in a legal environment.Valuations are not undertaken for their own sake, but rather for the purpose of serving one or more of the parties’ self interest. Therefore, predictions about future performance must always be evaluated in light of unavoidable adversarial tensions—between litigants in court or between buyers and sellers in arm’s length transactions.

Despite the inherent imprecision and biases that often color estimates of returns, their relevance to the valuation task remains. Consider the example of valuing a medical degree in an equitable distribution.

Example

Dr. Jones, an ophthalmologist, is 45 when she separates from her husband Mr. Smith of 25 years. They married the summer after she graduated from college with a degree in biology (Phi Betta Kappa, 3.9 GPA). Jones then attended Hale Medical School, where she finished in the top 10% of her class. After a residency and a series of prestigious fellowships, Jones and Smith moved to Carlton, New Columbia. Jones joined a private practice and soon became a partner. She worked grueling hours and on weekends. Smith was a homemaker.

The couple has separated and are negotiating a settlement of their marital estate. What is the value of Jones's medical license? (More>>)
2.1 Risk and Return Fundamentals

©2003 Professor Alan R. Palmiter

This page was last updated on: March 16, 2004