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Chapter 8 VALUATION of securities limitations • Valuation is not an exact science • Consideration governing share valuation are varied and numerous BONDS AND THEIR VALUATION Introduction Assets can be real or financial; securities like shares and bonds are called financial assets while physical assets like plant and machinery are called real assets. The concepts of return and risk, as the determinants of value, are as fundamental and valid to the valuation of securities as to that of physical assets. BONDS AND The Basic Valuation Model THEIR VALUATION 1. The Basic Valuation Model: The value of an security is the present value of all future cashflows associated with it over the specified period. The expected returns are discounted, using the required return matching with the risk of asset as the appropriate discount rate. Symbolically, • Vo= A1 A2 -------- + -------- + (1+k) 1 (1+k) 2 An ----- + -------(1+k) n • Where Vo = Value of security at time zero (t = 0) • At = cash flow stream expected at the end of year t • K = appropriate discount rate • n=life of the asset • Alternatively, where expected cash flows is a mixed stream • V = [ ( A1 x PVIFk,1 ) + ( A2 x PVIFk,2 ) +- - - - - + ( An x PVIFk,n) Where PVIF1, PVIF2, PVIFn = present value interest factor in different period at discount rate k. • If expected cash flow is an Annuity, V = A * PVIFA (k,n) Illustration 6: Assuming a discount rate of 10 percent, and the associate d cash flows detailed below. Compute the value of assets X and Y. • Year Expected cash flow X • 1 • 2 • 3 Rs.10,000 10,000 10,000 Y 5,000 10,000 15,000 Solution: • Value of asset X = Rs 10,000 x PVIFA (10%,3) = Rs 10,000 x 2.4870 = Rs. 24,870 • Value of asset Y: = [(Rs.5, 000 x PVIF10%,1 ) + (Rs. 10,000 xPVIF10%,2 ) + ( Rs. 15,000 x PVIF10%,3) = [(Rs.5, 000 x 0.909) + (Rs. 10,000 x 0.826) + (Rs. 15,000 x 0.751) = Rs.4545+ RS.8260+Rs.11265 = Rs. 24,070 Valuation of Bonds / Debentures A bond / debenture are a long term debt instrument used by the government/ business/ enterprises to raise a large sum of money. • Par value: face value • Coupon rate and interest: Coupon is the specified interest rate. The interest payable to the bondholder is equal to: (par value x coupon rate). • Maturity period: corporate bonds 3-10 years. Govt. bond have maturity upto 20-25 years. Most bonds (i) pay interest half yearly at a stated coupon interest rate, (ii) have a maturity of 10years(Maturity period refers to the number of years after which the par value is payable to the bondholder). (iii) Have a par /face value of Rs 1,000 that must be repaid at maturity. (Par value i s the value on the face of the bond. It represents the amount the entity borrows and promises to repay at the time of maturity). A Basic Bond Valuation: Value of bond is the present value of the contractual payments its issuer is obliged to make from the beginning till maturity. The appropriate discount ratewould be the required return matching with risk and the prevailing interest rate. Symbolically, • B = I x (PVIFAkd n) + M x (PVIFkd n) • Where, B = value of the bond at t = 0 I = annual interest paid n = maturity period of the bond(term of the bond) M = Par/maturity value Kd = required return on the bond Illustration 7: A firm has issued 12% coupon rate, 8year bond with a Rs, 100 par value, that pays interest annually. The required rate of return is 14%. Compute the value of bond. Solution: Bo = [Rs 12 x (PVlFA14%, 8) + Rs 100 (PVlF14%, 8)] = (Rs 12 x 4.639) + (Rs 100 x 0.351) = Rs 90.77 Impact of required Return (RR) on Bond Value •When the - required Return (RR) =the coupon rate (CR) (the bond value equals the par value) •- (RR) > (CR) , the bond value would be less than its par value, that is, the bond would sell at a discount equal to (M-B) •- (RR) <(CR) , the bond value would be more than its par value, that is, the bond would sell at a premium equals to (B-M) Yield to Maturity The YTM is the rate of return that investors earn if they buy a bond at a specific price and hold it until maturity. Formula: B = I x (PVIFAkd,n) + M x (PVIFkd,n) • Illustration:The bonds of the Premier Company Ltd (PCL) are currently selling at Rs.10, 800. Assuming (i) coupon rate of interest, 10 per cent, (ii) par value, Rs 10,000, (iii) maturity 10 years and (iv) annual interest payment, compute the YTM or what rate of interest would an investor earn if he holds it till its maturity? • Solution: Substituting the values in following Equation B = I x (PVIFAkd,n) + M x (PVIFkd,n) Rs 10,800 = [Rs 1,000 x (PVIFAkd, 10) + Rs 10,000 x (PVIFkd, 10) If kd= 10 per cent, that is, equal to' the coupon rate, the value of the bond would be Rs 10,000. Since the value of the bond is Rs 10,800, the kd must be less than 10 per cent. Using 9 per cent discount rate gets = [Rs 1,000 x (PVIFA 9,10) + Rs 10,000 x (PVIF 9,10) = (Rs 1,000 x 6.418) + (Rs 10,000 x 0.422) = Rs 6,418 + Rs 4,220 = Rs 10,638 Since the value of the bond (Rs 10,638) at kd = 9 per cent is less than Rs 10,800 (current market price). Try a lower rate of discount (kd). Using 8 per cent, we get (Rs 1,000 x 6.710) + (Rs 10,000 x 0.463) = Rs 6,710 + Rs 4,630 = Rs 11,340 Since the bond value (Rs 11,340) is higher than the current price of Rs 10,800, the kd (YI'M) between 8 and 9 per cent. The exact value can be found by interpolation, which is 8.77% ` 2. Semi annual Interest and Bond Values: The procedure to value bonds paying interest semiannually(half yearly) is similar to that for compounding interest more frequently than annually. However, here we find out the present value. • B = I x (PVIFAkd/2, 2n) + M x (PVIFkd/2, 2n) 2 • • • Illustration 10: For facts in illustration4, assume (i) the bonds of the firm pay interest semiannually, (ii) the required stated return is 14 per cent for similar-risk bonds that also pays half-yearly interest. Compute the value of bond. • • • Solution: Substituting the values in following Equation we get B = I x (PVIFAkd/2, 2n) + M x (PVIFkd/2, 2n) 2 • • • • • • • • • • • • • • B = (Rs 1,000 / 2) x [PVlFA14I2 x 2; 10] + Rs 10,000 x [PVlF14I2 x 2; 10] = (Rs 1,000 / 2) x [PVlFA7, 20] + Rs 10,000 x [PVlF7, 20] = (Rs 500 x 10.594) + (Rs 1,000 x 0.258) = Rs 5,297 + Rs 2,580 = Rs 7,877 3. Valuation of Preference Shares: Preference shares like debentures are usually subject to fixed rate of return/dividend. In case of no stated maturity, their valuation is similar to perpetual bonds. Symbolically, V = Dp Kp The valuation of redeemable preference shares is given by following equation = Dp( PVIFAkp,n) + MV( PVIFpv,n) • • • • • • • • • • • • • • • 4. Valuation of Ordinary Shares: The ordinary / Equity shareholders buy / hold shares in expectation of periodic cash dividends and increasing share value. They would buy a share' when it is undervalued (i.e. its true value is more than its market price) and sell it when its market price is more than its true value (i.e. it is overvalued). The value of a share is equal to the present value of all future dividends it is expected to provide over an infinite time horizon. Symbolically, P = D1 + D2 +- - - - - + 2 Where , P = Value of shares Dt = per share dividend expected at the end of year, t Ke = required return on share D∞ The equation is designed to compute the value of shares with reference to the expected growth pattern of future dividends and the appropriate discount rate. We illustrate below the computation reference to (i) zero growth, (ii) constant growth and (iii) variable growth. BONDS AND THEIR VALUATION Valuation – Three Major Techniques Asset Valuation Approach: Asset side of the Balance Sheet Income Valuation Approach: Profit and Loss Statement Market Multiple Valuation Approach: Liability side of the Balance Sheet Valuation – Asset Based Approach Company valuation as a special case of asset valuation Analyze the “Asset” side of the balance sheet Assets are where company has already spent the money and assets will give cash flows in future Company’s value depends upon the size and reliability of these future cash flows BONDS AND THEIR VALUATION Occasions for Valuation Equity analysis Merger and Acquisition Employment (when ESOPs are involved) IPO, restructuring, divestiture Exit of a Joint-Venture partner Equity investment (VC Financing) Loan decision by a banker (financial health estimation and default probability estimation) Management Buyout, internal share transfer Company Valuation BONDS AND THEIR VALUATION Type of Companies being Valued Listed companies – market price (consensus of active traders, quarterly statements, guidance, forecasts) Companies with assets which are mostly physical – depreciation, appreciation, obsolescence Examples – transport operator, mechanical ancillary units Company Valuation BONDS AND THEIR VALUATION Type of Companies being Valued Knowledge-based companies have huge intangible assets Patents, trademarks, Copyright (Software source code) Processes, quality and development methodology, Goodwill, brand, customer base, relationships Team (education, experience, skills) Company Valuation BONDS AND THEIR VALUATION Difficulties in Valuing Early Stage Companies Immediate earnings are negative No past history No comparable companies No market prices Asymmetric information Management efficacy yet to be established Company Valuation BONDS AND Bonds and Their Valuation THEIR VALUATION Buying and selling pressures dominantly originate with active investors. And they follow certain rules of the game which are Rule 1 : Buy when value is more than price. This underlines the fact that shares are under priced and it was to be a bargain to buy now and sell when prices move up towards value. Rule 2 : Sell when value is less than price. In a situation like this, shares would be overpriced and it would advantageous to sell them now and avoid less when price later moves down to the level of the value. Rule 3 : Don’t trade when value is equal to price. This is a state when the market price is an equilibrium is not expected to change. BONDS AND Valuation of Fixed Income Securities: THEIR VALUATION A debenture is a legal document containing an acknowledgement of indebtedness by a company. It contains a promise to pay a stated rate of interest for a defined period and then to repay the principal at a given date of maturity. In short, a debenture is a formal legal evidence of debt and is termed as the senior securities of a company. BONDS AND THEIR VALUATION Features of a Bond Face Value Interest Rate—fixed or floating Maturity Redemption value Market Value BONDS AND REASONS FOR ISSUING BONDS THEIR VALUATION To Reduce the Cost of Capital: Bonds are the cheapest source of financing. To Widen the Sources of Funds: By issuing bonds, the corporation can attract funds from individual investors and especially from those investing institutions which are reluctant or not permitted to purchase equity shares. To Preserve Control: An increase in debt does not diminish the voting power of present owners since bonds ordinarily carry no voting right. To Gain the Benefit of Leverage: The presence of debt and / or preference shares in the company's financial structure means that it is using financial leverage. When financial leverage is used, changes in earnings before interest and tax (EBIT) translate into the larger changes in earnings per share. To Effect Tax Saving: Unlike dividends on equity, the interest on bonds is deductible in figuring up corporate income for tax purposes. BONDS AND THEIR VALUATION TYPES OF BONDS Convertible and Non-Convertible Bonds: Convertible bonds can be one of the finest holdings for the investor looking for both appreciation of investment and income of bond. Collateral Trust Bonds: Instead of being secured by a pledge of tangible property, as are mortgage bonds, collateral trust issues are secured by a pledge of intangibles, usually in the form of stocks and bonds of corporation. Income Bonds: Income bonds are bonds on which the payment of interest is mandatory only to the extent of current earnings. If earnings are sufficient to pay only a portion of the interest, that portion usually is required to be paid, but if the corporation is able to pay the unearned balance out of its cash resources, it is of course free to do so. Redeeemable and Irredeemable Bonds: A redeemable debenture is a bond which has been issued for a certain period on the expiry of which its holder will be repaid the amount thereof with or without premium. Participating Bonds: Companies with poor credit positions issue participating bonds. They have a guaranteed rate of interest but may also participate in earnings up to an additional specified percentage. Sinking Fund Bonds: Sinking fund bonds arise when the company decides to retire its bond issue systematically by setting aside a certain amount each year for the purpose. The payment, usually fixed annual rupees amount or percentage instalment, is made to the sinking fund agent who is usually the trustee. Serial Bonds: Like sinking fund bonds, serial bonds are not special types of bonds but just names given to describe the method of repayment. Thus, any bond can be such by merely specifying it in the indenture. Mortgage or Secured Bonds: The term mortgage generally refers to a lien on real property or buildings. Mortgage bonds may be open-end, close-end, and limited open-end. BONDS AND RISK MANAGEMENT IN BONDS THEIR VALUATION Default Risk: Default risk identifies the uncertainty prevalent in the repayment of interest and principal to the bondholders. Purchasing Power Risk: Debt instrument investors have to look at the real rate of return, or the actual return minus the rate of inflation. Price Risk: Investors who need their principal prior to maturity have to rely on the available market for the securities. Liquidity Risk: The exchange listing of debt securities does not guarantee liquidity. Reinvestment Risk: The maturity period of bonds are spread over a fixed time duration. BONDS AND THEIR VALUATION Bonds Values and Yields Bonds with maturity Pure discount bonds Perpetual bonds BONDS AND 2ND THEIR VALUATION Bond with Maturity Bond value = Present value of interest + Present value of maturity value: n B0 t 1 INTt Bn (1 kd )t (1 kd ) n Copyright © 2008, Dr Sudhindra Bhat 8 – 27 FINANCIAL MANAGEMENT, Dr. Sudhindra Bhat Excel Books BONDS AND THEIR VALUATION Yield to Maturity The yield-to-maturity (YTM) is the measure of a bond’s rate of return that considers both the interest income and any capital gain or loss. YTM is bond’s internal rate of return. A perpetual bond’s yield-to-maturity: n B0 t 1 INT INT (1 kd )t kd BONDS AND THEIR VALUATION Current Yield Current yield is the annual interest divided by the bond’s current value. Example: The annual interest is Rs. 60 on the current investment of Rs. 883.40. Therefore, the current rate of return or the current yield is: 60/883.40 = 6.8 per cent. Current yield does not account for the capital gain or loss. BONDS AND THEIR VALUATION Yield to Call For calculating the yield to call, the call period would be different from the maturity period and the call (or redemption) value could be different from the maturity value. Example: Suppose the 10% 10-year Rs 1,000 bond is redeemable (callable) in 5 years at a call price of Rs 1,050. The bond is currently selling for Rs 950.The bond’s yield to call is 12.7%. 5 950 100 t 1 1 YTC t 1,050 1 YTC 5 BONDS AND THEIR VALUATION Bond Value and Amortisation of Principal A bond (debenture) may be amortised every year, i.e., repayment of principal every year rather at maturity. The formula for determining the value of a bond or debenture that is amortised every year, can be written as follows: n CFt B0 t t 1 (1 k d ) Note that cash flow, CF, includes both the interest and repayment of the principal. BONDS AND THEIR VALUATION Pure Discount Bonds Pure discount bond do not carry an explicit rate of interest. It provides for the payment of a lump sum amount at a future date in exchange for the current price of the bond. The difference between the face value of the bond and its purchase price gives the return or YTM to the investor. BONDS AND 2ND THEIR VALUATION Pure Discount Bonds Example: A company may issue a pure discount bond of Rs 1,000 face value for Rs 520 today for a period of five years. The rate of interest can be calculated as follows: 520 1, 000 1 YTM 5 1, 000 1.9231 1 YTM 520 i 1.92311/ 5 1 0.14 or 14% 5 Copyright © 2008, Dr Sudhindra Bhat 8 – 33 FINANCIAL MANAGEMENT, Dr. Sudhindra Bhat Excel Books BONDS AND THEIR VALUATION Pure Discount Bonds Pure discount bonds are called deep-discount bonds or zero-interest bonds or zero-coupon bonds. The market interest rate, also called the market yield, is used as the discount rate. Value of a pure discount bond = PV of the amount on maturity: B0 Mn 1 kd n BONDS AND THEIR VALUATION Perpetual Bonds Perpetual bonds, also called consols, has an indefinite life and therefore, it has no maturity value. Perpetual bonds or debentures are rarely found in practice. BONDS AND 2ND THEIR VALUATION Perpetual Bonds Suppose that a 10 per cent Rs 1,000 bond will pay Rs 100 annual interest into perpetuity. What would be its value of the bond if the market yield or interest rate were 15 per cent? The value of the bond is determined as follows: INT 100 B0 Rs 667 kd 0.15 Copyright © 2008, Dr Sudhindra Bhat 8 – 36 FINANCIAL MANAGEMENT, Dr. Sudhindra Bhat Excel Books BONDS AND 2ND THEIR VALUATION Bond Values and Changes in Interest Rates The value of the bond declines as the market interest rate (discount rate) increases. The value of a 10-year, 12 per cent Rs 1,000 bond for the market interest rates ranging from 0 per cent to 30 per cent. 1200.0 1000.0 Bond Value 800.0 600.0 400.0 200.0 0.0 0% 5% 10% 15% 20% 25% 30% Interest Rate Copyright © 2008, Dr Sudhindra Bhat 8 – 37 FINANCIAL MANAGEMENT, Dr. Sudhindra Bhat Excel Books BONDS AND 2ND THEIR VALUATION Bond Maturity and Interest Rate Risk The intensity of interest rate risk would be higher on bonds with long maturities than bonds with short maturities. The differential value response to interest rates changes between short and long-term bonds will always be true. Thus, two bonds of same quality (in terms of the risk of default) would have different exposure to interest rate risk. Present Value (Rs) Discount rate (%) 5-Year bond 10-Year bond Perpetual bond 5 1,216 1,386 2,000 10 1,000 1,000 1,000 15 832 749 667 20 701 581 500 25 597 464 400 30 513 382 333 Copyright © 2008, Dr Sudhindra Bhat 8 – 38 FINANCIAL MANAGEMENT, Dr. Sudhindra Bhat Excel Books BONDS AND 2ND THEIR VALUATION Bond Maturity and Interest Rate Risk Copyright © 2008, Dr Sudhindra Bhat 8 – 39 FINANCIAL MANAGEMENT, Dr. Sudhindra Bhat Excel Books BONDS AND THEIR VALUATION Bond Duration and Interest Rate Sensitivity The longer the maturity of a bond, the higher will be its sensitivity to the interest rate changes. Similarly, the price of a bond with low coupon rate will be more sensitive to the interest rate changes. However, the bond’s price sensitivity can be more accurately estimated by its duration. A bond’s duration is measured as the weighted average of times to each cash flow (interest payment or repayment of principal). BONDS AND 2ND THEIR VALUATION Duration of Bonds Let us consider the 8.5 per cent rate bond of Rs. 1,000 face value that has a current market value of Rs. 954.74 and a YTM of 10 per cent, and the 12 per cent rate bond of Rs. 1,000 face value has a current market value of Rs. 1,044.57 and a yield to maturity of 10.8 per cent. Table shows the calculation of duration for the two bonds. Year 2001 2002 2003 2004 2005 Cash Flow 85 85 85 85 1,085 Year 2001 2002 2003 2004 2005 Cash Flow 115 115 115 115 1,115 8.5 Percent Bond Present Value at 10 % 77.27 70.25 63.86 58.06 673.70 943.14 11.5 Percent Bond Present Value at 10.2% 103.98 94.01 85.00 76.86 673.75 1,033.60 Proportion of Bond Price 0.082 0.074 0.068 0.062 0.714 1.000 Proportion of Bond Price x Time 0.082 0.149 0.203 0.246 3.572 4.252 Proportion of Bond Price 0.101 0.091 0.082 0.074 0.652 1.000 Proportion of Bond Price x Time 0.101 0.182 0.247 0.297 3.259 4.086 Copyright © 2008, Dr Sudhindra Bhat 8 – 41 FINANCIAL MANAGEMENT, Dr. Sudhindra Bhat Excel Books BONDS AND THEIR VALUATION Volatility The volatility or the interest rate sensitivity of a bond is given by its duration and YTM. A bond’s volatility, referred to as its modified duration, is given as follows: Volatility of a bond Duration (1 YTM) The volatilities of the 8.5 per cent and 11.5 per cent bonds are as follows: Volatility of 8.5% bond 4.252 3.87 (1.100) 4.086 Volatility of 11.5% bond 3.69 (1.106) BONDS AND THEIR VALUATION The Term Structure of Interest Rates Yield curve shows the relationship between the yields to maturity of bonds and their maturities. It is also called the term structure of interest rates. Yield Curve (Government of India Bonds) Yield (%) 7.5% 7.18% 7.0% 6.5% 6.0% 5.90% 5.5% Maturity (Years ) 5.0% 0-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 >10 BONDS AND THEIR VALUATION The Term Structure of Interest Rates The upward sloping yield curve implies that the long-term yields are higher than the short-term yields. This is the normal shape of the yield curve, which is generally verified by historical evidence. However, many economies in high-inflation periods have witnessed the short-term yields being higher than the long-term yields. The inverted yield curves result when the short-term rates are higher than the long-term rates. BONDS AND THEIR VALUATION The Expectation Theory The expectation theory supports the upward sloping yield curve since investors always expect the short-term rates to increase in the future. This implies that the long-term rates will be higher than the short-term rates. But in the present value terms, the return from investing in a long-term security will equal to the return from investing in a series of a short-term security. BONDS AND THEIR VALUATION The Expectation Theory The expectation theory assumes capital markets are efficient there are no transaction costs and investors’ sole purpose is to maximize their returns The long-term rates are geometric average of current and expected shortterm rates. A significant implication of the expectation theory is that given their investment horizon, investors will earn the same average expected returns on all maturity combinations. Hence, a firm will not be able to lower its interest cost in the long-run by the maturity structure of its debt. BONDS AND THEIR VALUATION The Liquidity Premium Theory Long-term bonds are more sensitive than the prices of the short-term bonds to the changes in the market rates of interest. Hence, investors prefer short-term bonds to the long-term bonds. The investors will be compensated for this risk by offering higher returns on long-term bonds. This extra return, which is called liquidity premium, gives the yield curve its upward bias. BONDS AND THEIR VALUATION The Liquidity Premium Theory The liquidity premium theory means that rates on long-term bonds will be higher than on the short-term bonds. From a firm’s point of view, the liquidity premium theory suggests that as the cost of short-term debt is less, the firm could minimize the cost of its borrowings by continuously refinancing its short-term debt rather taking on long-term debt. BONDS AND THEIR VALUATION The Segmented Markets Theory The segmented markets theory assumes that the debt market is divided into several segments based on the maturity of debt. In each segment, the yield of debt depends on the demand and supply. Investors’ preferences of each segment arise because they want to match the maturities of assets and liabilities to reduce the susceptibility to interest rate changes. BONDS AND THEIR VALUATION The Segmented Markets Theory The segmented markets theory approach assumes investors do not shift from one maturity to another in their borrowing—lending activities and therefore, the shift in yields are caused by changes in the demand and supply for bonds of different maturities.