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