Valuation, financial strategies, and capital markets

• Pages: 320-401
• Author: William A. Klein,John C. Coffee Jr.,Frank Partnoy

320

Chapter 5

VALUATION, FINANCIAL STRATEGIES,

AND CAPITAL MARKETS

I. VALUATION

A. THE INTEREST RATE

We are about to examine methods of valuing assets and enterprises,

beginning with so-called money-market instruments like bonds and

notes. These methods of valuation require the application of an appro-

priate rate of interest. That rate could be treated as a given, determined

by processes that need not concern us. It may be helpful, however, to

inquire briefly into some of the underlying attributes of the rate of

interest. The inquiry can best be framed by posing the question, for

what does the interest paid on a bond compensate the holder of that

bond?

Perhaps the most fundamental component of the interest rate is

compensation for the time value of money; this component is sometimes

called ‘‘pure’’ interest. It can best be described as what is left after

taking out the other elements to be described below; or as the amount

that would be paid on a risk-free bond in an era in which value of money

were expected to remain constant (that is, in an era of no inflation or

deflation). A recent economic study concludes that in the period 1926 to

2004, after properly accounting for inflation, the average (technically,

the geometric mean) annual yield on short-term U.S. Treasury obli-

gations was 0.7 percent and on a diversified portfolio of large company

common stocks was 7.2 percent.1

A second important element in the interest rate for a particular

obligation is compensation for the risk of default.

Another element in the interest rate has to do with the ‘‘term

structure of interest rates’’ (reflected graphically in the ‘‘yield curve’’).

These phrases refer to the fact that interest rates vary with the duration

of the debt. Generally (but not always), long-term obligations bear

higher interest rates than shorter-term obligations. The longer the

duration, the greater the effect on value of any change in market

interest rates and expected rates of inflation. Thus, part of the explana-

tion for higher interest rates on longer-term obligations may lie in their

greater volatility risk.

1 R. Ibbotson Associates, Stocks, Bonds,

Bills and Inflation: 2005 Yearbook at 83, 91

(2005). The return on small-company stocks

was 9.1 percent and on intermediate-term

government bonds was 2.2 percent.

321VALUATIONCh. 5

In recent years economists have come to accept the fact that the

interest rate includes compensation for expected inflation. If the expect-

ed rate of inflation is zero, the pure interest must be at least slightly

more than zero; otherwise people would hold their savings in the form

of cash. If the rate of inflation is high enough, however, the pure

interest element could be negative, at least in the short run. This is so

because people who are committed to a plan of saving (for example,

people who are saving for retirement) will be better off to invest at any

positive nominal interest rate, even though it is less than sufficient to

compensate for inflation, than to hold their savings in cash.

Another component referred to in the economic literature is the

‘‘liquidity’’ or ‘‘illiquidity’’ premium, described and discussed in Chapter

4 (Sec. II(D)). This may be thought of as part of compensation for

volatility risk.

B. MARKET PRICE

One way to determine the value of an asset is simply to look to the

price recently paid for identical or comparable assets in arm’s length

transactions. For example, if we want to know the value of shares of

common stock of General Motors Corporation, we can simply look in the

financial section of the daily newspaper and find the price at which such

shares traded the previous day on the New York Stock Exchange and can

equate this market price with value.

Valuation by reference to market transactions is also customary for

other assets, such as parcels of real estate, but with many such assets

comparability becomes a problem. Moreover, valuation by reference to

the market prices of comparable assets involves an obvious problem of

circularity; it is a method that tells us that similar assets have similar

values without telling us anything about how that value is determined.

The solution to the initial problem of circularity and to the problem of

determining what it is that makes assets comparable lies in the basic

economic tenet that the value of any asset is determined by the amount

and character of the returns that one can expect to derive from it. The

value of an asset is a function of its expected net returns and the

estimated volatility of those returns. Two assets are comparable if they

have the same expected return and the same (volatility) risk. (See

Chapter 4, Sec. II(A) and (B).)

Unfortunately, even this formulation leaves a problem of circularity.

If we know the volatility, we can determine an appropriate rate of

return, but only by looking to comparable assets or investments; it is a

market-determined rate. That leaves the question of how that rate is

itself determined. Some of the determinants of the market rate of

interest are suggested by the discussion, in Section A above, of the

compensatory elements included in the interest rate. Those determi-

nants in turn reflect the inclination of some people to borrow in order to

322 VALUATION, STRATEGIES & CAPITAL MARKETS Ch. 5

be able to consume now rather than later; the inclination of other

people to save now in order to be able to consume later (for example, on

retirement); the inclination of others to borrow in order to finance

productive processes, which is in turn a function, in part, of the produc-

tivity of capital; and the supply of money. The economic literature on

the determinants of the level of the interest rate is, at best, difficult. We

do know, however, that people lending money or investing in common

stocks or other assets have definable (though often only roughly so) ideas

about the rate of return that they expect from given kinds of assets. A

person investing in corporate bonds may expect a rate of return of, say, 9

percent. A person investing in a new business venture may insist on an

expected net rate of return of 20 percent. For our purposes this is

enough; it is not necessary to know how these figures are ultimately

determined—though we will return to some aspects of that problem later

in this Chapter (Sec. I(D)). All we need to know is that for a given type

of asset there will be an appropriate market-determined rate of return.

C. DISCOUNTED PRESENT VALUE

1. Single Amounts. Given the fact of a positive rate of interest,

a specified amount of money available to you today is worth more than a

claim to the same amount of money in the future. This is true

regardless of your inclination to save or consume. Suppose, for example,

that if you were to receive $1,000 today you would not spend it but

would instead save it for a trip to Europe a year from today. Even

though you don’t plan to spend the money until next year, you are still

better off to receive it today—for the obvious reason that you can earn

interest on it in the meantime. Suppose that you can make a risk-free

investment (for example, in an insured savings account) at 8 percent.

On that assumption, the $1,000 received today will be worth $1,080 a

year hence. Turning that around, $1,080 to be received one year hence

has a present value—often referred to somewhat redundantly as a

discounted present value—of $1,000. If the $1,000 were to be received

not today but, instead, one year from now, its present value would be

$926 (determined by the process to be described immediately below).

The $926 is the amount which, if invested at 8 percent, would grow to

$1,000 at the end of one year.

More generally, the present value of a future sum is simply the

amount that one must invest today at the appropriate interest rate in

order to have the future sum at the future date. Algebraically, then, for

an amount to be received one year hence,

P(1 v r)=A,

where P means the present amount, r means the annual interest rate,

and A means the future amount. To solve for P, we write the formula,