CCHHAAPPTTEERR--44 BBOONNDD VVAALLUUAATTIIOONN Lesson from this topic If we both exchange one rupee, we both have one rupee each, but if we exchange one good thought, we both have two thoughts. Comparison is the best way to judge your progress. But don’t compare with others, just compare your yesterday with your today. 18 16 14 12 10 8 P 6 4 2 0 M11 N11 M12 N12 M13 N13 M14 N14 M15 M11 = May-2011 N11=Nov-2011 CHAPTER-4 BOND VALUATION 4.1 4.1 Bond A negotiable certificates evidencing indebtness. It is normally unsecured. A company, municipality or government agency generally issues a debt security. Bond issues are considered fixed income securities because they impose fixed financial obligations on the issuers. The issuers agrees to (a) Pay fixed amount of interest periodically to the holder of bond. (b) Repay a fixed amount of principal at the date of maturity. 4.1.1 Some Basics of Bond (a) Face Value: This is the value stated on the face of the bond and is also known as par value. It represents the amount of borrowing by the firm which will be repaid after a specific period of time. (b) Redemption value of Bond: The Face value of bond is repaid at the end of maturity period, is known as redemption value of bond. A bond may be redeemed at par, at premium or at discount. (c) Market value: A bond may be traded in a stock exchange. Market value is the price at which the bond is usually bought or sold. Market value may be different from par value. (d) Coupon Rate or Interest: A bond carries a specific rate of interest which is also called a coupon rate. Interest Amt = Face value of Bond x Coupon Rate (e) Maturity: It is the number of years after which Redemption value is paid. (f) Call Date: Bonds which can be redeemed prior to maturity. The call date represents the date at which the bond can be called. (g) Call Price: It is a price at which Bond can be called back before maturity. 4.2 Bond Value and Yield to Maturity [From Q-1 to 17] ICAI ICSI ICWA Nov-2003 M-8 June-2002 M-6 Dec-2002 Nov-2007 M-6 Dec-2003 Nov-2008 M-5 Dec-2004 Nov-2009 M-4 Nov-2010 M-2.5+2.5 Nov-2010 M-5 Nov-2011 M-8 Nov-2013 M-5 May-2015 M-2+2+2 4.2.1 VALUE OF BOND (a) Bonds with Maturity B0 = Intt x PVAF (n years, RR) + RV x PVF (nth years, RR) (b) Perpetual Bond B0 = Intt/RR (c) Zero Coupon Bond B0 = RV x PVF (nth years, RR) 4.2.2 YIELD TO MATURITY (YTM) (a) The rate of return which makes the discounted value of cash flows equal to the bond's market value is known as the YTM of the bond. So, a bond’s YTM may be defined as the IRR CHAPTER-4 BOND VALUATION 4.2 for a given level of risk. (b) At YTM Market value of Bond = PV of Cash flow of Bond at YTM (c) Approximate YTM I (l-t)+(RV - NP)/N Kd = (RV+NP)/2 (d) Find Actual YTM First we should find two NPV at two different rates, then apply YTM = LR + [NPV LR x (Diff of Rate)]/(NPV LR – NPV HR ) (e) YTM is also known as yield means actual return of bond. (f) Yield to Maturity (i) Bonds with Maturity YTM = LR + [NPV LR ]*Diff of rate/[NPV LR – NPV HR ] (ii) Perpetual Bond YTM = Intt/Actual Market Price (iii) Zero Coupon Bond YTM = LR + [NPV LR ]*Diff of rate/[NPV LR – NPV HR ] 4.2.3 Pricing of BOND Conditions Pricing Action (a) IF B 0 > Actual price of Bond Overpriced It should not be purchased or it can be sold (b) IF B 0 < Actual price of Bond Underpriced It should be purchased or it should not be sold (c) IF B 0 = Actual price of Bond Correctly It may be purchased Note: The appropriate discount rate would depend upon the risk of the bond. The risk in holding the government bond is less than the risk associated with debentures issued by a company. Bonds with Maturity Question-1 A bond of Rs.1,000 bearing a coupon rate of 12% is redeemable at par in 10 years. Find out the value of the bond if: (a) Required rate of return of Ram-12%, Shyam-10% and Mohan-14%. [Ans: Rs.1,000; Rs.1,123.40; Rs.895.92] (b) If actual Price of Bond is Rs.1050, whether it should be bought or sold. (c) What is actual YTM for Ram, Shyam & Mohan. Imp Concept (a) Value of bond is depended on the required rate of return. Higher the required rate of return lower will be the value of the Bond and vice versa. (b) Required rate of return depends on Investor and it may vary from investor to investor. (c) Same bond may have different fair value for different investor depending on their required rate of return. (d) YTM is same for all investors because cash outflow, cash inflow and period are same for all investor. Question-1A A Rs.5,000 bond with a 10% coupon rate matures in 8 years. (a) Calculate value of bond for an investor whose required rate of return is 11 %. (b) If bond is selling at 97%. What is YTM. [Ans: PV = Rs.4,743; MP = Rs.4,850] CHAPTER-4 BOND VALUATION 4.3 Question-1B [Nov-2009] [N] [M-4] [SP] An investors is considering the purchase of the following Bond : Face value Rs.100 Coupon rate 11 % Maturity 3 years (a) If he wants a yield of 13% what is the maximum price he should be ready to pay for? (b) If the Bond is selling for Rs.97.60, what would be his yield? Question-1C [June-02-CS] [M-6] Question-1D [Nov-2010] [M-5] Question-1E [May-2015] [M-2] 4.3 BOND VALUATION BEHAVIOR [If Redemption value is equal to Face value] (a) If RR = CR then Bond Value = Par Value. (b) If RR > CR then Bond Value < Par Value. (c) If RR < CR then Bond Value > Par Value. 4.4 Bond Value in case of Semi-Annual Interest Bo = Intt/2 x PVAF (2n years, DR/2) + RV x PVF (2nth years, DR/2) Question-2 [Nov-2010] [M-2.5] Calculate Market Price of a bond with 7.5% coupon interest, Face value Rs.10,000 & Term to maturity of 2 years, presently yielding 6%. Interest payable half yearly. Question-2A [ICWA-Dec-2002] A Company invested in a 5 year bond issue of another company in 2010 carrying a coupon rate of 10% p.a. The interest payable at half yearly rests and the principal repayable after 5 years in 2014 end. The current market yield has fallen to 9% during 2011. The investor company wanted to take advantage of fall in market yield by selling the bond to any willing buyer. Compute the value of the bond at the end of 2011. Assume par value of each bond Rs.1000 Question-2B [SM] Question-2C [May-2015] [M-2] 4.5 Calculation of value of Bond if Coupon rate changes from year to year With the change in coupon rate, only interest amt p.a. will change and other part will remain same. Question-3 [Nov-2003] [M-8] M/s Agfa Industries is planning to issue a debenture series on the following terms: Face value Rs.100 Term of maturity 10 years Yearly coupon rate Years 1-4 9% 5-8 10% CHAPTER-4 BOND VALUATION 4.4 9-10 14% The current market rate on similar debentures is 15% per annum. The Company proposes to price the issue in such a manner that it can yield 16% compounded rate of return to the investors. The Company also proposes to redeem the debentures at 5% premium on maturity. Determine the issue price of the debentures. Question-3A [CS-Dec-2004] [SP] Blue Ltd is contemplating a debenture issue on the following terms: Face value Rs.100 Term of maturity 7 years Yearly coupon rate Years 1-2 8% 3-4 12% 5-7 15% The current market rate on similar debentures is 15% per annum. The Company proposes to price the issue in such a manner that it can yield 16% compounded rate of return to the investors. The Company also proposes to redeem the debentures at 5% premium on maturity. Determine the issue price of the debentures. 4.6 Bond value if required rate of return changes every year 1.26 Calculation of PVF 1) If Discount Rate for n years are same 1 PVF 1 = 1/(1+DR) 2 PVF 2 = 1/(1+DR) 3 PVF 3 = 1/(1+DR) Example Same Method 1 Method 2 Year Discount Rate PVF PVF PVF PVF 1 10% 1/(1.1) = 0.909 1/(1.1) = 0.909 2 10% 1/(1.1)(1.1) = 0.826 0.909/(1.1) = 0.826 3 10% 1/(1.1)(1.1)(1.1) = 0.751 0.826/(1.1) = 0.751 4 10% 1/(1.1)(1.1)(1.1)(1.1) = 0.683 0.751/(1.1) = 0.683 2) If Discount Rate for n years are not same PVF 1 = 1/(1+DR 1) PVF 2 = 1/(1+DR 1)*(1+DR 2) PVF 3 = 1/(1+DR 1)*(1+DR 2)*(1+DR 3) Example Different Method 1 Method 2 Year Discount Rate PVF PVF 1 10% 1/(1.1) = 0.909 1/(1.1) = 0.909 2 11% 1/(1.1)(1.11) = 0.819 0.909/(1.11) = 0.819 3 12% 1/(1.1)(1.11)(1.12) = 0.731 0.819/(1.12) = 0.731 4 13% 1/(1.1)(1.11)(1.12)(1.13) = 0.647 0.731/(1.13) = 0.647 CHAPTER-4 BOND VALUATION 4.5 Question-4 Consider a 10% bond having maturity of 4 years and face value of Rs.1000.