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BOND VALUATION-14
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BOND VALUATION 1. INTRODUCTION/WHY BOND VALUATION? Bond valuation is the process of determining the fair price of a bond. As with any security or capital investment, the fair value of a bond is the present value of the Future cash flows it is expected to generate. Bonds or Debentures are long term loan which pay periodical interest and principal amount upon maturity. Determining the value of the bond is an application of the present value concept . 2. BASIC BOND RELATED TERM Value of Bond : The amount which the investor will pay today to purchase the bond.It is also known as Current Value Of Bond / Present Value Of Bond / Intrinsic Value Of Bond / Theoretical Value Of Bond / Equilibrium Value Of Bond Coupon Rate : The annual interest rate on a bond.It is the rate at which company pays interest. Coupon Amount: The amount of interest which is paid by the company . Amount Of Interest = Face Value Of Debenture Coupon Rate Years to Maturity : The year on which the principal amount of a bond is fully repaid is known as years to maturity Note :If the question is silent about the maturity period of any investment say preference shares , bonds , debentures etc then we will assume such investmet as irredeemable or perpetual . Yield: The rate of return required by the investor of a bond.It is also known as Yield To Maturity / Cost Of Debt / Discount Rate for debentureholder / Kd / Going Rate Of Interest /Market Interest Rate Face Value : It is also called Par Value.Interest is paid on face value.Unless otherwise stated bond is assumed to be issued at Face Value or Par Value . The par value or face value may be normally assumed to be Rs. 100 or Rs.1000 depending upon the question . Redemption Value/Maturity Value : The value which the bondholder will get on maturity is called Redemption Value.If silent bond are always assumed to be redeemed at face value . 3. VALUE OF STRAIGHT COUPON BOND OR CLASSASS EQUAL COUPON BOND AADITYA JAIN SATELLITE SFM Meaning : Straight Coupon Bonds or Equal Coupon Bonds are those bonds which pay equal amount of interest upto maturity and also repay principal amount at the end of maturity period . Symbolically
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Value of Bond (B0 )
BOND VALUATION-15
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Interest Interest Interest Face Value or Maturity Value .................. 1 2 n (1 Yield) (1 Yield) (1 Yield) (1 Yield) n
= Interest x PVAF ( Yield %, n years) + Maturity Value x PVF ( Yield %, n years) Where n = Number of Years to Maturity 4. VALUE OF ZERO COUPON BOND OR DEEP DISCOUNT BOND Meaning :Zero Coupon Bonds are those bonds on which investors are not allowed to any interest but are entitled only to repayment of principal sum on the maturity period . Symbolically : Value of Bond (B 0 ) =
Face Value or Maturity Value (1 Yield) n
5. VALUE OF PERPETUAL BOND OR IRREDEEMABLE BOND Meaning : These are bonds where interest payment is paid forever i.e upto infinity. Symbolically : Value Of Bond (B0 )
Annual Interest Yield
6. VALUE OF SEMI ANNUAL INTEREST BOND Meaning : Semi Annual Interest Bonds are those bonds which pay interest semiannually . To value such bonds we have to make three changes : 1.
Annual Interest Amount 2
2.
Years To Maturity 2
3.
Yield 2
7. VALUE OF QUARTERLY COUPON INTEREST BOND 1.
Annual Interest Amount 4
2.
Years To Maturity 4
3.
Yield 4
8. VALUE OF MONTHLY COUPON INTEREST BOND 1.
Annual Interest Amount 12
2.
Years To Maturity 12
3.
Yield 12
9.VALUE OF BOND WITH FLUCTUATING COUPON RATE Sometimes bonds are issued with Fluctuating Coupon Rate.It means that coupon rate may change from one year to another as per the terms of the contract or as per given in question. 10. OVERPRICED AND UNDERPRICED BONDS When Current MarketAADITYA Price and Theoretical Market Price i.e price which we calculate by applying present JAIN SATELLITE SFM CLASSASS value concept are not same we will undertake following decision : Case Valuation Decision If Currenty Market Price > Present Value Market Price Overvalued Sell If Currenty Market Price < Present Value Market Price Undervalued Buy
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BOND VALUATION-16
If Currenty Market Price = Present Value Market Price Correctly Valued
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Hold
11. SELF AMORTIZING BONDS Bonds which pay a principal amount over a period of time rather than on maturity are called Self Amortizing Bonds 12.CALLABLE BOND A Callable Bond is one when the company has an option to retire or redeem the bonds prior to the date of maturity. 13.CALL PRICE The amount of money the issuer has to pay to call a Callable Bond is known as Call Price . 14.CALL DATE The date on which bonds is called by the company prior to the date of maturity is called Call Date . 15.PUTTABLE BOND A Puttable Bond is one where the investor has an option to get the bond redeemed prior to the date of maturity 16.PUT DATE The date on which bonds is sold by the investor prior to the date of maturity is called Put Date . 17.PUT PRICE The amount of money the investor receive by selling a Bond to the company prior to the date of maturity is known as Put Price . YIELD There are number of ways to express yield which are : (i) Coupon Yield / Normal Yield (ii) Current Yield / Flat Yield (iii) Yield to Maturity / Redemption Yield / Kd / Cost Of Debt / Market Interest Rate (iv) Yield To Call ( YTC) (v) Yield To Put ( YTP) (vi)Yield To Worst (YTW) (vii) Holding Period Return (HPR) (viii) Kd Of Perpetual Bond (ix) Capiatl Gain Yield Note : If Current Market Price and Intrinsic/Fair Value are different we will take Current Market Price and not Intrinsic Value ( Present Value) for all the calculation of yield .
AADITYA JAIN SATELLITE SFM CLASSASS 18. NORMAL YIELD / COUPON YIELD : When Yield of any bond is equal to Coupon Rate such yield is known as Normal Yield / Coupon Yield . It is possible when the bond is purchased at par value and redeemable also at par value .
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BOND VALUATION-17
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19. CURRENT YIELD / FLAT YIELD /CURRENT INTEREST YIELD/ BASIC YIELD : Current Yield =
I1 BO
I1 = Interest To Be Paid at Year End 1 Note : Current Yield is always calculated on per annum basis . 20. YIELD ( K d ) OR YIELD TO MATURITY (YTM) OR COST OF DEBT /REDEMPTION YIELD / INTERNAL RATE OF RETURN/MARKET RATE OF INTEREST/ MARKET RATE OF RETURN / PROMISED YTM / OPPORTUNITY COST OF DEBT Yield to Maturity is the overall return on the bond if it is held till maturity . Symbolically : It can be calculated by using two method : Trial n Error Method : Value of Bond (B0 )
Interest Interest Interest Face Value or Maturity Value .................. 1 2 n (1 Yield) (1 Yield) (1 Yield) (1 Yield) n
Now for finding Yield we should use IRR Technique : Lower Rate NPV
Kd = Lower Rate + Lower Rate NPV – Higher Rate NPV Difference in Rates Approximation Method : Maturity Value – Issue Value Interest n Kd Maturity Value Issue Value 2
21. YIELD TO CALL ( YTC ) :
Call Value – Bo Interest Call Years YTC Call Value Bo 2 22. YIELD TO PUT ( YTP ) :
Put Value – Bo Interest Put Years YTP Put Value Bo 2 23. YIELD TO WORST (YTW) : AADITYA JAIN SATELLITE SFM CLASSASS The yield to worst is the lowest yield of yield to maturity, yield to call, yield to put, and others. Example : Given the following data calculate Yield To Worst:YTM = 10%,YTC = 7%,YTP=9% Solution:YTW = 7 %
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BOND VALUATION-18
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24. HOLDING PERIOD RETURN (HPR): Holding Period Return (R) or Total Return =
I1 (B1 B 0 ) I1 (B1 B0 ) or or Current Interest Yield + Capital Gain Yield B0 B0 B0
Where B o is the Price of bond as on today , and B1 is the price of the bond at the end of the holding period or Sale Price of Bond at the end of holding period . Note : The holding period is generally assumed to be of one year period unless otherwise stated . 25.CAPITAL GAIN YIELD Capital Gain Yield =
(B1 B0 ) 100 B0
26. KD OF PERPETUAL BOND Yield or Kd
Annual Interest Bo
27. CALCULATION OF YTM OF HALF YEARLY INTEREST PAYMENT BOND Maturity Value – Issue Value Interest per 6 months nx2 Kd Of 6month Maturity Value Issue Value 2
Now Kd p.a = Kd for 6 month x 2 28. RELATIONSHIP BETWEEN YTM AND COUPON RATE Case Nature Of Bond Coupon Rate = YTM Par Value Bond i.e MP = Par Value Coupon Rate > YTM Premium Bond i.e MP > Par Value Coupon Rate < YTM Discount Bond i.e MP < Par Value Note : For the above relationship to be true the maturity value of the bond must be equal to face value . 29. RELATIONSHIP BETWEEN BOND VALUE AND YTM YTM and the Bond Value has inverse relationship : - If YTM increases the price or bond value will decrease - If YTM decreases the price or bond value will increase ......Other things remaining constantJAIN SATELLITE SFM CLASSASS AADITYA In other words An inverse relationship exists between bond prices and interest rates. Think of it as a seesaw relationship where one goes up whenever the other goes down and vice versa.
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BOND VALUATION-19
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30. RELATIONSHIP BETWEEN BOND VALUE & TIME TO MATURITY The value of the bond approaches its par value as the time to maturity approaches its maturity date other things remaining the same. As the maturity approaches a Premium Bond will decrease in value As the maturity approaches a Discount Bond will increase in value As the maturity approaches a Par Value Bond will remain same in value For the above relationship to be true the maturity value of bond must be equal to Face Value. 31.APPLICATION OF FLOTATION COST Flotation costs are the cost which are associated with issue of new debentures like underwriting , brokerage etc . If Flotation cost is given we simply take Bond Value Net of Flotation Cost .
Equation :
Maturity Value – B0 [1 - f ] Interest n Kd Maturity Value B 0 [ 1 - f ] 2
Where "f" is the flotation cost expressed in percentage . Flotation Cost may also be expressed in absolute amount in such case we will simply deduct flotation cost by bond value i.e B 0 -f 32.TAXATION EFFECT ON INTEREST INCOME If income tax rate is given in question then Interest should be taken after tax . 33.TAXATION EFFECT ON CAPITAL GAIN INCOME If Capital Gain Tax Rate is given then Maturity Value should be taken after tax i.e after adjusting it for Capital Gain Tax .Where Maturity Value Net Of Capital Gain Tax =Maturity Value - Capital Gain Tax = Maturity Value - Tax Rate[ Maturity Value -Issue Price ] Equation: Maturity Value Net Of Capital Gain Tax – Issue Value Interest(1 - Tax) n Kd Maturity Value Net Of Capital Gain Tax Issue Value 2
Note : If Capital Gain Tax is not given in question it is assumed to be Nil . 34. VALUE OF IRREDEMABLE PREFERENCE SHARES Value Of Irredemable Preference Shares =
Annual Dividend Kp
AADITYA JAIN SATELLITE SFM CLASSASS 35. COST OF REDEEMABLE PREFERENCE SHARES
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BOND VALUATION-20
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Maturity Value – PSC 0 Dividend n Kp Maturity Value PSC 0 2
36. COST OF IRREDEEMABLE PREFERENCE SHARES Kp =
Annual Dividend PSC O
Sometimes when relevant information is not given for calculation of Kp then we simply use : Kp = Rate Of Preference Dividend 37.FAIR VALUE OF CONVERTIBLE BONDS/STOCK VALUE OF BOND Convertible Bonds are bond that can be converted into number of equity shares after some time. Fair Conversion Value or Stock Vaue Of Bond = Number Of Equity Shares Received on Conversion x Market Price Per Share prevailing at the time of conversion Decision:If Convertible Bond is greater than Basic Bond Value Of Debenture,investor will convert otherwise not. 38. PERCENTAGE OF DOWNSIDE RISK Percentage of Downside Risk = Market Value Of Convertible Bond - Market Value Of Non-Convertible Bond or Straight Debt Value It should be further divided by Market Value Of Non-Convertible Bond to calculate answer in %. 39. CONVERSION PREMIUM Conversion Premium or Premium Over Conversion Value = Market Price Of Convertible Bond-Fair Value Of Convertible Bond. It should be further divided by Fair Value Of Convertible Bond to calculate answer in %. 40.CONVERSION RATIO Conversion Ratio directly specifies the number of shares we get per convertible bond. 41. EX-INTEREST & CUM INTEREST When Bond Value include the amount of Interest ,it is known as Cum-Interest,otherwise not. In all the Bond Equation Formula,Bond Value should be taken Ex-Interest.If Bond Value is given CumInterest then it should be first taken as Ex-Interest then we should proceed our calculation.
AADITYA JAIN REGARDING SATELLITECOUPON SFM CLASSASS 42. CONFUSION RATE & YTM Coupon Rate is the rate .at which company pays interest. YTM or Yield is the rate of return required by the investor of a bond. Note:It may be noted that any change in interest rate will only change yield and not coupon rate.In other
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BOND VALUATION-21
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words Coupon rate always remain constant unless otherwise specifically stated. 43. BASIS POINT 1 % = 100 basic points 44. BOND INDENTURES Bond Indenture is a written agreement or contract between the company and the bond holder.It provides the specific terms of the bond agreement such as the rights and responsibilities of both parties. 45. RETURN CALCULATION WHEN BONDS ARE PURCHASED & SOLD WITHIN A TIME FRAME Students are required to solve a practical question on this conccept. 46. REQUIREMENT OF CREDIT RATING Most Bond/Debenture issues are rated by specialised credit rating agencies. Credit rating agencies in India are CRISIL, CARE, ICRA and Fitch. A credit rating estimates the credit worthiness of an individual, corporation, or even a country It measures the probability of the timely repayment of principal and interest of a bond. For Example : AAA”Highest Credit Quality”AA”Superior Credit Quality”A”Satisfactory Credit Quality 47. CALCULATION OF PRICE & YIELD OF TAX FREE BOND TO REMAIN INDIFFERENT WITH TAXABLE BOND CALCULATION OF YIELD OF TAX FREE BOND : In this case yield of tax free bond must be equal to yield of taxable bond. CALCULATION OF PRICE OF TAX FREE BOND : Now price of Tax Free Bond can be calculated with the help of yield of tax free bond calculated above. 48. CONVERSION PARITY PRICE Conversion Parity Price =
Market Price Of Convertibl e Bond No.of Shares on Conversion
49.FLOOR VALUE The minimum of the two will be termed as Floor Value Value Of Convertible Bond & Value of Non-Convertible Bond i.e Straight Value Of Bond 50. FLOATING RATE NOTES (FRNS) Floating rate notes (FRNs) are those bonds on which Interest Rate changes according to market conditions.In other words under such Bond Kd & Coupon Rate will be same
AADITYA JAIN SATELLITE SFM CLASSASS
51. IMMUNIZATION Immunization means protecting a bond portfolio from damage due to fluctuations in market interest rates How we can achieve Immunization : This can be attained by selecting the bonds whose duration is equal
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BOND VALUATION-22
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to the investment horizon or Imunization Period. A portfolio is immunized when it is “unaffected” by interest rate changes. 52. BOND STRIPS Bond Strips = Interest Strips + Principal Strips Value of a Bond is the sum of present value of two distinct cash flows streams viz Present Value Of Interest called the Interest Strips and Present Value of Principal repaid on maturity called the Principal Strip . Example :Nominal Value of 12% bonds issued by a company is Rs.100.The bonds are redeemable at Rs.125 at the end of year 5.Coupons are paid annually.Determine value of interest strip & principal strip.Annual Yield rate is 10%. Solution: Interest Strip = 12 x PVAF (10%,5 Years) = 12 x 3.791 = 45.49 Principal Strip = 125 x PVF (10%,5Years) = 125 x .621 = 77.63 53. DURATION OF NORMAL BOND OR FREDRIC MACAULAY 'S DURATION Symbolically : Duration Of Bond
1
Interest
Interest
Interest
= B 1 (1 Kd)1 2 (1 Kd) 2 ............n (1 Kd) n n o
Maturity Value (1 Kd) n
54. DURATION OF A ZERO COUPON BOND : For a zero coupon bond , the duration is simply equal to the maturity of the bond while the duration of a normal coupon bond is less than the maturity. 55. DURATION OF PERPETUAL BOND Duration Of Perpetual Bond =:
1 YTM YTM
56. VOLATILITY /SENSITIVITY/MODIFIED DURATION : Meaning : Modified Duration is a measure of volatility.In other words , Modified Duration is a measure of % change in bond value for every 1 % change in Yield to Maturity or Market Interest Rate . Symbolically :Volatility or Modified Duration or Sensitivity [ % ] =
Duration Of Bond Yield To Maturity
Note : % Change in Bond Price = Modified Duration Change In Yield To Maturity The Modified Duration will always be lower than the Macaulay Duration
AADITYA JAIN SATELLITE SFM 57.RELATIONSHIP BETWEEN DURATION OFCLASSASS BOND AND MATURITY Duration Of Bond due for maturity is zero. In other words duration gradually comes down to zero with the approach of maturity. In other words we can say Shorter the Maturity , Lesser is the Duration
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BOND VALUATION-23
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58.RELATIONSHIP BETWEEN DURATION AND YTM The duration of a bond and YTM are inversely related. The higher the YTM , the lower is the duration . The lower the YTM , the higher is the duration other things remaining constant . 59.RELATIONSHIP BETWEEN DURATION AND COUPON RATE The duration of a bond and Coupon Rate are inversely related. The higher the Coupon Rate , the lower is the duration . The lower the Coupon Rate , the higher is the duration other things remaining constant . 60.% INCREASE & DECREASE IN PRINCIPAL & INTEREST AMOUNT DUE TO CHANGE IN YIELD PLZ REFER CLASS REGISTER FOR THIS CONCEPT 61.VALUE OF BOND AT THE END OF EACH YEAR PLZ REFER CLASS REGISTER OR SOLUTION BOOK FOR THIS CONCEPT 62.GAIN & LOSS DUE TO CHANGE IN BOND VALLUE Bo At Old Yield xxx Bo At New Yield xxx Gain Or Loss Due To Change In Yield xxx 63.CALCULATION OF EPS BEFORE & AFTER CONVERSION OF PREFERENCE SHARE CAPITALTO EQUITY SHARE CAPITAL PLZ REFER CLASS REGISTER FOR THIS CONCEPT 64.CONVERSION RATIO IN RESPECT OF CONVERTIBLE PREFERENCE SHARE CAPITAL Conversion Ratio directly specifies the number of shares we get per convertible Preference Share Capital . 65.FAIR CONVERSION VALUE IN RESPECT OF CONVERTIBLE PREFERENCE SHARE CAPITAL OR PREFERENCE SHARE CONVERSION VALUE Fair Conversion Value = Number Of equity Shares Received on Conversion x Market Price Per Share prevailing at the time of conversion 66. CONVERSION PREMIUM IN RESPECT OF CONVERTIBLE PREFERENCE SHARE CAPITAL Conversion Premium or Premium Over Conversion Value AADITYA JAIN SATELLITE SFM CLASSASS = Market Price Of Convertible Preference Share Capital-Fair Value Of Preference Share Capital It should be further divided by Fair Value Of Preference Share Capital to calculate answer in %. 67. MARKET VALUE OF CONVERTIBLE BOND
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BOND VALUATION-24
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Market Value Of Convertible Bond(assuming Conversion at year end 5)
Interest Interest Interest Interest Interest CV5 1 2 3 4 5 (1 Kd) (1 Kd) (1 Kd) (1 Kd) (1 Kd) (1 Kd) 5
Where,CV5 = Conversion Value Of Year End 5 = MPS at Year End 5 x No. Of Equity Shares 68. CALCULATION OF YIELD WHEN COUPON PAYMENTS ARE NOT AVAILABLE FOR REINVESTMENT In such case our equation is : B0
Coupon Rate x n Face Value (1 YTM) n
SUMMARIZED NOTES IS PREPARED BY SIR FOR HELPING STUDENTS FOR LAST TIME REVISION JUST BEFORE EXAM OR STUDENTS WHO WANT TO HAVE A QUICK REVISION OF ALL THE CONCEPT IN SHORT PERIOD OF TIME.WE WILL APPRECIATE YOUR FEEDBACK REGARDING THIS SUMMAAADITYA JAIN SATELLITE SFM CLASSASS RIZED NOTES WHETHER YOU LIKED IT OR NOT AT :
[email protected];SMS-8285042929 DONT HESITATE TO EXPRESS......IT WILL HELP US TO PREPARE SUCH NOTES IN OTHER SUBJECTS TOO.
