Chapter 6 Chapter 6

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24 Q. No. 32: The following are the details about a 6% bond: Market price: par Maturity 10 years. Face value = 1000 Find the duration of the bond. Find the convexity of the bond. Suppose the YTM rises to 7%, find the value of the bond (i) using duration (ii) using convexity (iii) without using duration or convexity. Comment on the results. Answer: X W XW XW(1+X) 1 60 x 0.943 =56.58 56.58 113.16 2 60 x 0.890 = 53.40 106.80 320.40 3 60 x 0.840 = 50.4 151.20 604.80 4 60 x 0.792 =47.52 190.08 950.40 5 60 x 0.747 = 44.82 224.10 1344.60 6 60 x 0.705 = 42.3 253.80 1776.60 7 60 x 0.665 = 39.9 279.30 2234.40 8 60 x 0.627 = 37.62 300.96 2708.64 9 60 x 0.592 = 35.52 319.68 3196.80 10 1060 x 0.558 = 591.48 5914.80 65062.80 Total 999.54* 7797.30 79312.60 *It should have been 1000.The difference is due to calculation approximations. • Duration = 7797.30/999.54 = 7.80 Modified duration = 7.80/1.06 = 7.3585. If YTM rises to 7%, the bond value decreases by 7.3585%. New bond value = 926.42 • Convexity = 79312.60/999.54 = 79.35 % change in Bond price : % Change in the price of the bond if YTM increases from 6% to 7%:
25 = [(-1 )(Modified Duration)(Yield change in terms of percentage points)} + [(C/200) (Yield Chg in terms of percentage points) 2 ] = [{(-1)( 7.3585)(1)} + {(79.35)/200)(1)}] = 6.96% New Price of Bond = 1000 – 69.60 = 930.40 • Present value of cash flow method : New price of bond (YTM 7%) = 60(7.024) + 1000 x 0.508 = 929.44 % Error by duration method = (926.42 – 929.44) / 929.44 = 0.325% % Error by convexity method = (930.40 – 929.44) / 929.44 = 0.103% Comment : The new price of bond ( calculated on the basis of changed YTM) is more accurate when calculated by convexity (rather than by duration) CONVERTIBLE BONDS These are the bonds which have / can to be converted into specified number of equity shares of the company issuing these bonds within a specified period. In India most of the convertible bonds have been issued on the basis of compulsory conversion i.e. the bonds are compulsorily convertible into number of specified number of shares, there is no discretion of the bond holder. In USA and European countries, convertible bonds are option convertible bonds i.e. conversion takes place if the bond holder so desire, An Example of option convertible bond: Suppose a company issues 7% convertible bonds of $100 each, maturity 7 years, redemption at par. The bondholder can get his bond converted into 4 equity shares after 2 years of issuance. Now whether the bond will be converted into equity shares or not, it is at the discretion of the bond holder. Suppose he gets the bonds converted into shares, the company’s liability towards principal and interest will extinguish. If he does not get the bond converted, he will be emitted to receive interest periodically and on maturity he will get the redemption amount of $100. The convertibility option lowers the interest rate that the issuer would otherwise have to pay without this feature, and it appeals to investors who want current income, but would like to take advantage of any growth in the issuer company. Let’s understand a few terms related to convertible debentures: (i) The number of shares that each bond can be converted to is known as the conversion ratio. (ii) Conversion price is the exercise price at which the investor converts his bond into equity shares. It is obtained by dividing the par value of the bond by the conversion ratio.
Page 1 and 2: J B GUPTA CLASSES 98184931932, drja
Page 3 and 4: 3 Q. No. 3 : A company has outstand
Page 5 and 6: 5 • Present value of Rs.1,000 to
Page 7 and 8: 7 The current market rate on simila
Page 9 and 10: 9 Duration is the weighted average
Page 11 and 12: 11 Q. No. 19 : Find the current mar
Page 13 and 14: 13 (Rs.1,000) Bond B (Rs.1,000) Pre
Page 15 and 16: 15 EXPECTATION THEORY: As per this
Page 17 and 18: 17 Suppose you are interested in pu
Page 19 and 20: 19 Limitations of Modified Duration
Page 21 and 22: 21 Convexity is a better technique
Page 23: 23 YTM (%) Bond value As per PV met
Page 27 and 28: 27 Answer (i) Stock value of bond =
Page 29 and 30: 29 Duration = ∑XW / ∑W = 34,064
Page 31 and 32: 31 Q. No. 37: An 18-years maturity
Page 33 and 34: 33 To achieve the target return, he
Page 35 and 36: 35 (c) Assuming that total earnings
Page 37 and 38: 37 Interest rate for 3 months = 27/
Page 39 and 40: 39 be issued at the third year. The
Page 41 and 42: 41 Q. 48 A 10 years maturity bond r
Page 43 and 44: 43 [1% change in YMT causes 1.81% c
Page 45 and 46: 45 The present value of bond princi
Page 47 and 48: 47 payable annually. The next inter
Page 49 and 50: 49 (a) Let YTM = r 260(1+r) 8 = 100

Chapter 6 Chapter 6

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