Lecture 2 Valuation of Fixed Income Securities (a)

Lecture 2 Valuation of Fixed Income Securities (a) Since we all now have a basic idea of how time value of money works, it is time we put the techniques we learned to some use 1

Fixed Income Securities Bonds Recall the start of the first lecture, we defined financial assets as the assets which give the bearer claims on the firm s real assets and the cash those assets will produce. Today we will initiate our coverage of financial assets by deliberating on bonds. As a lot of you already know, a bond is a long-term debt instrument and represents a contract under which a borrower agrees to make payments of interest and principal on specific dates to the holders of the bond. Depending on who the issuer is, we can categorize bonds into four broad categories. Treasury bonds These are the bonds which are issued by the federal government. They are also known as Government Bonds. An example in our case would be of Pakistan Investment Bonds (PIBs). 2

Fixed Income Securities Bonds Corporate Bonds As the name implies, these bonds are issued by corporations to fulfill there financing needs. Example on our case would be of Term Finance Certificates (TFCs) issued by several banking and non-banking organizations. Municipal Bonds These are the bonds which are issued by local and state governments. These are also known as Munis and have little relevance in Pakistan s context. Foreign Bonds These are the bonds issued by foreign governments or corporations. Depending upon the type of the bond, there are certain risk factors affecting that bond. Can you identify them in each of the above four cases? 3

Fixed Income Securities Key Characteristics of Bonds Before going into the depths of valuing a bond, it is imperative that we understand the following terms: Par Value: It is the stated face value of the bond. The par value generally represents the amount of money the firm borrows and promises to repay on the maturity date. Coupon Interest Rate: It is the stated annual interest rate of the bond. That is, the interest rate which the issuer pays over the life of the bond. Maturity Date: A specific date agreed in advance on which the par value of the bond must be repaid. Discount Rate: The rate of interest which is used to discount the cash flows arising because of the bond. In order to fuel its expansionary requirements, Engro Chemicals issued 10 million TFCs of worth PKR 5 billion. The company promises that it will pay an annual coupon of PKR 500 per TFC and will repay the face value after 15 years. The prevailing interest rate is 12%. Please identify the value of the abovementioned four variables in this example? 4

The Term Structure of Interest Rates Yield Curve The term structure of interest rates describes the relationship between long and short term interest rates; A graph showing the relationship between yields and maturities is known as the yield curve. 15.50% Selected PKRV Rates (January 10, 2011) 15.00% 14.50% 14.00% 13.50% 13.00% 3 Month 6 Month 1 Year 2 Year 5 year 10 year 15 Year 20 Year 30 Year 5

Yield Curve Possible Shapes 16.00% Upward Sloping Yield Curve 15.50% 15.00% 14.50% 14.00% 13.50% 13.00% 12.50% 12.00% 11.50% 3 Month 6 Month 1 Year 2 Year 5 year 10 year 15 Year 20 Year 30 Year 6

Yield Curve Possible Shapes 16.00% Downward Sloping Yield Curve 15.50% 15.00% 14.50% 14.00% 13.50% 13.00% 12.50% 12.00% 11.50% 3 Month 6 Month 1 Year 2 Year 5 year 10 year 15 Year 20 Year 30 Year 7

Yield Curve Possible Shapes 16.00% Humped Yield Curve 15.50% 15.00% 14.50% 14.00% 13.50% 13.00% 12.50% 12.00% 11.50% 3 Month 6 Month 1 Year 2 Year 5 year 10 year 15 Year 20 Year 30 Year 8

Yield Curve Possible Shapes 16.00% Flat Yield Curve 15.50% 15.00% 14.50% 14.00% 13.50% 13.00% 12.50% 12.00% 11.50% 3 Month 6 Month 1 Year 2 Year 5 year 10 year 15 Year 20 Year 30 Year 9

Bond Valuation Valuing Zero Coupon Bonds A zero coupon bond is a bond that pays no annual interest but is sold at a discount below par, thus providing compensation to investors in the form of capital appreciation. They are also known as Zeros. On the issue date, zeros are sold to investors at a substantial discount below their par value and upon maturity the issuer pays back the face value of the zero coupon bond to the investors. Valuing a zero coupon bond is a much simpler task as compared to coupon bonds. In simplest of terms, the case of a zero coupon bond is similar to the discounting of a single cash flow which is to be received in future. 10

Bond Valuation Valuing Zero Coupon Bonds IBF Cosmetics is planning to issue a zero coupon bond with a maturity of 6 years and a face value of PKR 1,000. The applicable required rate of return is 13%. Calculate the price at which the zero should be issued. Market Price Face Value n (1 i) 1,000 Market Price (1 0.13) 1,000 Market Price 6 (1.13) Market Price PKR 480 6 11

Bond Valuation Conceptual Review (Coupon Bonds) A bond is a long-term debt instrument and a contract under which a borrower agrees to make payments of interest and principal on specific dates to the holders of the bond. Based upon the definition, it is clear that the holder will receive two genres of cash flows. One is the coupon interest payment and the other is the principal repayment at maturity. Also recall that the fair value of any financial asset is the present value of all the expected cash flows. So in case of bonds, its fair value will be the present value of coupon payments and principal repayment. That is, Bond Fair Value = PV Coupon Payments + PV Principal Repayment 12

Financial Assets Bond Valuation (Coupon Bonds) 0 1 2 3 N K d % K d % K d % K d % Bond s Value Interest Interest Interest Interest + Face value Here, Bond s Value = Present value of all the expected future cash flows; K d % = Applicable discount rate used to calculate the present value of the bond s cash flows; Interest = Interest payment made by the issuer of the bond as per the coupon rate; N = Number of years/periods before the bond matures. 13

Bond Valuation Simple But Unrealistic Company X wants to raise PKR 5 billion by issuing a total of 1 million TFCs. The TFCs offer a coupon rate of 20% paid on annual basis with the face value being repaid upon maturity. The maturity of the issue is 4 years. As per financial analysts in the industry, it has been estimated that investors are demanding a required rate of return of 18% on such investments. The BATS screen reveals that the proposed TFC issue of company X is available at a price of PKR 5,525 per TFC. Given the required rate of return and the listed price, compute the fair value of the issue and make your investment decision. 14

Bond Valuation In Practice Corporate bonds, in essence, are a combination of multiple zero-coupon bonds. That is the individual coupons and the repayment of face value at maturity are effectively individual zero coupon bonds maturing at their respective dates. Consequently, given the existence of a yield curve and various risk premiums, the discount rates used to value payments at different nodes of time should be exclusive of each other. That is, the required rate of return used to discount a cash inflow at the end of 1 year should be different from the rate used to discount a cash inflow coming in after 2 years. 15

Bond Valuation In Practice (Contd.) 0 1 2 3 N Bond s Value Interest Interest Interest Interest + Face value 1 Year Spot Rate 2 Year Spot Rate 3 Year Spot Rate Nth Year Spot Rate 16

Bond Valuation In Practice (Contd.) Given the following yield curve, recalculate the fair value of bond X and revisit your investment decision. 14.40% 14.20% 14.25% 14.00% 13.98% 13.80% 13.60% 13.40% 13.20% 13.21% 13.40% 13.62% 13.00% 1 Year 2 Year 3 Year 4 Year 5 Year 17

Sources of Return (%) From the Perspective of Coupon Bonds The return associated with any bond can be dissected into the following three components: Coupon Payments Periodic interest payments associated with a bond and are usually disbursed on semi-annual basis; Capital Gain or Loss The appreciation or depreciation of the principal amount itself (Selling price or maturity value minus the purchase price); Reinvestment Income is the interest income generated by reinvesting coupon payments and any partial repayment of principal from the time of receipt to the bond s maturity. Given the sources, the return associated with a bond is measured by using the following tools: Current Yield Yield to Maturity (YTM) 18

Sources of Return (%) Current Yield Current Yield: It is the annual interest income offered by the bond divided by its market price. Current yield provides information regarding the amount of cash income that a bond will generate in a given year. Mathematically, Current Yield (%) Annual Interest Income Current Market Price If a bond is offering a quarterly coupon payment of PKR 125 over a face value of PKR 1,500, calculate the current yield if its market price is PKR 1,394. Current yield is greater (less) than the coupon rate, when the bond sells at a discount (premium) The current yield is a weak measure of return because: No consideration is given to the capital gain or loss; Reinvestment income is also not considered; No consideration is given to time value of money. 19

Sources of Return (%) Yield to Maturity (YTM) Yield to Maturity: It is the rate of return that the investor will earn if he/she decides to hold the bond till maturity. In simplest of terms, it is the discount rate at which the present value of all future cash flows is equal to the market price. Mathematically, Coupon Coupon Market Price 1 2 (1 YTM) (1 YTM)... Coupon (1 YTM) If we talk about fixed-coupon paying bonds, then we can also rewrite the above equation as: 1 1- (1 Market Price = C YTM YTM) YTM is usually calculated by either following a trial and error approach, by using financial calculators or with the help of an excel sheet. Now, calculate the YTM of bond X; n n Face Value n (1 YTM) Face Value n (1 YTM) 20

Sources of Return (%) Yield to Maturity (Contd.) For bonds selling at a discount (premium), YTM is greater (lesser) than the current yield which in turn is greater (lesser) than the coupon rate on the bond; Suppose an investor has a 5 year 10% annual coupon bond trading at a par value of PKR 100. Since the bond is trading at par then YTM will also be 10%; If PKR 100 are invested at the YTM of 10% then they translate into a total future value of PKR 161 (100*1.10^5); Decomposing this value gives a principal value of PKR 100 and a return of PKR 61; Without reinvesting income, the dollar return would have only been PKR 40 of coupon payment and PKR 0 of capital gain (Since it is trading at par); Thus, the dollar return shortfall of PKR 21 (PKR 61 PKR 40) is in fact the reinvestment income this bond generates; Consequently, a YTM of 10% is only realized if all coupon payments are reinvested at an interest rate equal to the YTM (Which in this case is 10%). 21

Sources of Return (%) Yield to Maturity (Contd.) The above example illustrates that YTM takes into account all the three sources of return but under the following set of assumptions: All the intermediate cash flows (Whether in the form of coupon payments or partial principal repayments) are reinvested at an interest rate equal to that of YTM. If such is the case then the ultimate return realized may actually be different from YTM and is known as the reinvestment risk; The bond is held till maturity (If the bond is not held till maturity and is sold prematurely then the investor faces the risk of selling it at a value less than the purchase price, this exposes the investor to interest rate risk). 22

Bond Valuation Tying it Altogether Based upon the comparison of the required rate of return and the coupon rate offered by the bond, we can create an estimate about the price of a bond: Bonds with coupon rate greater than the required rate of return are known as Premium Bonds. And their fair value is always greater than the par value; Bonds with coupon rate less than the required rate of return are known as Discount Bonds. And their fair value is always less than the par value; Bonds with coupon rate equal to the required rate of return are known as Par Bonds. And their fair value is always equal to the par value. We can make our investment decision upon the comparison of the fair value and the market value of the security. That is, If any security is UNDERPRICED (fair value > market value), then we will BUY the security; If any security is OVERPRICED (fair value < market value), then we will NOT BUY the security or if we already have it in our portfolio we will SELL it off. 23

Bond Valuation Tying it Altogether Given a yield curve, the discount rate used to calculate the fair value of a bond may vary over the periods of time: In case of a flat yield curve, a single discount rate is used to calculate the fair value of the cash flows; In case of a non-flat yield curve (Humped, upward or downward sloping), the discount rate used varies across different time periods. The percentage of a bond can be reported in the following two forms: Current Yield is the annual interest income divided by the market price of the bond. It only provides information as to the cash income that will be generated by the bond over a given year; Yield to Maturity is the rate of return that the investor will earn if he/she holds the bond till its maturity. In simplest of terms, it is the required rate of return at which the present value of all future cash flows is equal to the current market price. 24

Bond Valuation Tying it Altogether The relationship between YTM, price, current yield and coupon rate can be summarized as follows: For bonds selling at par, YTM is equal to the current yield which is equal to the coupon rate; For bonds selling at a discount, YTM is greater than current yield which is greater than the coupon rate; For bonds selling at a premium, YTM is less than current yield which is less than the coupon rate. Reinvestment risk is the risk that intermediate cash flows from the bond may not be invested at an interest rate equal to the YTM; Interest rate risk is the risk associated with a depreciation in the price of a bond given an adverse interest rate movement; As bonds reach their maturity, the fair value of the bond (present value of future cash flows) come closer to its par value. 25