How to Value Bonds and Stocks

How bonds are valued,Since the future cashflows of bonds are known, application of net-present-value techniques is fairly straightfor-ward. The uncertainty of future cash flows makes the pricing of stocks according to NPVmore difficult.


A bond is a certificate showing that a borrower owes a specified sum. In order to repay themoney, the borrower has agreed to make interest and principal payments on designateddates. For example, imagine that Kreuger Enterprises just issued 100,000 bonds for $1,000each, where the bonds have a coupon rate of 5 percent and a maturity of two years. Intereston the bonds is to be paid yearly. This means that:
1. $100 million (100,000  $1,000) has been borrowed by the firm
.2. The firm must pay interest of $5 million (5%  $100 million) at the end of one year
.3. The firm must pay both $5 million of interest and $100 million of principal at the end oftwo years.

We now consider how to value a few different types of bonds.


Pure Discount Bonds
The pure discount bond is perhaps the simplest kind of bond. It promises a single payment,say $1, at a fixed future date. If the payment is one year from now, it is called a one-year dis-count bond; if it is two years from now, it is called a two-year discount bond, and so on. Thedate when the issuer of the bond makes the last payment is called the maturity date of thebond, or just its maturity for short. The bond is said to mature or expire on the date of its fi-nal payment. The payment at maturity ($1 in this example) is termed the bond’s face value.
Pure discount bonds are often called zero-coupon bonds or zeros to emphasize the factthat the holder receives no cash payments until maturity. We will use the terms zero, bullet,and discount interchangeably to refer to bonds that pay no coupons.

The first row of Figure 5.1 shows the pattern of cash flows from a four-year pure dis-count bond. Note that the face value, F, is paid when the bond expires in the 48th month.There are no payments of either interest or principal prior to this date.

In the previous chapter, we indicated that one discounts a future cash flow to determineits present value. The present value of a pure discount bond can easily be determined by thetechniques of the previous chapter. For short, we sometimes speak of the value of a bondinstead of its present value.

Consider a pure discount bond that pays a face value of F in T years, where the interestrate is r in each of the T years. (We also refer to this rate as the market interest rate.) Becausethe face value is the only cash flow that the bond pays, the present value of this face amount is

The present value formula can produce some surprising results. Suppose that the in-terest rate is 10 percent. Consider a bond with a face value of $1 million that matures in 20years. Applying the formula to this bond, its PV is given by

Level-Coupon Bonds
Many bonds, however, are not of the simple, pure discount variety. Typical bonds issued byeither governments or corporations offer cash payments not just at maturity, but also at reg-ular times in between. For example, payments on U.S. government issues and Americancorporate bonds are made every six months until the bond matures. These payments arecalled the coupons of the bond. The middle row of Figure 5.1 illustrates the case of a four-year, level-coupon bond: The coupon, C, is paid every six months and is the same through-out the life of the bond.

Note that the face value of the bond, F, is paid at maturity (end of year 4). F is some-times called the principal or the denomination. Bonds issued in the United States typicallyhave face values of $1,000, though this can vary with the type of bond.

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