Foundations of Financial Management: An Analysis (part 31)

 “Happiness is not in the mere possession of money; it lies in the joy of achievement, in the thrill of creative effort.” 

– Franklin D. Roosevelt

Valuation and Rates of Return

by

Charles Lamson

The factors that determine valuation are varied, and you will be exposed to many of them in the next several posts.

In the last several posts we considered the basic principles of the time value of money. In the next few posts we will use many of those concepts to determine how financial assets (bonds, preferred stock, and common stock) are valued and how investors establish the rates of return they demand. We will use material from these next few posts to determine the overall cost of financing to the firm. We merely turn The coin over. Once we know how much bondholders and stockholders demand in the way of rates of return, we will then observe what the corporation is required to pay them to attract their funds. The cost of corporate financing capital is subsequently used in analyzing whether a project is acceptable for investment or not. These relationships are depicted in Figure 1.

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. 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 the competing companies that did not manage their the resources as well.

In the next few posts, we apply concepts of evaluation to corporate bonds, preferred stock, and common stock. Although we describe the basic characteristics of each form of security as part of the valuation process, extended discussion of each security is deferred until later posts.

Valuation of Bonds

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 produces 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. More will be said about the concept of yield to maturity in the next section. 

 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).

This relationship can be expressed mathematically as follows.

Although the price of the bond could be determined with extensive calculations, it is much simpler to use present value tables. 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 In this case we determine the present value of a $100 annuity for 20 years. The discount rate is 10 percent. Using Table 1 above, the present value of an annuity, we find the following:

Present Value of Principal Payment (Par Value) at Maturity This 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. Using Table 2, present value of a single amount, we find the following:

Table 2 Present value of a single amount

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.

The price of this bond in this case is essentially the same as its par, or stated, value to be received at maturity of $1,000. This is because the annual interest rate is 10 percent (the annual interest rate of $100 divided by $1,000) the and the yield to maturity, or discount rate, is also 10 percent. When the interest rate on the bond and the yield to maturity are equal, the bond will trade at par value. Later we shall examine mathematical effects of varying the yield to maturity above or below the interest rate on the bonnd. But first we will examine more fully the concept of yield to maturity, which is where we turn our attention in the next post.

*MAIN SOURCE: BLOCK & HIRT, 2005, FOUNDATIONS OF FINANCIAL MANAGEMENT, 11TH ED., PP. 268-271*

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