Valuation Concepts
The valuation of a financial asset is based on determining the present value of future cash flows. Thus we need to know the value of future cash flows and the discount rate to be applied to the future cash flows to determine the current value.
The market-determined required rate of return, which is the discount rate, depends on the market’s perceived level of risk associated with the individual security. Also important is the idea that required rates of return are competitively determined among the many companies seeking financial capital. For example ExxonMobil, due to its low financial risk, relatively high return, and strong market position, is likely to raise debt capital at a significantly lower cost than can United Airlines, a financially troubled firm. This implies that investors are willing to accept low return for low risk, and vice versa. The market allocates capital to companies based on risk, efficiency, and expected returns—which are based to a large degree on past performance. The reward to the financial manager for efficient use of capital in the past is a lower required return for investors than that of competing companies that did not manage their financial resources as well.
Throughout this course, we apply concepts of valuation to corporate bonds, preferred stock, and common stock. For that purpose we have to be aware of the basic characteristics of each form of security as part of the valuation process. We have to consider the following:
· The valuation of a financial asset is based on the present value of future cash flows.
· The required rate of return in valuing an asset is based on the risk involved.
· Bond valuation is based on the process of determining the present value of interest payments plus the present value of the principal payment at maturity.
· Preferred stock valuation is based on the dividend paid.
· Stock valuation is based on determining the present value of the future benefits of equity ownership.
List of terms:
required rate of return
That rate of return that investors demand from an investment to compensate them for the amount of risk involved.
yield to maturity
The required rate of return on a bond issue. It is the discount rate used in present-valuing future interest payments and the principal payment at maturity. The term is used interchangeably with market rate of interest.
real rate of return
The rate of return that an investor demands for giving up the current use of his or her funds on a noninflation-adjusted basis. It is payment for forgoing current consumption. Historically, the real rate of return demanded by investors has been of the magnitude of 2 to 3 percent.
inflation premium
A premium to compensate the investor for the eroding effect of inflation on the value of the dollar.
risk-free rate of return
Rate of return on an asset that carries no risk. U.S. Treasury bills are often used to represent this measure, although longer-term government securities have also proved appropriate in some studies.
risk premium
A premium associated with the special risks of an investment. Of primary interest are two types of risk, business risk and financial risk. Business risk relates to the inability of the firm to maintain its competitive position and sustain stability and growth in earnings. Financial risk relates to the inability of the firm to meet its debt obligations as they come due. The risk premium will also differ (be greater or less) for different types of investments (bonds, stocks, and the like).
business risk
The risk related to the inability of the firm to hold its competitive position and maintain stability and growth in earnings.
financial risk
The risk related to the inability of the firm to meet its debt obligations as they come due.
perpetuity
An investment without a maturity date.
dividend valuation model
A model for determining the value of a share of stock by taking the present value of an expected stream of future dividends.
dividend yield
Dividends per share divided by market price per share. Dividend yield indicates the percentage return that a stockholder will receive on dividends alone.
dual trading
Exists when one security, such as General Motors common stock, is traded on more than one stock exchange. This practice is quite common between NYSE-listed companies and regional exchanges.
par value
Sometimes referred to as the face value or the principal value of the bond. Most bond issues have a par value of $1,000 per bond. Common and preferred stock may also have assigned par values.
price-earnings ratio
The multiplier applied to earnings per share to determine current value. The P/E ratio is influenced by the earnings and sales growth of the firm, the risk or volatility of its performance, the debt-equity structure, and other factors.
supernormal growth
Superior growth a firm may achieve during its early years, before leveling off to more normal growth. Supernormal growth is often achieved by firms in emerging industries.
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1. Bonds
The price, or current value, of a bond is equal to the present value of interest payments (It) over the life of the bond plus the present value of the principal payment (Pe) at maturity. The discount rate used in the analytical process is the yield to maturity (Y). The yield to maturity (required rate of return) is determined in the marketplace by such factors as the real rate of return, an inflation premium, and a risk premium.
We add these two values together to determine the price of the bond. We use both annual or semiannual analysis.
The value of the bond will be strongly influenced by the relationship of the yield to maturity in the market to the interest rate on the bond and also the length of time to maturity.
If you know the price of the bond, the size of the interest payments, and the maturity of the bond, you can solve for the yield to maturity through a trial and error approach by an approximation approach, or by using financially oriented calculators or appropriate computer software.
2. Preferred Stock
In determining the value of preferred stock, we are taking the present value of an infinite stream of level dividend payments. This would be a tedious process if the mathematical calculations could not be compressed into a simple formula.
To find the preferred stock price (Pp) we take the constant annual dividend payment (Dp) and divide this value by the rate of return that preferred stockholders are demanding (Kp).
If, on the other hand, we know the price of the preferred stock and the constant annual dividend payment, we can solve for the required rate of return on preferred stock as:
Kp = Dp / Pp
3. Common Stock
The value of common stock is also based on the concept of the present value of an expected stream of future dividends. Unlike preferred stock, the dividends are not necessarily level. The firm and shareholders may experience:
3.1. No growth in dividends.
2.2. Constant growth in dividends.
3.3. Variable or supernormal growth in dividends.
It is the second circumstance that receives most of the attention in the financial literature. If a firm has constant growth (g) in dividends (D) and the required rate of return (Ke) exceeds the growth rate, this formula can be utilized.
P0=(D1/Ke) −g
In using that formula, all we need to know is the value of the dividend at the end of the first year, the required rate of return, and the discount rate. Most of our valuation calculations with common stock utilize the same Formula.
If we need to know the required rate of return (Ke) for common stock, the following Formula can be employed:
Ke= (D1 / P0) + g
The first term represents the dividend yield on the stock and the second term the growth rate. Together they provide the total return demanded by the investor.
As previously stated, the value of a financial asset is based on the concept of the present value of future cash flows. Let’s apply this approach to bond valuation. A bond provides an annuity stream of interest payments and a $1,000 principal payment at maturity. These cash flows are discounted at Y, the yield to maturity. The value of Y is determined in the bond market and represents the required rate of return for bonds of a given risk and maturity.
The price of a bond is thus equal to the present value of regular interest payments discounted by the yield to maturity added to the present value of the principal (also discounted by the yield to maturity).
Let’s assume that It (interest payments) equals $100; Pn (principal payment at maturity) equals $1,000; Y (yield to maturity) is 10 percent; and n (total number of periods) equals 20. We could say that Pb (the price of the bond) equals to:
Present Value of interest payments in every period (t) + Present Value of the Principal Payment at maturity (Pn)
Although the price of the bond could be determined with extensive calculations, it is much simpler to use computer software or financial calculators. We take the present value of the interest payments and then add this value to the present value of the principal payment at maturity.
Present Value of Interest Payments
Let’s assume that It (interest payments) equals $100; Pn (principal payment at maturity) equals $1,000; Y (yield to maturity) is 10 percent; and n (total number of periods) equals 20.
In this case, first, we determine the present value of a $100 annuity for 20 years. The discount rate is 10 percent, and we find the following:
PVA= A×PVIFA (n=20), i=10%
PVA=$851.40
Present Value of Principal Payment (Par Value) at Maturity
The single value of $1,000 will be received after 20 years. Note the term principal payment at maturity is used interchangeably with par value or face value of the bond. We discount $1,000 back to the present at 10 percent. For the present value of a single amount, we find the following:
PV=FV×PVIF (n=20,i=10%)
PV=$1,000×.149=$149
The current price of the bond, based on the present value of interest payments and the present value of the principal payment at maturity, is $1,000.40.
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Concept of Yield to Maturity
In the previous example, the yield to maturity that was used as the discount rate was 10 percent. The yield to maturity, or discount rate, is the rate of return required by bondholders. The bondholder, or any investor for that matter, will allow three factors to influence his or her required rate of return.
1. The required real rate of return—This is the rate of return the investor demands for giving up the current use of the funds on a noninflation-adjusted basis. It is the financial “rent” the investor charges for using his or her funds for one year, five years, or any given period. Although it varies from time to time, historically the real rate of return demanded by investors has been about 2 to 3 percent.
2. Inflation premium—In addition to the real rate of return discussed above, the investor requires a premium to compensate for the eroding effect of inflation on the value of the dollar. It would hardly satisfy an investor to have a 3 percent total rate of return in a 5 percent inflationary economy. Under such circumstances, the lender (investor) would be paying the borrower 2 percent (in purchasing power) for use of the funds. This would represent an irrational action. No one wishes to pay another party to use his or her funds. The inflation premium added to the real rate of return ensures that this will not happen. The size of the inflation premium will be based on the investor’s expectations about future inflation. In the last two decades, the inflation premium has been 2 to 4 percent. In the late 1970s, it was in excess of 10 percent.
If one combines the real rate of return (part 1) and the inflation premium (part 2), the risk-free rate of return is determined. This is the rate that compensates the investor for the current use of his or her funds and for the loss in purchasing power due to inflation, but not for taking risks. As an example, if the real rate of return were 3 percent and the inflation premium were 4 percent, we would say the risk-free rate of return is 7 percent.
3. Risk premium—We must now add the risk premium to the risk-free rate of return. This is a premium associated with the special risks of a given investment. Of primary interest to us are two types of risk: business risk and financial risk. Business risk relates to the inability of the firm to hold its competitive position and maintain stability and growth in its earnings. Financial risk relates to the inability of the firm to meet its debt obligations as they come due. In addition to the two forms of risk mentioned above, the risk premium will be greater or less for different types of investments. For example, because bonds possess a contractual obligation for the firm to pay interest to bondholders, they are considered less risky than common stock where no such obligation exists.
The risk premium of an investment may range from as low as zero on a very-short-term U.S. government–backed security to 10 to 15 percent on a gold mining expedition. The typical risk premium is 2 to 6 percent. Just as the required real rate of return and the inflation premium change over time, so does the risk premium. For example, high-risk corporate bonds (sometimes referred to as junk bonds) normally require a risk premium of about 5 percentage points over the risk-free rate. However, in September 1989 the bottom fell out of the junk bond market as Campeau Corp., International Resources, and Resorts International began facing difficulties in making their payments. Risk premiums almost doubled. The same phenomenon took place in the spring of 2008.
There is a strong correlation between the risk the investor is taking and the return the investor demands. Supposedly, in finance as in other parts of business, “There is no such thing as a free lunch.” If you want a higher return, you must take a greater risk.
Let us assume that in the investment we are examining the risk premium is 3 percent. If we add this risk premium to the two components of the risk-free rate of return developed in parts 1 and 2, we arrive at an overall required rate of return of 10 percent.
In this instance, we assume we are evaluating the required return on a bond issued by a firm. If the security had been the common stock of the same firm, the risk premium might be 5 to 6 percent and the required rate of return 12 to 13 percent.
Finally, you should recall that the required rate of return on a bond is effectively the same concept as required yield to maturity.
Changing the Yield to Maturity and the Impact on Bond Valuation.
In the earlier bond value calculation, we assumed the interest rate was 10 percent ($100 annual interest on a $1,000 par value bond) and the yield to maturity was also 10 percent. Under those circumstances, the price of the bond was basically equal to par value. Now let’s assume conditions in the market cause the yield to maturity to change:
Increase in Inflation Premium
For example, assume the inflation premium goes up from 4 to 6 percent. All else remains constant. The required rate of return would now be 12 percent.
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With the required rate of return, or yield to maturity, now at 12 percent, the price of the bond will change. A bond that pays only 10 percent interest when the required rate of return (yield to maturity) is 12 percent will fall below its current value of approximately $1,000. The new price of the bond, as computed below, is $850.90.
Present Value of Interest Payments
We take the present value of a $100 annuity for 20 years. The discount rate is 12 percent. Using Appendix D:
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Present Value of Principal Payment at Maturity
We take the present value of $1,000 after 20 years. The discount rate is 12 percent. Using Appendix B:
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Total Present Value
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In this example we assumed increasing inflation caused the required rate of return (yield to maturity) to go up and the bond price to fall by approximately $150. The same effect would occur if the business risk increased or the demanded level for the real value of return became higher.
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