Stock and 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.

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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:

n i PV FV PMT Results 2 ? -$1,100 $1,100 $120 6.51%

The result gives us 6.51% yield to maturity. Note that PV must be given as a negative number when using excel or a financial calculator.

The closer to maturity, the closer the PV will be equal to the FV. At maturity, all bonds are equal to their face value. A premium bond will decrease over time until it reaches the face value at maturity and a discount bond will increase over time until it reaches the face value at maturity.

Other Factors that Influence Bond Values

The duration of the bond, or time until maturity, also influences the value of the bond. The longer the time to maturity, the more sensitive the bond is to changes in interest rates. These bonds have a higher risk premium. Therefore, the interest rate of a long-term bond is generally higher than a short-term bond.

Another rule of thumb is the higher the coupon, the lower the interest rate. Bonds with higher coupons have more cash flows in the earlier years and are less sensitive to interest rate risk. At one end of the spectrum is the zero coupon bond which has no coupon, only its face value at maturity. The present value of a zero coupon bond can vary significantly with fluctuations in interest rates because the payment is so far out into the future. This kind of bond will have a much higher interest rate than a simple bond.

The special features of a bond that were discussed earlier can also impact the value of the bond. If the feature benefits the holder of the bond, then the interest rate is lower. If the feature helps the issuer, then the interest rate increases. In the first column are features that generally provide the investor with upside and as a result, the investors will sacrifice some yield versus a simple bond without this feature. Features in the second column reduce upside potential for the investor, so the interest rates for these bonds would be higher.

Increases Upside Potential For Investors Convertible Putable Callable Sinking Fund (can be both) Decreases Upside Potential For Investors Sinking Fund Interest Rate Floor Interest Rate Cap

Since bondholders are creditors of a company, credit risk is another important component of a bond's value. Credit risk is the potential that the issuer will default on its debt obligation. The higher the issuer credit risk, the higher the interest rate. Although bonds generally have a lower risk than stocks, there is always a chance of losing your investment. If a bond is defaulted, an investor can lose interest as well as principle. Credit ratings, which can help asses risk, are published by companies such as Moody's and Standard and Poor's. These companies rate bonds based on the probability that the company will default. The two main categories are investment grade bonds and Junk Bonds. Investment grade bonds have a lower chance of default than Junk Bonds, which are highly speculative. Interest coverage ratios (EBIT/Interest Expense) can also provide insight into credit risk. If a company's earnings do not have enough cushion to cover interest expense, then there is a high risk of default.

Investment Grade Junk Bonds Moody's Aaa, Aa, A, Baa Ba, B, Caa, C S AAA, AA, A, BBB BB, B, CCC, D

When a company does default, there are two alternatives.

• Chapter 11 -- a reorganization in which the company remains a going concern. This option stops creditors from closing the company down and seizing the assets. Management must make a case that it can successfully reorganize the business to generate more value than if the parts were sold off.
• Chapter 7 -- a liquidation or sale of the assets of the company. In a liquidation event, unsecured creditors usually get nothing.

Stock Basics

When an investor purchases a share of common stock in a corporation, it gives that investor ownership in the company. As a common stockholder, an investor is entitled to voting rights as well as residual claims to future earnings and assets once all debts/obligations are satisfied. However, in the event of bankruptcy, common stockholders usually receive nothing. Voting rights are important because common shareholders use this right to elect a Board of Directors. One of the primary duties of the Board of Directors is to hire the management team and determine their compensation packages. Since shareholders are more content when they are making higher returns, the ultimate goal of management, if they want to keep their jobs, it to maximize share price or value of the stock.

Along with voting rights comes the claim to dividends. When a company makes a profit it can either reinvest the profits (retained earnings) or distribute it to stockholders (dividends). Dividends are usually cash distributions, but can also be additional stock. Many investors look at dividends as a measure of the health of the company. Changes in dividend policy can signal changes in the company's value. A company that forgoes dividends and reinvests in its business must choose investments that have a higher return than the discount rate. If not, the company could increase its earnings, but it would erode shareholder value. As a result, stock price would decline.

Preferred stock is a hybrid security that has some components of debt and some features of common stock. The preferred stockholder has claims on earnings and assets of the company that are senior to that of common stockholders. Usually there are no voting rights in this class of stock. Preferred stock generally provides for an annual fixed dividend payment that is to be paid in full, for past and present dividends, before common stockholders can begin to receive any dividends. However, failure to pay dividends cannot force a company into bankruptcy.

There are a number of public stock exchanges where an investor can buy and sell stocks. These exchanges facilitate the buying and selling of specific stocks listed on their exchanges. The New York Stock Exchange (NYSE) and NASDAQ are two of the most well-known US exchanges. The Tokyo Stock Exchange and London Stock Exchange are two of the largest stock exchanges outside the US. Investment banks market and issue new shares of a stock on these exchanges. New equity issued by firms that already have outstanding stock is called a seasoned offering. An initial public offering (IPO) involves firms that are not yet traded.

Valuing Stocks

There are several accepted methods for valuing common stock. We will discuss three of the most widely used techniques.

• Present value of all future dividends
• Free Cash Flow method
• Multiples of comparable firms

Dividend Model:

The first method we will discuss for valuing common stock is to determine the present value (PV) of all future dividends. What if a stock has no dividends? Is it worthless? No, it is not worthless because a firm always has the potential to start paying dividends and if the firm is sold in a takeover, the sale price can be considered a lump sum dividend at the end. The formula for this method is illustrated below with future dividend estimates (DIV) discounted back with the required rate of return (i) for an infinite number of periods.

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Because this formula requires forecasting an infinite number of dividends into the future, it is not a realistic method. Therefore, a more practical application called the dividend growth model was developed. The dividend growth model makes some simplifying assumptions, but the basic premise of the theory remains intact. The dividend growth model assumes that dividend growth (g) is constant and that stock price is expected to appreciate at the same rate.

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Take the following example of Company A, which is expected to pay dividends of $5 this year and thereafter; the dividend is expected to grow by 5%. If the required rate of return is 10%, the company's share price is $100.

5/(0.1-0.05) = $100

The dividend growth model is criticized because constant growth is a major assumption that does not apply to many companies. For this reason, we will now look at alternative methods for valuing stock.

Free Cash Flow Model:

The free cash flow valuation model is often preferred to the dividend growth model in cases where firms do not pay dividends or the dividends and growth are hard to forecast. The basic premise for the free cash flow model is to take the present value of the cash the firm could distribute after meeting all obligations. Free cash flow is the amount of cash available to investors (revenues less all costs and investments). To get the present value of the free cash flow, we forecast out each year's free cash flow (FCF) and then add a terminal value that assumes constant growth (g). We then discounted all those values back with the cost of capital (i).

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Let us take an example of Company B that has free cash flow of $100 for year 1, $200 year 2, then is expected to reach a constant free cash flow growth rate of 5%. Cost of capital is 10%. The present value of the cash flows is:

((100/(1+0.1)^1))+((200/(1+0.1)^2))+((200*1.05)/(0.1-0.05))/(1+0.1 1)^3 = $3412

If the company is being sold or closed, an alternative terminal value would be to determine what the sale price or liquidation value is during the final year and discount that number back instead of using the constant growth perpetuity.

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Coming back to valuing the common stock, we now take the present value of the free cash flow and subtract the value of debt and value of preferred stock.

Common Stock Value = PV_FCF-V_d-Vps

In our example above, if debt is worth $400 and there is no preferred stock, the common stock value is $3412-$400 = $3012. This is the value of the firm. We can take this number and divide by the amount of shares outstanding to come up with a price per share.

Multiples:

Using multiples is one of the simplest ways to value a stock. The premise of this model is to find a company in a similar industry, with a similar risk profile and similar business model. The known critical statistics of the comparable company are then used to extrapolate value for the company in question. The most commonly used comparison is price per share compared to earnings per share. This is referred to as the P/E ratio.

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If a company's earnings per share are $20 with price per share of $40, then it has a P/E ratio of 2. If we apply that to a comparable company with earnings per share of $10M, then the price per share should be $20.

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There are other multiples that can also be applied. Price per Share/Cash Flow is a popular multiple because it takes into account all capital investments. In other industries, Price per Share/Revenue would be a good comparison. The appropriate multiple really depends on the company and industry specifics. For a web portal, it could be Price per Share/Click-Throughs or for a cable system it could be Price per Share/Subscribers.

Critics of this method point out that no two companies are exactly alike and therefore cannot be used for direct comparison. This method is often used in conjunction with other methods as a check to make sure the stock price is reasonable.

Valuing Preferred Stock

As noted earlier, preferred stock differs from common stock in several ways. It is really a hybrid, somewhere between a bond and a stock. Therefore, the valuation technique takes lessons from both stocks and bonds. To value preferred stock, we simply assume the fixed dividend payment (DIV) in perpetuity and then discount it back (i) to present day.

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Take the following example: If Company C provides an annual dividend of $2.50 on its preferred stock and the discount rate is 10%, the value of the preferred stock is $25.

2.5/0.1 = $25

Conclusion

Stocks and bonds are two of the most prevalent investment vehicles. Bonds have a certain amount of security because fixed payments are guaranteed unless the company goes into default. Stock returns are much more risky, but also have a higher rate of return. Certain information about a publicly traded stock is required to be disclosed to investors. Using historical data and the information the company provides, an investor can estimate the future cash streams that will come from the stock and analyze the risk associated with those cash streams. In the end, no investment comes without risk, so it is best to diversify your portfolio.

An investment portfolio can utilize bonds to offset the volatility of stocks. This kind of asset allocation can reduce overall risk. Each asset class (stocks and bonds) should also be diversified to guard against poor performance of any one investment. The optimal ratio of stocks to bonds varies for each investor. The portfolio for an aggressive investor has a higher mix of stocks and generally has a long-term time horizon (5+ years). On the other side of the spectrum is the conservative investor. This investor will hold a greater majority of bonds and is interested in the stable income that the coupons can provide. An investor close to retirement should consider this kind of conservative portfolio.

Terms & Concepts

Bond: Security that pays fixed interest (coupon) for a specified amount of time and then upon maturity it will pay a predetermined lump sum (face value). A bond that has a market price lower than its face value is called a Discount Bond. A bond that has a market price higher than its face value is called a Premium Bond.

Common Stock: A share in the ownership of a company with voting rights and residual claims to earnings and assets once all senior claims are satisfied.

Coupon: Interest rate on a bond that is paid at fixed intervals off its face value.

Default Risk: Risk that a debt holder will not make timely payments of interest and principle as they come due. Firms such as Moody's and Standard and Poor's provide ratings to assess this risk.

Discount Rate: Rate that could be earned on an alternate investment (opportunity cost).

Dividend: Distribution of earnings by a company to its shareholders.

Face Value: Face amount of a bond that is paid at maturity. Also called Par Value.

Free Cash Flow: Amount of cash available to stockholders of a company. Calculation based on net operating profit less taxes, investments, and changes in net working capital.

Maturity: Time period that a bond is held by an investor before it is paid off in full.

P/E Ratio: Price of a stock divided by its earnings per share. Also known as a multiple, it gives an investor an idea of how much they are paying for each dollar of earnings.

Preferred Stock: Class of stock that pays dividends and has preference over common stock with respect to claims on dividends and liquidation of assets.

Present Value: Value of future cash streams discounted back to today's dollars with a discount rate appropriate for the investment.

Yield to Maturity: Rate of return on a bond if the bond is held to maturity.

Bibliography

Bodie, Z. & Merton, R. C. (1998). Finance. Upper Saddle River, New Jersey: Prentice-Hall.

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Brigham, E. F., & Houston, J. F. (2003). Fundamentals of Financial Management. Cincinnati, Ohio: South-Western College Publishing.

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Kosnett, J. R. (2013). Dump your bonds? No way. Kiplinger's Personal Finance, 67 (11), 46. Retrieved November 20, 2013 from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=90617040&site=ehost-live

Luehrman, T. A. (1997). What's it worth? A general manager's guide to valuation. Harvard Business Review, 75(3), 132-141. Retrieved April 6, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=9705196207&site=bsi-live

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Suggested Reading

Black, F. (1990). Why firms pay dividends. Financial Analysts Journal 46(3), 5. Retrieved April 6, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=6936554&site=ehost-live

Fabozzi, F. J., Kalotay, A. J., & Williams, G. O. (1993). A model for valuing bonds and embedded options. Financial Analysts Journal, 49(3), 35-46. Retrieved April 6, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=6936590&site=ehost-live

Feldman, A. (2013). The benefit of fearing disaster. Fortune, 168 (5), 57. Retrieved November 20, 2013 from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=90052563&site=ehost-live

Hodges, S. D. & Schaefer, S. M. (1977). A model for bond portfolio improvement. Journal of Financial and Quantitative Analysis, 12(2), 243-260. Retrieved April 6, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=4762255&site=ehost-live

P´stor, L. & Pietro, V. (2003). Stock valuation and learning about profitability. Journal of Finance, 58 (5), 1749-1790. Retrieved April 6, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=10832847&site=ehost-live

A penny in whose pocket? (2001). Economist, 359(8223), 71-72. Retrieved April 6, 2007, from EBSCO Online Database Academic Search Premier. http://search.ebscohost.com/login.aspx?direct=true&db=aph&AN=4487594&site=ehost-live

Valuing stocks with the dividend discount model. (2001). Dow Theory Forecasts, 57(26), 7. Retrieved April 6, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=5791938&site=ehost-live