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The VaLuation of Long-Term Securities

In the last chapter we discussed the time value of money and explored the wonders of compound interest. We are now able to apply these concepts to determining the value of different securities. In particular, we are concerned with the valuation of the firm's long-term securities - bonds, preferred stock, and common stock (though the principles discussed apply to other securities as well). Valuation will, in fact, underlie much of the later development of the book. Because the major decisions of a company are all interrelated in their effect on valuation, we must understand how investors value the financial instruments of a company.

Liquidation Value versus Going-Concern Value

Liquidation value is the amount of money that could be realized if an asset or a group of assets (e.g., a firm) is sold separately from its operating organization. This value is in marked contrast to the going-concern value of a firm, which is the amount the firm could be sold for as a continuing operating business. These two values are rarely equal, and sometimes a company is actually worth more dead than alive.

Book Value versus Market Value

The book value of an asset is the accounting value of the asset - the asset's cost minus its accumulated depreciation. The book value of a firm, on the other hand, is equal to the dollar difference between the firm's total assets and its liabilities and preferred stock as listed on its balance sheet. Because book value is based on historical values, it may bear little relationship to an asset's or firm's market value.

Market Value versus Intrinsic Value

Based on our general definition for market value, the market value of a security is the market price of the security. For an actively traded security, it would be the last reported price at which the security was sold. For an inactively traded security, an estimated market price would be needed.

Bond Valuation

A bond is a security that pays a stated amount of interest to the investor, period after period, until it is finally retired by the issuing company. Before we can fully understand the valuation of such a security, certain terms must be discussed. For one thing, a bond has a face value. This value is usually $1,000 per bond in the United States. The bond almost always has a stated maturity, which is the time when the company is obligated to pay the bondholder the face value of the instrument. Finally, the coupon rate, or nominal annual rate of interest, is stated on the bond's face.2 If, for example, the coupon rate is 12 percent on a $l,000-face-value bond, the company pays the holder $120 each year until the bond matures.

Perpetual Bonds

The first (and easiest) place to start determining the value of bonds is with a unique class of bonds that never matures. These are indeed rare, but they help illustrate the valuation technique in its simplest form. Originally issued by Great Britain after the Napoleonic Wars to consolidate debt issues, the British consol (short for consolidated annuities) is one such example. This bond carries the obligation of the British government to pay a fixed interest payment in perpetuity.

Common Stock Vatuation

The theory surrounding the valuation of common stock has undergone profound change during the last few decades. It is a subject of considerable controversy, and no one method for valuation is universally accepted. Still, in recent years there has emerged growing acceptance of the idea that individual common stocks should be analyzed as part of a total portfolio of common stocks that the investor might hold. In other words, investors are not as concerned with whether a particular stock goes up or down as they are with what happens to the overall value of their portfolios.

Are Dividends the Foundation?

When valuing bonds and preferred stock, we determined the discounted value of all the cash distributions made by the firm to the investor. In a similar fashion, the value of a share of common stock can be viewed as the discounted value of all expected cash dividends provided by the issuing firm until the end of time. This seems consistent with what we have been doing so far.

Dividend Discouni Modets

Dividend discount models are designed to compute the intrinsic value of a share of common stock under specific assumptions as to the expected growth pattern of future dividends and the appropriate discount rate to employ. Merrill Lynch, CS First Boston, and a number of other investment banks routinely make such calculations based on their own particular models and estimates. What follows is an examination of such models, beginning with the simplest one.

Rates of Return

So far, this chapter has illustrated how the valuation of any long-term financial instrument involves a capitalization of that security's income stream by a discount rate (or required rate of return) appropriate for that security's risk. If we replace intrinsic value in our valuation equations with the market price (P0) of the security, we can then solve for the market required rate of return. This rate, which sets the discounted value of the expected cash inflows equal to the security's current market price, is also referred to as the security's (market) yield. Depending on the security being analyzed, the expected cash inflows may be interest payments, repayment of principal, or dividend payments. It is important to recognize that only when the intrinsic value of a security to an investor equals the security's market value (price) would the investor's required rate of return equal the security's (market) yield.

Yield to Maturity (YTM) on Bonds

The market required rate of return on a bond (kd) is more commonly referred to as the bond's yield to maturity. Yield to maturity (YTM) is the expected rate of return on a bond if bought at its current market price and held to maturity; it is also known as the bond's internal rate of return (IRR). Mathematically, it is the discount rate that equates the present value of all expected interest payments and the payment of principal (face value) at maturity with the bond's current market price. For an example, let's return to, the valuation equation for an interest-bearing bond with a finite maturity.

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