## Stock & Bond Values

This article explains the basic concepts that govern two of the most common financial instruments: stock and bonds. The first step in understanding stocks and bonds is to look at the underlying features of each security and how they can impact value. This article focuses on the discussion of common financial techniques for valuing stocks and bonds.

Stocks and bonds are two of the most common types of investments. Stocks are equity instruments whereas bonds are debt. A stock holder owns a portion of a company, but is not given a fixed return. A bond holder is considered a creditor of the company and is promised fixed interest payments, as well as a lump sum payment upon maturity. An investment portfolio is generally comprised of a mix of each of these securities. The value of both stocks and bonds can be determined by analyzing discounted cash flows. Although stock and bonds are each governed by the same overall market principles, these investments are very different with respect to risk and return. The mechanisms and processes for capturing value also vary between stocks and bonds.

This article will look at each security individually. We discuss bonds in detail, starting with basic bond characteristics. Subsequently, we will examine the mechanics for valuing and trading bonds, as well as factors that impact their value. We will then move our discussion to stocks. The media tends to focus on stocks more than bonds because the value of these securities can fluctuate significantly. There is a wealth of information available to the investor about any stock listed on a public exchange. We will use that information to understand how stocks capture value. In conclusion, we will explore the methods for combining stocks and bonds in a portfolio to maximize value and return for an investor.

### Bond Basics

A bond is a debt security. In this arrangement, the debtor agrees to make fixed payment of interest and principle over a specified time period to the holders of the bond. This kind of financial instrument usually pays a fixed interest rate (coupon) for a period of time and at the end of that duration (the maturity), it will pay the investor a predetermined lump sum (face value). The stream of cash flows for a bond investment is illustrated below, where there are n time periods until maturity, PMT is the coupon, and FV is the face value. A bond's interest rate is determined by general market interest rates at the time of issuance along with the credit risk and other features specific to that bond.

Bonds are traded using the full service of a discount brokerage house. There are several types of bonds that can be traded:

- Treasury Bonds -- Lowest risk bonds because they are backed by the US government. The interest income is exempt from state taxes, but not federal.
- Mortgage Bonds or Government Agency Bonds -- Bonds comprised of mortgage loans issued by the government agencies Ginnie Mae, Fannie Mae, and Freddie Mac. Interest is taxable and except for Ginnie Maes -- these bonds are not backed by the U.S. government.
- Municipal Bonds -- Bonds issued by state and local governments. Interest is often federal and state tax-exempt.
- Corporate Bonds -- Bonds issued by companies. Interest is taxable and these bonds are more risky because the chance of default is much higher than for the government.
- Eurobonds -- Bonds that are issued in one country's currency but then traded in a different country.
- Bond Funds -- Mutual funds which compile different bonds together for the investor to purchase.
- Junk Bonds -- High-risk bonds that are below investment grade as measured by credit agencies such as Moody's.

### Bond Features

A bond contract lists the features of a bond, the coupon, par value, maturity, covenants, and repayment details. Bonds generally have fixed coupon payments and a fixed lifespan. However, a bond can possess certain features that can alter this arrangement. Special features of a bond can include the following:

- Convertible -- The bond can be converted into a number of predetermined shares of stock at the bond holder's option or some cases, the company can retain the right to force conversion if the stock reaches a specified price level.
- Callable -- The issuers of a bond can refund the bond by paying a predetermined fixed price, usually at a premium price, prior to maturity.
- Putable -- The holder of a bond can sell the bond back to the company prior to maturity and receive full face value.
- Floating Interest Rate -- With this feature, the coupon rate is not fixed. The rate is linked to an index (e.g., Treasury bill, LIBOR) and fluctuates with that market index.
- Interest Rate Cap or Floor -- In order to limit extremes and risk in a floating interest rate bond, the cap and/or floor feature can be employed. The cap sets forth a maximum interest rate that will be paid by the issuer. The floor sets forth a minimum interest rate that will be paid by the issuer.
- Sinking Fund -- In this case, the issuer would have the option to pay off a portion of the face value over time, rather than at maturity. In other words, this gives the issuer the option to prepay the face value.
- Covenants -- Restrictions that are put on the company by the bondholders to help limit risk and default exposure. Common covenants include restricting the types of investments the company can make and limiting the dividends that can be paid out to stockholders.
- Zero Coupon -- Bond where no coupon is paid. The only cash flow for this bond is the payment of face value at maturity.

We will come back to each of these features later in this article and examine how value is impacted by their inclusion.

### Valuing Bonds

The initial price for a bond will be based on expected cash flows, discounted at an interest rate that is appropriate for the type of bond and the riskiness of the issuer. The expected cash flows of a simple bond are comprised of two parts. First, we look at the coupon (PMT) paid for n number of years until the bond matures with a discount rate of i. Interest rates used to discount cash flows are determined by general interest rates in the market, as well as by the term structure of the bond and the credit risk of the issuer. The second part of the equation is the face value (FV) discounted back to today's dollars.

Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed.

Take the example of Bond A, a 5-year bond with discount rate of 12%, annual coupon payments of $120, and a face value of $1000.

(120/(1.12)^1)+(120/(1.12)^2)+(120/(1.12)^3)+(120/(1.12)^4)+(120/( (1.12)^5)+(1000/(1.12)^5) = $1000

Financial calculators and software applications such as Excel have functions that can also quickly calculate the present value of a bond.

One of the most critical factors that impact a bond's value is interest rate fluctuations. As a rule, bond prices fall when interest rates and inflation rise. Bonds are acutely sensitive because they have coupon payments that are fixed into the future and do not adjust for changes in interest rates or inflation. Therefore, when interest rates and inflation rise, the present value of the bond is worth less than its purchase price.

To price the impact on interest rate fluctuations for a bond that is already on the market, we go back to our present value (PV) equation. To figure out whether a bond is selling at a discount or a premium we simply change the discount rate (i) to the going market rate and compare the PV to the FV. If interest rates fall and the coupon rate is greater than the discount rate then the bond will sell at a premium. This is called a premium bond. Take our previous example and suppose that the discount rate drops to 10%. The bond is worth $1075.82, a premium over the $1000 that was paid at issuance.

(120/(1.1)^1)+(120/(1.1)^2)+(120/(1.1)^3)+(120/(1.1)^4)+(120/(1.1)^5)+(1000/( (1.1)^5) = $1075.82

If interest rates rise and the coupon rate is less than the discount rate, then the bond will sell at a discount. This is called a discount bond. Let us go back to our example and see what happens when the discount rate rises to 14%. The bond is worth $931.34, a discount compared to the $1000 that was paid at issuance.

(120/(1.14)^1)+(120/(1.14)^2)+(120/(1.14)^3)+(120/(1.14)^4)+(120/( (1.14)^5)+(1000/(1.14)^5) = $931.34

Because bonds are bought and sold on public markets before their maturity, most investors are also interested in the annual rate of return they will receive if they hold a bond to maturity. Once a bond has been traded, its yield to maturity can be computed easily using a financial calculator or Excel. The bond's current return is based on the above equation for present value (PV). We are now just solving for i to get yield to maturity. You will enter the pieces of information you know and solve for the yield to maturity. For example, if Bond A only has 2 years left to maturity and is currently selling for $1200, what is its yield to maturity? On a financial calculator, you can solve for yield to maturity (i) by plugging in the following data:

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(The entire section is 4098 words.)