ISS RATHORE INSTITUTE. Strategic Financial Management

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1 1 ISS RATHORE INSTITUTE Strategic Financial Management Solution Booklet By CA. Gaurav Jain 100% Conceptual Coverage Not a Crash Course More than 400 Questions covered in Just 30 Classes Complete Coverage of Study Material, Practice Manual & Previous year Exam Questions All Classes at: 1/50 iss Building, Lalita Park, Laxmi Nagar, New Delhi -92 Contact Details: ; Web Site:

2 2 ISS RATHORE INSTITUTE CA FINAL Batches for Nov % Coverage Not a Crash Course STRATEGIC FINANCIAL MANAGEMENT (SFM) By CA Gaurav Jain [FCA, CFA L1, NCFM, NISM] More than 300 Concepts & 400 Questions covered in Just 30 classes including Theory Batch Start Date Days End Date Timing Evening 28 th May Mon to Fri 06 th July 5:00 to 8:30 PM Morning 18 th June Mon to Sat 21 st July 7:00 to 10:30 AM Morning 23 rd July Mon to Sat 25 th Aug 7:00 to 10:30 AM Evening 20 th Aug Mon to Sat 22 nd Sept 5:00 to 8:30 PM * 2 Free Trial Classes Fee for Full Course Rs. 6,000/- Only

3 3 BOND VALUATION Lists of Concepts Concept No. 1: Introduction (Fixed Income Security) Concept No. 2: Terms used in Bond Valuation Concept No. 3: Valuation of Straight Bond/ Steps in the Bond Valuation Process Concept No. 4: Coupon Rate Structures Concept No. 5: Valuation of Perpectual Bond/ Irredeemable Bond/ Non Callable Bond Concept No. 6: Valuation of Zero-Coupon Bond Concept No. 7: Valuation of Semi annual Coupon Bonds Concept No. 8: Valuation of Bond with Changing Coupon Rate Concept No. 9: Over Valued & Under Valued Bonds Concept No. 10: Self Amortization Bond Concept No. 11: Holding Period Return (HPR) for Bonds Concept No. 12: Calculation of Current Yield Concept No. 13: Normal Yield or Coupon Yield Concept No. 14: YTM (Yield to Maturity) / Kd / Cost of debt/ Market rate of Interest/ Market rate of return Concept No. 15: YTM (Yield to Maturity) / Kd of Half yearly Bond Concept No. 16: Treatment of Floating Cost Concept No. 17: Treatment of Tax Concept No. 18: Yield to call (YTC) & Yield to Put (YTP)

4 4 Concept No. 19: Yield to worst Concept No. 20: YTM of a perpetual Bond / Irredeemable Bond Concept No. 21: Cost of Redeemable Preference Share Concept No. 22: Cost of Irredeemable Preference Share Concept No. 23: Value of a non-callable, Non-convertible Preferred Stock Concept No. 24: Confusion regarding Coupon Rate & YTM Concept No. 25: Fair Value of Convertible Bond Concept No. 26: Credit Rating Requirement Concept No. 27: Cum Interest &Ex-interest Bond Value Concept No. 28: Strips (Separate Trading of Registered Interest & Principal Securities) Program Concept No. 29: Relationship between Coupon Rate & YTM Concept No. 30: Relationship between Bond Value & YTM Concept No. 31: Value of the Bond at the end of each Year Concept No. 32: Relationship between Bond Value & Maturity Concept No. 33: Floating Rate Bonds Concept No. 34: Duration of a Bond (Macaulay Duration) Concept No. 35: Duration of a Zero - Coupon Bond Concept No. 36: Relationship between Duration of Bond & YTM Concept No. 37: Calculation of yield when Coupon Payment is not available for Re-Investment Concept No. 38: Modified Duration/ Sensitivity/ Volatility Concept No. 39: Duration of a Portfolio Concept No. 40: Return Calculation

5 5 Concept No. 41: Downside Risk, Conversion Premium, Conversion Parity Price Concept No. 42: Callable Bond Concept No. 43: Overlapping Interest Concept No. 44: Bond issued under an open ended scheme Concept No. 45: Bond Purchased between two coupon dates Concept No. 46: Spot Rate Concept No. 47: Relationship between Forward Rate and Spot Rate Concept No. 48: Calculation of After-tax yield of a taxable security & taxequivalent yield of a tax-exempt security Concept No. 49: Re Investment Income

6 6 Concept No. 1: Introduction (Fixed Income Security) Bonds are the type of long term obligation which pay periodic interest & repay the principal amount on maturity. Purpose of Bond s indenture & describe affirmative and negative covenants The contract that specifies all the rights and obligations of the issuer and the owners of a fixed income security is called the Bond indenture. These contract provisions are known as covenants and include both negative covenants (prohibitions on the borrower) and affirmative covenants (actions that the borrower promises to perform) sections. 1. Negative Covenants : This Includes a) Restriction on asset sales (the company can t sell assets that have been pledged as collateral). b) Negative pledge of collateral (the company can t claim that the same assets back several debt issues simultaneously). c) Restriction on additional borrowings (the company can t borrow additional money unless certain financial conditions are met). 2. Affirmative Covenants: This Includes a) Maintenance of certain financial ratios. b) Timely payment of principal and interest. Common Options embedded in a bond Issue, Options benefit the issuer or the Bondholder Security owner options: a) Conversion option b) Put provision c) Floors set a minimum on the coupon rate Security issuer option: a) Call provisions b) Prepayment options c) Caps set a maximum on the coupon rate Concept No. 2: Terms used in Bond Valuation (i) Face Value Rs (ii) Maturity Year 10 years (iii) Coupon rate 10%

7 7 Coupon Rate is used to calculate Interest Amount. Face Value is always used to calculate Interest Amount. (iv) Coupon Amount 1000 X 10% = Rs. 100 p.a. (v) B 0 / Value of the Bond as on Today/ Rs. 950 Current Market Price/Issue Price (vi) Yield to Maturity/ Kd / Discount Rate/ 12% Required return of investor/ Cost of debt/ Expected Return/ Opportunity Cost (vii) Redemption Value/ Maturity Value Rs Note: If Maturity Value is not given, then it is assumed to be equal to Face Value. If Face Value is not given, then it is assumed to be Rs. 100 or Rs according to the Question. If Maturity Year is not given, then it is assumed to be equal to infinity. Concept No. 3: Valuation of Straight Bond/ Steps in the Bond Valuation Process Straight Coupon Bonds are those bonds which pay equal amount of interest and repay principal amount on Maturity. Step 1: Estimates the cash flows over the Life of the bond. Two type of Cash Flows:- a) Coupon Payments b) Return of Principal Step 2: Determine the appropriate discount rate. Step 3: Calculate the present value of the estimated cash flow using appropriate discount rate. B 0 = () + () () + () Or Interest PVAF (Yield %, n year) + Maturity Value PVF (Yield %, nth year) n = No. of years to Maturity QUESTION NO. 1 (SFM Study Material) A Rs. 1,000 par value bond bearing a coupon rate of 14 per cent matures after 5 years, the required rate of return on this bond is 13 per cent. Calculate the value of the bond.

8 8 Concept No. 4: Coupon Rate Structures 1. Zero Coupon Bond (Pure Discount Securities) a) They do not pay periodic interest. b) They pay the Par value at maturity and the interest results from the fact that Zero Coupon Bonds are initially sold at a price below Par Value. (i.e. They are sold at a significant discount to Par Value). 2. Step up Notes a) They have coupon rates that increase over time at a specified rate. b) The increase may take place one or more times during the life cycle of the issue. 3. Deferred Coupon Bonds a) They carry coupons, but the initial coupon payments are deferred for some period. b) The coupon payments accrue, at a compound rate, over the deferral period and are paid as a lump sum at the end of that period. c) After the initial deferment period has passed, these bonds pay regular coupon interest for the rest of the life of the issue (to maturity). 4. Floating Rate Securities a) These are bond for which coupon interest payments over the life of security vary based on a specified reference rate. b) Reference Rate may be LIBOR [London Interbank Offered Rate] or EURIBOR or any other rate and then adds or subtracts a stated margin to or from that reference rate. New coupon rate = Reference rate ± quoted margin 5. Inflation indexed Bond (TIPS) a) They have coupon formulas based on inflation. E.g.: Coupon rate = 3% + annual change in CPI Concept No. 5: Valuation of Perpectual Bond/ Irredeemable Bond/ Non Callable Bond They are infinite bond, never redeemable, non- callable bond. Kd= Cost of debt /Yield to Maturity Value of Bond = / QUESTION NO. 2A (SFM Study Material) A bond pays Rs. 90 interest annually upto perpetuity, (i) What is its value if the current yield is 10 %? (ii) If the current yield changes to 8% and 12%, then what it its value? QUESTION NO. 2B (CA. Final May 2000) John inherited the following securities on his uncle's death: Type of Security Nos. Annual Coupon Maturity Years Yield

9 9 Bond A (Rs. 1,000) 10 9% 3 12 Bond B (Rs. 1,000) Preference Shares C (Rs. 100) % 11% 5 * 12 13* Preference Shares D (Rs. 100) % * 13* Compute the current value of his uncle's portfolio. Concept No. 6: Valuation of Zero-Coupon Bond Zero- coupon Bond has only a single payment at maturity. Value of Zero- Coupon Bond is simply the PV of the Par or Face Value. Kd= Discount rate/ Yield to Maturity n = No. Of years Bond value = ( ) Example: Valuing a Zero-coupon bond Compute the value of a 10-year, Rs face value zero-coupon bond with yield to maturity of 8%. Solution: To find the value of this bond given its yield to maturity of 8%, We can calculate: Bond value = (.) = (.) =Rs QUESTION NO. 3A Suppose we are considering investing in a zero-coupon bond that matures in 5 years and has a face value of Rs If these bonds are priced to yield 10%, what is the present value of the bonds? QUESTION NO. 3B (RTP) On 1 June 2003 the financial manager of Gadgets Corporation's Pension Fund Trust is reviewing strategy regarding the fund. Over 60% of the fund is invested in fixed rate long-term bonds. Interest rates are expected to be quite volatile for the next few years. Among the pension fund's current investments are two AAA rated bonds: 1. Zero coupon June % Gilt June 2018 (interest is payable semi-annually) The current annual redemption yield (yield to maturity) on both bonds is 6%. The semi-annual yield may be assumed to be 3%. Both bonds have a par value and redemption value of $ 100. Required: Estimate the market price of each of the bonds if interest rates (yields):(i) increase by 1 %; (ii) decrease by 1 %. [Given PVF (2.5%, 30) = , PVF (3%, 30) = 0.412, PVF (3.5%, 30) = ] Concept No. 7: Valuation of Semi annual Coupon Bonds Pay interest every six months

10 10 a) b). c) n 2 YTM always given annually unless/otherwise specified in the question. Note: If quarterly use 4 instead of 2 If monthly use 12 instead of 2 QUESTION NO. 4A (Study Material) A 6 years bond of Rs. 1,000 has an annual rate of interest of 14 %. The interest is paid half yearly. If the required rate of return is 16 % what is the value of bond? QUESTION NO. 4B (RTP) Bond face Value: 1000; Issue Value = 900; Interest paid half yearly; Coupon Rate=10%; Life= 5 years. Calculate YTM? QUESTION NO. 4C (CA Final SFM, Nov 2010) A bond with 7.5% coupon interest, Face Value Rs. 10,000 & term to maturity of 2 years, presently yields 6% Interest payable half yearly. Calculate Market Price. Concept No. 8: Valuation of Bond with Changing Coupon Rate Coupon rate changes from one year to another year as per the terms of bond-indenture. QUESTION NO. 5 (CA. Final Nov. 2003) (CS Final Dec 2004, 10 Marks) The Elu Co. is contemplating a debenture issue on the following terms: Face Value = Rs. 100 per debenture Term to maturity =7 years Coupon rate of interest: Years 1-2 8%p.a %p.a %p.a. The current market rate of interest on similar debentures is 15% per annum. The company proposes to price the issue so as to yield a (compounded) return of 16% per annum to the investor. Determine the issue price. Assume redemption at a premium of 5% on face value. Note: Present value interest 16% p.a. Period Factor Concept No. 9: Over Valued & Under Valued Bonds Case Value Decision

11 11 PV of MP of Bond < Actual MP of Bond Over Valued Sell PV of MP of Bond > Actual MP of Bond Under Valued Buy PV of MP of Bond = Actual MP of Bond Correctly Valued Either Buy/ Sell QUESTION NO. 6 Namita owns Rs.1000 face value bond with five years to maturity. The bond has an annual coupon of Rs.75. The bond is currently priced at Rs.970.Given an appropriate discount rate of 10 % should Namita hold or sell the bond? Concept No. 10: Self Amortization Bond They make periodic interest and principal payments over the life of the bond. i.e. at regular interval. QUESTION NO. 7 (SFM Study Material) A PSU is proposing to sell 8 years bond of Rs at 10% coupon rate per annum Bond amount will be amortized equally over its life. If an investor has a minimum required rate of return of 8%, what is the bond's present value? Concept No. 11: Holding Period Return (HPR) for Bonds HPR = = + (Capital gain Yield/ Return) (Interest Yield /Current Yield) Note: HPR are assumed to be per annum basis unless specified in the question. QUESTION NO. 8 (SFM Study Material) A had purchased a bond at a price of Rs. 800 with a coupon payment of Rs.150 and sold it for Rs. 1,000. a. What is the holding period return? b. If bond is sold for Rs.750 after receiving Rs. 150 as coupon payment, then what is his holding period return? Concept No. 12: Calculation of Current Yield Current Yield = Note: Current Yield is always calculated on per annum basis.

12 12 Example: Consider a 20-year, Rs Par value, 6% annual pay bond that is currently trading at Rs Calculate the current yield. Solution: The annual cash coupon payment total: Annual cash coupon payment = par value X stated coupon rate = Rs X 0.06 = Rs. 60 Since the bond is trading at Rs , the current yield is: Current Yield = = , or 7.48%. QUESTION NO. 9 (SFM Study Material) What is the current yield of the 6.5 % August 2005 maturity bond, which has a maturity value of Rs The current bond price is Rs ? Concept No. 13: Normal Yield or Coupon Yield When Coupon Rate = K d / YTM, Such situation is known as Normal Yield or Coupon Yield. This situation is possible only when bond is purchased at Par Value and is also redeemable at Par Value. B 0 = Par Value and Maturity Value = Face Value Note: Basis Point: Sometimes interest is expressed in terms of Basis Point 1% = 100 Basis Points Concept No. 14: YTM (Yield to Maturity) / K d / Cost of debt/ Market rate of Interest/ Market rate of return YTM is an annualized overall return on the bond if it is held till maturity. Alternative 1: By IRR technique. B 0 = ( ) + ( ) ( ) + ( ) YTM & price contain the same information If YTM given, calculate Price. If Price given, calculate YTM. YTM = Lower Rate + Difference in Rate Example: Consider a 20year, Rs par value bond, with a 6% coupon rate with a full price of Rs Calculate the YTM. Solution:

13 = ( ) + ( ) K d = % Alternative 2: By approximation formula ( ) + ( ) If existing bond :- YTM = B 0 = Current Market Price of Bond ( Ist preference is given to this) Or Present value Market Price of Bonds. If new bond issued :- B0 = Net Proceeds = Issue Price = Face value Discount + Premium (-) Floating Cost QUESTION NO. 10A Ganesh, wishes to find the YTM on his company's 10-year, 10% bond which is currently selling for 900.Face Value is Calculate the YTM, using (i)the approximation formula.(ii) the trialand-error method. QUESTION NO. 10B (RTP Nov 2009) It is now January 1,2009, and Mr. X is considering the purchase of an outstanding Municipal Corporation bond that was issued on January 1,2007, the Municipal bond has a 9.5 percent annual coupon and a 30-year original maturity. Interest rates have declined since the bond was issued, and the bond now is selling at % of par, or Rs. 1, Determine the yield to maturity (YTM) of this bond for Mr. X. QUESTION NO. 10C (SFM Nov Marks) An investors is considering the purchase of the following Bond: Face value Rs.100 Coupon rate 11% Maturity 3 years (i) If he wants a yield of 13% what is the maximum price he should be ready to pay for? (ii) If the Bond is selling for Rs.97.60, what would be his yield? Concept No. 15: YTM (Yield to Maturity) / K d of Half yearly Bond YTM per 6 months =

14 14 YTM per annum = YTM of 6 month 2 Example: Bond Face Value = 1000 Issue Price = 950 Coupon Rate = 10% Life = 5 years Interest paid Half-yearly Calculate YTM? Solution: YTM per 6 months = = 5.64% YTM per annum = => 11.28% QUESTION NO. 11 A Bond with a face value of Rs. 1000, a 12% coupon payable half yearly is refundable at a premium of 4% 5 years from today. The bond is currently trading at The yield applicable for such bonds is T + 2%, where T = 8%. a) Find the Market Price of the bond? b) What is the current yield? c) What is the YTM on the bond? d) What will be the investment action? Concept No. 16: Treatment of Floating Cost Floating Cost is cost associated with issue of new bonds. e.g. Brokerage, Commission, etc We should take Bond value (B 0 ) Net of Floating Cost. Note: YTM = ( ) () Where (f) is floating cost expressed in percentage. If floating cost is given in absolute amount then simply deduct floating cost from Bond Value i.e. B 0 f. QUESTION NO. 12 Suppose a bond with nominal value of Rs. 100 carries an interest rate of 10 % per year. The bondholder purchase the bond from the market at Rs. 125.The redemption price of the bond is Rs. 140.The bond is due for maturity in 5 years. A flotation cost of Rs. 2 per bond is to be paid on the issue of the bond. Calculate YTM?

15 15 Concept No. 17: Treatment of Tax Tax is important part for our analysis, it must be considered if it is given in question. Two types of Tax rates are given :- 1. Interest Tax rate We should take Interest Net of Tax i.e. Interest Amount (1 Tax) 2. Capital Gain Tax rate Take Maturity value after Capital Gain Tax i.e. Maturity Value Capital Gain Tax Amount Maturity value (Maturity value B0) Capital gain tax rate Formulae: YTM = ( ) QUESTION NO. 13 (CA Final, May 2004) There is a 9%, 5 year bond issue in the market. The issue price is Rs.90 and the redemption price is Rs For an investor with marginal Income tax rate of 30% and capital gains tax of 10% (assuming no indexation), what is the post tax yield to maturity? Concept No. 18: Yield to call (YTC) & Yield to Put (YTP) 1. Yield to Call Callable Bond: When company call its bond or Re-purchase its bond prior to the date of Maturity. Call Price: Price at which Bond will call by the Company. Call Date: Date on which Bond is called by the Company prior to Maturity. n = No. of Years upto Call Date. 2. Yield to Put YTC = Puttable Bond: When investor sell their bonds prior to the date of maturity to the company. Put Price: Price at which Bond will put/ Sell to the Company. Put Date: Date on which Bond is sold by the investor prior to Maturity. n = No. of years upto Put Date. YTP = QUESTION NO. 14

16 16 (i) Nominal value of 10% debentures of a company is Rs The debentures can be called at call price of Rs. 110 after 4 years. Interests are paid annually. Determine Yield To Call (YTC) if current market price of debentures is Rs (ii) Nominal value of 8% debentures of a company is Rs The debentures are Puttable at exercise price Rs. 105 after 5 years. Interests are paid annually. Determine Yield To Put (YTP) if current market price of debentures is Rs Concept No. 19: Yield to worst It is the lowest yield between YTM, YTC, YTP, Yield to first call. Yield to worst is lowest among all. QUESTION NO. 15 Given the following data calculate Yield To Worst: YTM - 10%, YTC = 7%, YTP=9% Concept No. 20: YTM of a perpetual Bond / Irredeemable Bond We know that the value of a perpetual bond (B 0 ) = So, YTM = QUESTION NO. 16 A Rs. 100 perpetual bond is currently selling for Rs.95. The coupon rate of interest is 14.5 per cent and the appropriate discount rate is 16 per cent. Calculate the value of the bond. Should it be bought? What is its yield at maturity? Concept No. 21: Cost of Redeemable Preference Share K p = ( ) ( ) QUESTION NO. 17 Preferential Ltd issued 30,000,15% Preference Shares of Rs. 100 each, redeemable at 10% premium after 20 years. Issue Management Expenses were Rs.30,000.Find out the cost of Preference Capital if they were issued at (i) Par (ii) Premium of 10% (iii) Discount of 10% Concept No. 22: Cost of Irredeemable Preference Share

17 17 QUESTION NO. 18 K p = ( ) Preferred Ltd issued 30,000, 15% Preference Shares of Rs.100 each. The cost of issue was Rs.30,000. Determine the cost of Preference Capital if they were issued at (i) Par (ii) Premium of 10% (iii) Discount of 10% Concept No. 23: Value of a non-callable, Non-convertible Preferred Stock Preferred stock pays a dividend that is usually fixed, and usually has an indefinite maturity. When the dividend is fixed and the stream of dividends is finite, the infinite period dividend discount model reduces to simple ratio: Preferred stock value = Example: A company s Rs. 100 par preferred stock pays a Rs annual dividend and has a required return of 8%. Calculate the value of the preferred stock. Solution: Value of preferred stock = =.. = Rs Concept No. 24: Confusion regarding Coupon Rate & YTM YTM Required Return / Investor s Expectation Coupon Rate Rate of Interest paid by the company. Note 1: YTM is always subjected to change according to Market Conditions. Note 2: Coupon Rate is always constant throughout the life of the bond and it is not affected by change in market condition UNLESS OTHERWISE SPECIFICALLY STATED IN QUESTION. Example: Existing CR = 15% and Existing YTM = 16%, Market Interest Rate is Expected to rise by 50 Basis Point. Calculate Revised CR & YTM. Solution: CR = 15% YTM = = 16.5% QUESTION NO. 19 (CA Final SFM, Nov 2010) Calculate Market Price of: 10% Government of India security currently quoted at Rs. 110, but interest rate is expected to go up by 1 %. Concept No. 25: Fair Value of Convertible Bond

18 18 Converted into equity shares after certain period. When Conversion Value > Bond value, option can be exercised otherwise not. Conversion Value = No. of equity shares issued Market value at the time of Conversion Conversion Ratio = No. of share Received per Convertible Bond QUESTION NO. 20A There is conversion option on an 8% convertible debenture, if unconverted it is redeemable at par in 10 years' time; conversion will be for 20 ordinary shares, the current share price being The current required return on unconvertible debentures with a 10-year maturity is 12%. Find the straight debt value i.e value obtained when securities are not converted and conversion value of this security as on today.should the bond be converted as on today. QUESTION NO. 20B (Supplementary Study Material) (CA Final Nov 2009, 4 Marks) XYZ Ltd. has issued convertible debentures with interest rate of 12%. Every debenture has an option to convert to 20 equity shares at any time until the date of maturity. Debentures will be redeemed at Rs. 100 on maturity which is after 5 years. An investor normally requires a rate of return of 8% p.a. on a five year security. As an investor when will you exercise conversion if the current market price of equity shares is (i) Rs. 4 (ii) Rs. 5 (iii) Rs. 6 Concept No. 26: Credit Rating Requirement As per SEBI regulation, no public or right issue of debt/bond instruments shall be made unless credit rating from credit rating agency has been obtained and disclosed in the offer document. Rating is based on the track record, financial statement, profitability ratios, debt servicing capacity ratios, credit worthiness & risk associated with the company. QUESTION NO. 21 (CA Final Nov 2008, 5Marks) (CA Final Nov 2011,8Marks) Based on the credit rating of bonds Mr. Mohan has decided to apply the following discount rates for valuing bonds: Credit rating Discount rates AAA 364-day T-bill rate + 3% spread AA AAA + 2% spread A AAA + 3% spread He is considering to invest in a AA rated, Rs face value bond currently selling at Rs The bond has five years to maturity and the coupon rate on the bond is 15% p.a. payable annually. The next interest payment is due one year from today and the bond is redeemable at par. (Assume the 364-day T-bill rate to be 9%). 1. You are required to calculate the intrinsic value of the bond for Mr. Mohan. Should he invest in the bond? 2. Calculate the current yield and yield to maturity of the bond.

19 CA. Gaurav Jain Strategic Financial Management 19 Concept No. 27: Cum Interest &Ex-interest Bond Value When Bond value include amount of interest it is known as Cum-Interest Bond Value, other -wise not. If question is Silent, we will always assume ex-interest. Assume value of Bond (B 0 ) as ex interest. If it is given Cum-Interest then deduct Interest and proceeds your calculations. QUESTION NO. 22 C Ltd. has Rs. 500,000 of 7 % debentures outstanding which are redeemable in 8 years' time at par. The current price is Rs. 81 cum interest and the company pays corporation tax at 35 %. Calculate the after-tax cost of this debt finance. Concept No. 28: Strips (Separate Trading of Registered Interest & Principal Securities) Program Under this, Strip the coupons from the principal, repackage the cash flows and sell them separately as Zero Coupon Bonds, at discount. Bond Coupon Strip Principal Strip Value of Bond = ( ) + ( ) ( ) + ( ) Coupon Strips Principal Strips QUESTION NO. 23 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%.

20 20 Concept No. 29: Relationship between Coupon Rate & YTM Bonding Selling At Par Discount Premium Coupon Rate = Yield to Maturity Coupon Rate < Yield to Maturity Coupon Rate > Yield to Maturity QUESTION NO. 24 Calculate value of bond if rate of return is (i) 12 % (ii) 10%, (iii) 14%. Coupon rate = 12%, Bond face value = Rs. 1,000 Redeemable at Par, Maturity 10 years. What conclusion can you draw? Concept No. 30: Relationship between Bond Value & YTM When the coupon rate on a bond is equal to its market yield, the bond will trade at its par value. If yield required in the market subsequently rises, the price of the bond will fall & it will trade at a discount. If required yield falls, the bond price will increase and bond will trade at a premium. Crux: If YTM increases, bond value decreases & vice-versa, other things remaining same. YTM & Bond value have inverse relationship. QUESTION NO. 25A ICICI Bank Ltd. has issued the following bond: Face Value of bond = Rs Market Price of bond = Rs. 750

21 21 Coupon Rate = 15% Year to Maturity = 5 years Required: (a) Compute YTM (b) If YTM decreases to 15%, what is the percentage change in the market price of the bond. QUESTION NO. 25B (RTP) Given a five-year, 8% coupon bond with a face value of Rs. 1,000 and coupon payments made annually, determine its values given it is trading at the following yields: 8%, 6%, and 10%. Comment on the price and yield relation you observe. What are the percentage changes in value when the yield goes from 8% to 6% and when it goes from 8% to 10%? Concept No. 31: Value of the Bond at the end of each Year B 0 = () B 1 = () So on QUESTION NO. 26 (RTP) A 7% Bond was issued several years ago when the market interest rate was also 7%.Now the bond has a remaining life of 3 years when it would be redeemed at par value of Rs. 1,000. The market rate of interest has increased to 8%. Find out the current market price, price after 1 year and price after 2 years from today. Concept No. 32: Relationship between Bond Value & Maturity Prior to Maturity, a bond can de selling at significant discount or premium to Par value. Regardless of its required yield, the price will converge to par value as Maturity approaches. Value of premium bond decrease to par value, value of Discount bond increases to Par value. Premium and discount vanishes. Example: Consider Rs 1000 par value bond, 3 year life, paying 6% semi annual coupons. The bond value corresponding to required yields of 3,6,12% as the bond approaches maturity are present in the table below : Bond Values and the Passage of Time

22 22 Time to Maturity YTM = 3% YTM = 6% YTM = 12% 3.0 years Rs Rs Rs QUESTION NO. 27 Coupon rate on three bonds A,B & C are 10%, 12% and 8%.Face Value is Rs. 100.On Maturity all three bonds are repayable at par value. Yield Rate is 10%.Life-5 years. Demonstrate the following: (i) A Premium bond decreases as the maturity decreases and becomes equal to par value on maturity. (ii) A Discount bond increases as the maturity decreases and becomes equal to par value on maturity. (iii) A Par value bond always remains a par value bond till maturity Others things remaining constant Concept No. 33: Floating Rate Bonds Floating Rate Bonds are those bonds where coupon rate is decided according to the Reference rate (Market Interest Rate). Coupon Rate should be changed with the change in Reference rate (Market Interest Rate). In this case YTM = Coupon Rate. QUESTION NO. 28 (RTP)

23 23 ABC Ltd. has the following outstanding bonds. Bond Coupon Maturity Series X 8% 10 Years Series Y Variable 10 Years Changes annually comparable to prevailing Rate Initially these bonds were issued at face value of Rs. 10,000 with yield to maturity of 8%. Assuming that: (i) After 2 years from the date of issue, YTM is 10%, then what should be the price of each bond for the remaining 8 years? (ii) If after 2 years YTM is 7%, then what should be the price of each bond for the remaining 8 years? (iii) What conclusion you can draw from the prices of bonds computed above. Concept No. 34: Duration of a Bond (Macaulay Duration) Duration of the bond is a weighted average of the time (in years) until each cash flow will be received i.e. interest & Principal repayment is fully recovered. Duration of bond will always be less than or equal to maturity years. Formulae : Duration = (+ ) (+ ) (+ ) (+ ) QUESTION NO. 29A Consider a bond which has the following features: Face Value: Rs. 100 Coupon (interest rate): 15% payable annually Years the maturity: 6 years. Redemption Value: 100 Current Market Price: Rs Yield to Maturity: 18% What is the duration of bond? QUESTION NO. 29B (CA Final May Marks) Find the current market price of bond having face value Rs. 1,00,000 redeemable after 6 year maturity with YTM at 16% payable annually and duration years. [Given: (1.16) 6 = ] Concept No. 35: Duration of a Zero - Coupon Bond Duration of a Zero Coupon Bond will always be equal to its Maturity Years. QUESTION NO. 30 Suppose we are considering investing in a zero-coupon bond that matures in 5 years and has a face value of Rs If these bonds are priced to yield 10%, what is the present value of the bonds? What is its Duration?

24 24 Concept No. 36: Relationship between Duration of Bond & YTM If YTM increases, Bond Value decreases so duration of the bond decreases (recovery is less) & vice versa. Higher the YTM, lower will be duration of a bond. Lower the YTM, higher will be duration of a bond, other things remaining constant. QUESTION NO. 31 (CA Final SFM May marks) a) Consider two bonds one with 5 years to maturity and the other with 20 years to maturity. Both the bonds have a face value of Rs. 1,000 and coupon rate of 8% (with annual interest payments) and both are selling at par. Assume that the yields of both the bonds fall to 6%, whether the price of bond will increase or decrease? b) What percentage of this increase/ decrease comes from a change in the present value of bond's principal amount and what percentage of this increase/ decrease comes from a change in the present value of bond's interest payments? c) Consider a bond selling at par value of Rs. 1,000 with 6 years to maturity and a 7% coupon rate (with annual interest payment), what is bond's duration? d) If the YTM of the bond in (b) above increases to 10%, how it affects the bond's duration? And why? e) Why should the duration of a coupon carrying bond always be less than the time to its maturity? Concept No. 37: Calculation of yield when Coupon Payment is not available for Re-Investment QUESTION NO. 32 (CA Final SFM Nov 2008)(6Marks)(RTP Nov 09 SFM) XL Ltd. has made an issue of 14 per cent non-convertible debentures on January 1, These debentures have a face value of Rs. 100 and is currently traded in the market at a price of Rs.90.The bond is redeemable at par on December 31,2011 at the end of 5 years. Required: (i) Estimate the current yield and the YTM of the bond. (ii) Calculate the duration of the NCD. (iii) Assuming that intermediate coupon payments are, not available for reinvestment calculate the realized yield on the NCD. Concept No. 38: Modified Duration/ Sensitivity/ Volatility Modified Duration = Modified duration will always be lower than Macaulay s Duration. Volatility measures the % change in the bond value with 1% change in YTM. Example: If Volatility is 5%, it means if YTM increases by 1% bond value will decrease by 5% or vice versa.

25 25 QUESTION NO. 33 (CA. Final Nov, 2005/RTP Nov 08)(CS Final Dec 2007,6Marks) The following data are available for a bond Face Value: Rs. 1,000 Redemption value: Rs. 1,000 Coupon Rate: 16% Yield to maturity: 17% Years of Maturity: 6 What are the current market price, duration and volatility of this bond? Calculate the expected market price, if increase in required yield is by 75 basis points. Concept No. 39: Duration of a Portfolio It is simply the weighted average of the durations of the individual securities in the Portfolio. Portfolio Duration = W 1 D 1 + W 2 D 2 + W 3 D W n D n W i = Di = Duration of bond (i) N = No. Of bonds in the Portfolio Example: Calculating portfolio duration Suppose you have two-security portfolio containing Bonds A and B. The market value of bond A is Rs. 6000, and the Market Value of Bond B is Rs The duration of Bond A is 8.5, and the duration of Bond B is 4.0. Calculate the duration of portfolio. Solution: First, calculating the weights of each bond. Since market value of the portfolio is Rs.10,000 ( ), the weight of each security bond is : Weight in Bond A =, = 60% Weight in Bond B =, = 40% Portfolio Duration = ( ) + ( ) = 6.7 Concept No. 40: Return Calculation When bonds are purchased and sold within time frame. QUESTION NO. 34 (SFM Study Material) Vipin purchased at par a bond with a Face Value of Rs. 1,000. The bond had five year to maturity and a 10% coupon rate. The bond was called two years later for a price of Rs. 1,200 after making its second annual interest payment. Vipin then reinvested the proceeds in a bond selling at its Face Value of Rs. 1,000 with three years to maturity and a 7% coupon rate. What was Vipin's actual YTM over the five-year period?

26 26 Concept No. 41: Downside Risk, Conversion Premium, Conversion Parity Price 1. Downside Risk or Premium over Non-Convertible Bond Downside Risk reflects the extent of decline in market value of convertible bonds at which conversion option become worthless. = Market value of Convertible bond ( - ) Market value of Non- Convertible bond % Downside Risk/ % Price Decline = 2. Conversion Premium/ Premium over Conversion Value Conversion Premium shows the percentage increase necessary to reach a parity price relationship between the underlying equity shares and the convertible bond = Market value of Convertible bond ( - ) CV or Fair value of Convertible bond ( No. of Shares MPS) % Conversion Premium = 3. Conversion Parity Price/ No Gain No Loss =. 4. Floor Value: Floor Value is the minimum of : a) Market Value of Convertible Bond. b) Market Value of Non-Convertible Bond. Note: Market Value of Convertible Bond (Assume 5 Years) = () + () () + ( ) () CV 5 = MPS at the end of Year 5 No. of Shares. QUESTION NO. 35A (CA Final SFM Nov 2008)(8 Marks) The data given below relates to a convertible bond : Face value: Rs.250 Coupon rate: 12% No. of shares per bond: 20 Market price of share: Rs.12 Straight value of bond: Rs.235 Market price of convertible bond: Rs.265 Calculate: (i) Stock value of bond. or Conversion Value Of Bond (ii) The percentage of downside risk. (iii) The conversion premium (iv) The conversion parity price of the stock.

27 27 QUESTION NO. 35B A Ltd. has in issue 9% bonds which are redeemable at their par value of 100 in five years' time. Alternatively, each bond may be converted on that date into 20 ordinary shares of the company. The current ordinary share price of A Ltd. is 4.45 and this is expected to grow at a rate of 6.5% per year for the foreseeable future. A Ltd. has a cost of debt of 7% per year. Required: Calculate the following current values for each 100 convertible bond: (i) market value; (ii) floor value; (iii) Conversion premium. Note: This concept is also used for Convertible Preference Shares QUESTION NO. 35C (CA Final SFM Nov 2009)(8 Marks) XYZ company has current earnings of Rs. 3 per share with 5,00,000 shares outstanding. The company plans to issue 40,000, 7% convertible preference shares of Rs. 50 each at par. The preference shares are convertible into 2 shares for each preference shares held. The equity share has a current market price of Rs. 21 per share. (i) What is preference share s conversion value? (ii) What is conversion premium? (iii) Assuming that total earnings remain the same, calculate the effect of the issue on the earning per share (a) Before conversion (b) After conversion. (iv) If profits after tax increases by Rs. 1 million what will be the basic EPS (a) Before conversion and (b) After conversion. Concept No. 42: Callable Bond Those bonds which can be called before the date of Maturity. Step 1: Calculate Net Initial Outflow. Step 2: Calculate Tax Saving on Call Premium & Unamortized Issue Cost. Step 3: Calculate Net Annual Cash Outflow. Step 4: Calculate Present Value of Total Net Savings by replacing Outstanding Bonds with New Bonds. QUESTION NO. 36 (CA. Final Nov, 2001) A firm has a bond outstanding of Rs.300,00,000. The bond has 12 years remaining until maturity, has a 12.5 % coupon and is callable at Rs. 1,050 per bond; it had flotation costs of Rs. 4,20,000, which are being amortized at Rs. 30,000 annually. The flotation costs for a new issue will be Rs. 9,00,000& the current interest rate will be 10 %. After tax cost of the debt (K d ) is 6%, Should the firm refund the outstanding debt (and issue new bond)? Consider Corporate Incometax rate at 50%.

28 28 Concept No. 43: Overlapping Interest QUESTION NO. 37 (CA. Final Nov, 2005) T is contemplating calling Rs. 3 crores of 30 years, Rs. 1,000 bond issued 5 years ago with a coupon interest rate of 14%. The bonds have a call price of Rs.1,140 and had initially collected proceeds of Rs crores due to a discount of Rs. 30 per bond. The initial floating cost was Rs. 3,60,000. The company intends to sell Rs. 3 crores of 12% coupon rates, 25 years bonds to raise funds for retiring the old bonds. It proposes to sell the new bonds at their par value of Rs. 1,000. The estimated floatation cost is Rs. 4,00,000. The company is paying 40% tax and its after cost of debt is 8%. As the new bonds must first be sold and their proceeds, then used to retire old bonds, the company expects a two months period of overlapping interest during which interest must be paid on both the old and new bonds. What is the feasibility of refunding bonds? Concept No. 44: Bond issued under an open ended scheme QUESTION NO. 38 (CA. Final May, 2001) The HLL has Rs 8 crore of 10 % mortgage bonds outstanding under an open-ended scheme. The scheme allows additional bonds to be issued as long as all of the following conditions are met: (i) Pre-tax interest coverage (Income before tax + Bond interest/bond interest) remains greater than 4 (ii) Net depreciated value of mortgage assets remain twice the amount of the mortgage debt. (iii) Debt to equity ratio remains below 5. The HLL has a net income, after taxes of Rs 2 crore and a 40 % tax rate, Rs 40 crore in equity and Rs 30 crore in depreciated assets, covered by the mortgage. Assuming that 50 % of the proceeds of a new issue would be added to the base of mortgaged assets and that the company has no sinking fund payments until next year, how much more 10 % debt could be sold under each of the three conditions? Which protective covenant is binding? Concept No. 45: Bond Purchased between two coupon dates QUESTION NO. 39 (CA Final Nov, 2007(6 Marks)) MP Ltd. issued a new series of bonds on January 1,2000. The bonds were sold at par (Rs. 1,000), having a coupon rate 10% p.a. and mature on 31st December, Coupon payments are made semi-annually on June 30th and December 31st each year. Assume that you purchased an outstanding MP Ltd. Bond on 1st March, 2008 when the going interest rate was 12%. Required: (i) What was the YTM of MP Ltd. Bonds as on January 1, 2000? (ii) What amount you should pay to complete the transaction [for purchasing the bond on 1st March 2008]? Of that amount how much should be accrued interest and how much would represent bonds basic value.

29 29 Concept No. 46: Spot Rate Yield to maturity is a single discount rate that makes the present value of the bond s promised cash flow equal to its Market Price. The appropriate discount rates for individual future payments are called Spot Rate. Discount each cash flow using a discount rate i.e. specific to the maturity of each cash flow. Example Consider an annual-pay bond with a 10% coupon rate and three years of maturity. This bond will make three payments. For a Rs bond these payments will be Rs. 100 in one year, Rs. 100 at the end of two years, and Rs.100 three years from now. Suppose we are given the following spot rates: 1 year = 8% 2 year = 9% 3 year = 10% Solution: Discounting each promised payment by its corresponding spot rate, we can value the bond as: (.) = Concept No. 47: Relationship between Forward Rate and Spot Rate Forward Rate is a borrowing/ landing rate for a loan to be made at some future date. 1f 0 = Spot Rate or Current YTM (rate of 1 year loan) 1f 1 = Rate for a 1 year loan, one year from now 1f 2 = Rate for a 1 year loan to be made two years from now Relationship: (1+S 1 ) 1 = (1 + 1 f 0 ) (1+S 2 ) 2 = (1 + 1 f 0 ) (1 + 1 f 1 ) Or S 2 = {(1 + 1 f 0 ) (1 + 1 f 1 )} 1/ 2-1 (1 + S 3 ) 3 = (1+ 1 f 0 ) (1+ 1 f 1 ) (1 + 1 f 2 ) Or S 3 = {(1 + 1 f 0 ) (1 + 1 f 1 ) (1 + 1 f 2 )} 1/ 3-1 Crux: The idea here is that borrowing for three years at the 3-year rate or borrowing for 1 year period, three year is succession, should have the same cost. Example: Using forward rates: The current 1-year rate ( 1 f 0 ) is 4%

30 30 The 1-year forward rate for lending from time =1 to time=2 is 1 f 1 =5%, and The 1-year forward rate for lending from time =2 to time =3 is 1 f 2 =6%. Calculate value of a 3-year annual-pay bond with 5% coupon and a par value of Rs Solution: Bond value = ( ) + + ( )( ) ( )( )( ) = (.) + + = Rs (.)(.) (.)(.)(.) QUESTION NO. 40A (CA Final Nov Marks) From the following data for Government Securities, calculate the forward rates (Yield To Maturity): Face Value (Rs.) Interest Rate Maturity (Year) Current Price (Rs.) 1,00,000 0% 1 91,500 1,00,000 10% 2 98,500 1,00, % 3 99,000 QUESTION NO. 40B (CA.FinalSFMNov2008) (4Marks)(RTP Nov09SFM) The following is the Yield structure of AAA rated debenture: Period (or Maturity) Yield (%) 3 months 8.5% 6 months year years years and above (i) Based on the expectation theory calculate the implicit one-year forward rates in year 2 and year 3. (ii) If the interest rate increases by 50 basis points, what will be the percentage change in the price of the bond having a maturity of 5 years? Assume that the bond is fairly priced at the moment at Rs. 1,000.Assume that the entire amount is received at the end of Year 5. QUESTION NO. 40C (CA FINAL, May 10, 8Marks) Consider the following data for Government securities: Face value ( Rs.) Interest rate% Maturity (years) Current Price (Rs) 1,00, ,000 1,00, ,000 1,00, ,500 1,00, ,900 Calculate the forward interest rates. Concept No. 48: Calculation of After-tax yield of a taxable security & taxequivalent yield of a tax-exempt security After-tax yield = taxable yield (1 marginal tax rate)

31 31 Taxable-equivalent yield is the yield a particular investor must earn on a taxable bond to have the same after-tax return they would receive from a particular tax-exempt issue. Taxable-equivalent yield = ( ) Example: Consider a municipal bond that offers a yield of 4.5%. If an investor is considering buying a fully taxable Government security offering a 6.75% yield, should she buy the Government security or the municipal bond, given that her marginal tax rate is 35%? Solution: We can approach this problem from two perspectives. First, the taxable equivalent yield on.% municipal bond is = 6.92%, which is higher than the taxable yield, so the municipal (.) bond is preferred. Alternatively, the after-tax return on the taxable bond is X (1 0.35) = 4.39%. Thus, the after-tax return on the municipal bond (4.5%) is greater than the after-tax yield on the taxable bond (4.39%), and the municipal bond is preferred. Either approach gives the same answer; She should buy the municipal bond. Concept No. 49: Re-investment income Reinvestment income is important because if the reinvestment rate is less than the YTM, the realized yield on the bond will be less than the YTM. If a bond holder holds a bond until maturity and reinvests all coupon interest payments at YTM, the total amount generated by the bond over its life has three components: (i) Bond Principal (ii) Coupon interest (iii) Interest on reinvested coupons Once we calculate the total amount needed for a particular level of compound return over a bond s life, we can subtract the principal and coupon payments to determine the amount of reinvestment income necessary to achieve the target yield. Example: Calculating required reinvestment income for a bond. If you purchased a 6%, 10-year Government bond at par, how much reinvestment income must be generated over its life to provide the investor with a compound return of 6% on a Semi annual basis? Solution: Assuming the bond has par value of Rs. 100, we first calculate the total value that must be generated ten years (20 semi annual periods) from now as: P (1+ r) n = 100(1.03) 20 = Rs

32 32 There are 20 bond coupons of Rs. 3 each, totaling Rs. 60, and a payment of Rs.100 of principal at maturity. Therefore, the required reinvestment income over the life of the bond is: = Rs.20.61

33 33 Miscellaneous Questions QUESTION NO. 1 Ram purchases a 5 years, bond of Rs par value, which pays a coupon of 8%. If Mr. Ram's required rate of return is 10%, how much he should pay to receive the same principal amount or face value on Maturity? If the price quoted in the market is Rs.900, then would he benefit by buying at this price? QUESTION NO. 2 A Rs.100 perpetual bond is currently selling for Rs.95. Coupon rate of interest is 13.5 % &appropriate discount rate is 15 %. Calculate fair value of bond. Should it be bought? What is its YTM. QUESTION NO. 3 Consider a Deep Discount Bond with the face value of Rs.1000 and with 10 % yield to maturity. Compute the discount on bond or bond value if the bond's maturity period is one year or two years or three years or four years or five years. QUESTION NO. 4 (SFM Study Material) If a Rs.100 par value bond carries a coupon rate of 12 per cent and a maturity period of 8 years & interest payable semi-annually then what will be the value of the bond with required rate of return of 14%? QUESTION NO. 5 (RTP) A company proposes to sell ten-year debentures of Rs. 10,000 each. The company would repay Rs. 1,000 at the end of every year and will pay interest annually at 15 per cent on the outstanding amount. Determine the present value of the debenture issue if the capitalization rate is 18 per cent. QUESTION NO. 6 (RTP) A Ltd. has sold Rs. 1000,12% perpetual debentures 10 years ago. Interest rates have risen since then, so that debentures of this company are now selling at 15% yield basis. Determine the current/indicated / expected market price of the debentures. Would you like to buy the debentures for Rs.700? Now assume that the debentures of the company are selling at Rs.825. Moreover, if the 12%, Rs debentures are not perpetual & have 8 years to run to maturity, compute the approximate effective yield an investor would earn on his investment. QUESTION NO. 7 (SFM Study Material) If the price per bond is Rs. 90 and the bond has a par value of Rs. 100, a coupon rate of 14 per cent, and a maturity period of 6 years, calculate it's Yield to Maturity?

34 34 QUESTION NO. 8 (RTP) Given a two-year, 8% annual coupon bond with a face value of Rs. 1,000 and with annual coupon payments that is fully taxable and selling at par, and an identical bond that is tax free, what would the yield and price on the tax-free bond have to be for an investor in a 35% tax bracket to be indifferent between the two bonds? QUESTION NO. 9 A Company issues Rs. 10,00,000 12% debentures of Rs. 100 each. The debentures are redeemable after the expiry of fixed period of 7 years. The Company is in 35% tax bracket. Required: (i)calculate the cost of debt after tax, if debentures are issued at (a) Par (b) 10% Discount (c) 10% Premium. (ii) If brokerage is paid at 2%, what will be the cost of debentures, if issue is at par? [Ans: (i) 7.8, 9.71, 6.07 (ii) 8.17] QUESTION NO. 10 (SFM Study Material) Bond's face value = Rs. 1000, Coupon Rate-10%, Years to Maturity = 5 years, Value/Price of the Bond = 1025, Calculate: (a) YTM (b) If the bond can be called three years from now at a price of Rs what is its yield to call? QUESTION NO. 11 Yield on one year Bond = 10%; Yield on two year Bond =11%.Interest is payable annually. Determine one year Forward Rate one year from now? QUESTION NO. 12 (CA Final SFM May marks) ABC Ltd. has Rs. 300 million, 12 percent bonds outstanding with six years remaining to maturity. Since interest rates are falling, ABC Ltd. is contemplating of refunding these bonds with a Rs. 300 million issue of 6 year bonds carrying a coupon rate of 10 percent. Issue cost of the new bond will be Rs. 6 million and the call premium is 4 per cent. Rs. 9 million being the unamortized portion of issue cost of old bonds can be written off no sooner the old bonds are called off. Marginal tax rate of ABC Ltd. is 30 per cent. You are required to analyse the bond refunding decision. Face Value to be Rs.300. QUESTION NO. 13 ( RTP) New Chem Corporation has issued a fully convertible 10% debenture of Rs. 10,000 face value, convertible into 20 equity shares. The current market price of the debenture is Rs. 10,800, whereas the current market price of equity share price is Rs You are required to calculate (i) the conversion premium and (ii) the conversion value. QUESTION NO. 14 Tata Ltd. have issued earlier a 11.5% convertible bond of face value Rs maturing in After a period of 3 years, on the option of the investors each of these bonds can be converted into 50 equity shares of face value of Rs. 10 each. The investment value of similar nonconvertible bond is Rs. 870.The current market prices of the bond and the share are Rs. 970