Unit 5: Valuation of Bonds and Stocks

Bonds

A bond is a debt security that contractually obligates the issuer to make fixed coupon payments at fixed intervals for a fixed amount of time plus it also pays out the face value of the bond at maturity together with the last coupon payment. The total annual coupon payments are equal to the coupon rate multiplied by the face value of the bond. e coupon payments may be split into more than one payment per year. ese specified payments are in the form of coupon payments and par value. Par value (also called face value or nominal value) indicates how much the issuer will repay to the bondholder at maturity. Par value of Turkish bonds in general is T100 whereas US bonds typically have a par value of $1.000. e coupon rate of a bond determines the coupon (interest) payments. Bonds can usually only be issued by governments or large, well known firms. As time passes, the cash flows from the bond stays the same but market interest rates may change. As a result, the value of the bond changes with the changes in interest rates. If market interest rates increase, the price of bonds decrease.

Valuing Bonds

The value of the bond is the present value of these cash flows. To find its value, you need to calculate present value of each future payment discounted at the current market interest rate (r). The formula used for the calculation can be seen on page 132.

Interest Rates and Bond Values

There is an inverse relationship between value of bonds and market interest rates. As market interest rates increase, the present value of future cash flows declines and the value of bond decreases. Conversely, if market interest rates decrease, the present value of future cash flows increases and the value of bond increases. It is important to note that market interest rates might change but there is no change in coupon interest rate. Bonds exhibit interest rate risk, which is the risk that the return from the bond will change according to changes in the interest rates. An increase in interest rates reduces bond values. Bonds carry reinvestment rate risk, which is the risk that cash flows received may not be able to be reinvested at the expected rates if market rates have changed.

Yield-To-Maturity

Yield-to-maturity is the average rate of return that will be earned on a bond if it is bought at the market price and held until it matures. It is the discount rate that makes the present value of its future cash flows equal to its market price. It is like an internal rate of return of a bond. Calculating yield-to-maturity of a bond selling at par is easy. It is equal to its coupon interest rate. For discount bonds, yield-to-maturity is greater than their coupon rate whereas yield-to-maturity of premium bonds is less than their coupon rate.

Yield-to-maturity has two components. The first one is the return you get from coupon payments, called current yield (annual coupon/current bond price) . The second one is the return you get from the change in the value of bond, called capital gains yield. Capital gains yield is negative when there is a decline in value of a bond.

If an investor does not want to hold the bond until its maturity, she may sell it after holding it for some time, like a year. Holding period rate of return can be calculated with the formula given on page 136.

If the market rate of interest and the bond’s yield-tomaturity does not change over this period, then the bond’s rate of return will be equal to its yield-to-maturity. If there is a decline in interest rates, the rate of return will be higher than the bond’s yield-to-maturity as in the case of the example. If there is an increase in interest rates, the rate of return will be less than the bond’s yield to maturity because of the decline in the value of the bond with the increase in interest rates.

Nominal and Real Interest Rates

The interest rates you observe in the world around you are typically nominal rates. However, they are usually assumed to have a real interest rate component and another component to compensate for expected inflation. Investors in bonds expect to receive fixed payments in the future (fixed coupon payments and par value at maturity), however, they are not certain about what they can buy with these cash flows in the future (purchasing power of these cash flows). Real interest rate can be calculated with the formula given on page 137.

The Yield Curve

Yield curve plots the relationship between bond yields and maturity. In general, yield curves are upward sloping because investors may require more yield to invest in long- term bonds. First, as maturity increases, uncertainty in investing long-term bonds is higher. Second, prices of long-term bonds fluctuate more with the changes in interest rates. Long-term bonds have higher interest rate risk. Upward sloping yield curve implies that short-term interest rates will increase in the future.

Bond Ratings and Risk of Default

Government bonds are usually considered to be default free, especially if they are denominated in the local currency. Governments are expected to pay their obligations, i.e., coupon payments and par value, on time. If they do not have enough cash, they can print their own money. In general, this is true but there are some exceptions.

Corporations cannot print money and it is possible to default if they do not make their payments on time. They hold default risk, i.e., the risk that a bond issuer may default on its obligations. In order to invest in the bonds of corporations with higher default risk, investors require higher returns than the yields on government bonds. The higher the default risk, the higher is the yield on the bonds.

Stocks

If you purchase stocks of a company, you become an owner of that company. As an owner, you have several rights. One of them is voting right. You have a right to vote in the shareholders’ meeting. Second, you have a right to receive dividends, if the corporation decides to distribute any. They will be cash flows you expect to get in investing in stocks. Third, you have pre-emptive right. If the company issues additional shares, you have a right to purchase your share of these shares (sometimes at a discount) before the new stocks are offered to the public in order to protect your initial share in the company. Fourth, the right to receive your share of the residual (AssetsLiabilities) in case of dissolution of the company. The first time the company offers its shares to the public is called initial public offering (IPO).

Market Values Versus Book Values

The book value of a company’s stocks is an accounting figure calculated from the balance sheet of a company. Every quarter all listed companies report their financial statements. The difference between total assets and total liabilities is the book value of the company’s equity. Since book value indicates what was collected and retained in the company, it is like historical value whereas market value is based on the expectations about the future cash flows from investing in the company’s stocks.

Stock Valuation

Stock valuation is similar to bond valuation. e value of stock is equal to the present value of its future cash flows. However, it is more difficult than calculating the value of a bond for a few reasons. First, the timing and amount of future cash flows are not known with certainty as in case of coupons and par value. It is not possible to know how much dividend the company will distribute in the future. Second, unlike bonds, stocks do not have any maturity. It is generally assumed that the corporations will live forever. Third, the discount rate used in calculating present values is difficult to estimate. It is not easy to estimate the rate of return the market requires for investing in a specific stock. e cash flows that are associated with stocks are the dividends that the firm may pay and price that the investor receives when she sells the shares. Dividends are paid only after interest and other required payments are made to creditors and they are not fixed amounts; Dividends depend on the profitability, growth prospects, investment requirements and payout decisions of the company. As a result, their timing and quantities are uncertain and they are more risky than debt securities. In order to compensate for this greater risk, they need to offer greater expected returns in order to make them attractive to investors.

Valuing by Comparables

Compared to bonds, there are uncertainties about cash flows of stocks and several assumptions have to be made. It can be assumed that the stocks of similar companies should be priced in a similar way because investors are prepared to pay similar price for each lira of assets or earnings. It is called valuation by comparables. e common ratios used as comparables are price-earnings (P/E) ratio, market value-to- book value (MV/BV) ratio, price-to-sales ratio, price-to-cash flows ratio and PEG, defined as the P/E ratio divided by the growth rate of earnings.

Dividend Discount Model

According to this model, the value of stock is equal to the present value of all future dividends that investors expect to get from that stock. The formula given on page 143 can be used for the calculation. It is not possible to estimate all future dividends, we make some simplifying assumptions about future dividends.

Zero Growth

The simplest assumption is that the company will distribute same dividend forever. There is no change in dividend payments. It is same as assuming that there is zero growth in dividends. Formula given on page 143 can be used to calculate its value.

Constant Growth

It can be assumed that dividends will grow at a constant rate (g) every year. It is possible to identify all future dividends. e intrinsic value of a stock is calculated with the equation given on page 144.

Supernormal Growth

The amount of dividend the company pays may change every year. However, it is assumed that after certain time period, say in year T, it may reach to its steady state level and have a constant growth rate after year T. e intrinsic value is still the present value of its future dividends. e present value of dividends are calculated one by one until time T and the present value of the value of stock at time T is added.

Valuation with Free Cash Flows

Another approach to calculate stock price is to discount free cash flows of a firm. It is similar to dividend discount model. Free cash flows are defined as cash flows available to the firm or to the shareholders after the company makes its capital expenditures. is approach can be used for the valuation of companies that do not distribute dividends. A stock price is found by dividing the present value of free cash flows to equity holders by the number of shares outstanding.

Expected Rate of Return

Expected rate of return of stocks has two components. e first component is the return from dividends, called dividend yield (Div1/P0). e second component is the return from price appreciation, called capital gains yield ((P1-P0)/P0). At equilibrium, the expected rate of return needs to be equal to the required rate of return. is is the case because the intrinsic value of this stock is equal to its market price. Also, for a company that is growing at a constant rate, the rate of increase in stock price will be equal to the rate of increase in dividends.

Stocks that provide all or almost all of their returns from dividend yield are referred to as income stocks. Whereas, stocks that pay no or very low dividends and still have prices that increase are called growth stocks. Rapidly growing companies require a lot of investments, growth stock companies usually are using their profits and cash flows to support these investments and as a result do not have resources to pay dividends. Different types of investors may prefer one type of stock over another for reasons like differences in taxation, consumption time preference, risk tolerance, etc.