\nMaturity<\/td>\n | 3 years<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n (i) If he wants a yield of 13%, what is the maximum price he should be ready to pay for? \n(ii) If the Bond is selling for \u20b9 97.60, what would be his yield? [Nov. 2009] [4 Marks] \nAnswer: \n(i) Calculation of Maximum price \nThe present value of future inflows (comprising both interest as well as redemption value) discounted at 13% is the maximum price the investor would be ready to pay. \nAnnual Interest (I) = Rs. 100 \u00d7 \\(\\frac{11}{100}\\) = Rs. 11 \nRedemption Value (RV) = Rs. 100 \nMaturity Period (n) = 3 Years \nAccordingly, Present value of future inflows can be calculated as \n= \u20b9 11 \u00d7 PVIFA(13%, 3)<\/sub> + \u20b9 100 PVIF(13%, 3)<\/sub> \n= \u20b9 11 \u00d7 2.361 + \u20b9 100 \u00d7 0.693 \n= \u20b9 25.97 + 69.30 \n= \u20b9 95.27 \nThe maximum price that the investor is ready to pay is Rs. 95.27.<\/p>\n(ii) Calculation of yield \nIt may be noted that the price of bond and yield\/return are inversely related. The fair value is Rs. 95.28 at 13% yield. It means, if the bond is selling at higher than this fair value at Rs. 97.60, the return will be less than 13%.<\/p>\n Let us find out approximate yield: \n \n= 0.1194 or 11.94% \nThe present value of future inflows (comprising both interest as well as Value at 12% \n= \u20b9 11 \u00d7 PVIFA(12%3) + 100 \u00d7 PVIF(12% 3) \n= \u20b9 11 \u00d7 2.402 + \u20b9 100 \u00d7 0.712 \n= \u20b9 26.42 + \u20b9 71.20 \n= \u20b9 97.62 \nThis value is almost equal to the price of \u20b9 97.60. Therefore, the YTM of the bond would be 12%.<\/p>\n Question 2. \nThe Nominal value of 10% Bonds issued at par by M\/s SK Ltd. is Rs. 100. The bonds are redeemable at Rs. 110 at the end of year 5. \n(I) Determine the value of the bond if required yield is : [Nov. 2019 Old Syllabus [5 Marks]] \n(i) 8% \n(ii) 9% \n(iii) 10% \n(iv) 11% \n(II) When will the value of the bond be highest ? \nGiven below are Present Value Factors : \n \nAnswer: \nGiven \nCoupon rate 10% \nFace value Rs. 100 \nRedemption Value Rs. 110 \nLife 5 yrs. \n(I) Value of the bond if required yield is \n \n(II) The price and yield are inversely related. Therefore, the highest price will be at the lowest yield. In the given case the value of the bond will be highest when yield is 8%.<\/p>\n <\/p>\n Question 3. \nCalculate Market Price of: \n(i) 10% Government of India security currently quoted at \u20b9 110, but interest rate is expected to go up by 1%. \n(ii) A bond with 7.5% coupon interest, Face Value \u20b9 10,000 & term to maturity of 2 years, presently yielding 6%. Interest payable half yearly. [Nov. 2010] [5 Marks] \nAnswer: \n(i) Current yield: \n= (Coupon Interest\/Market Price) \u00d7 100 = (10\/110) \u00d7 100 = 9.09% \nWhen current yield go up by 1%: \nExpected Yield = Current Yield + 1% = 9.09% + 1 = 10.09% \nCalculation of new market price at a yield of 10.09%: \nYield =(Coupon Interest\/Market Price) \u00d7 100 Or 10.09 \n= 10\/Market Price \u00d7 100 New Market Price \n= \u20b9 99.11<\/p>\n (ii) Market Price of Bond: \nThe market price of the bond shall be the present value of future inflows, which comprises interest as well as redemption value. \nMarket Price = P. V. of Interest + P. V. of Principal \nHalf-yearly Interest (I) = Rs. 10,000 \u00d7 \\(\\) = Rs. 375 \nRedemption Value (RV) = Rs. 10,000 \nMaturity Period (n) = 2 Years or 4 half Years \nYTM (r) = 6% p.a. or 3% half yearly \nMarket Price = \u20b9 375 \u00d7 PVIFA(3%4)<\/sub> + \u20b9 10,000 \u00d7 PVIF(3%4)<\/sub> \n= (\u20b9 375 \u00d7 3.7171) + (\u20b9 10,000 \u00d7 .8885) \n= \u20b9 1,394 + \u20b9 8,885 \n= \u20b9 10,279<\/p>\nTutorial Note: \nSince, the coupon (7.5%) is higher than YTM (6%), therefore the bond will be selling at premium i.e. above Rs. 10,000.<\/p>\n Question 4. \nBased on the credit rating of the bonds, A has decided to apply the following discount rates for valuing bonds:<\/p>\n \n\n\nCredit rating<\/td>\n | Discount rate<\/td>\n<\/tr>\n | \nAAA<\/td>\n | 364-day T-bill rate + 3% spread<\/td>\n<\/tr>\n | \nAA<\/td>\n | AAA + 2% spread<\/td>\n<\/tr>\n | \nA<\/td>\n | AAA + 3% spread<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n He is considering to invest in a AA rated \u20b9 1,000 face value bond currently selling at \u20b9 1,025.86. The bond has five years to maturity and the coupon rate on the bond is 15 per cent per annum payable annually. The next inter-est payment is due one year from today and the bond is redeemable at par. \n(Assume the 364-day T-bill rate to be 9 per cent). \nYou are required to calculate: \n(i) The intrinsic value of the bond for A. Should he invest in the bond? \n(ii) The Current Yield (CY) and \n(iii) The Yield to Maturity (YTM) of the bond. [Nov. 2011] [8 Marks] \nAnswer: \n(i) Calculation of Intrinsic Value of the bond: \nAs per table given in the question, the appropriate discount rate for valuing the AA rated bond for A is: \nYTM = 996 + 396 + 2% = 1496 \nThe other parameters are: \nAnnual Interest (I) = 1596 of Rs. 1,000 = Rs. 150 \nRedemption Value (RV) = Rs. 1,000 \nMaturity Period (n) = 5 Years \nAccordingly, Intrinsic Value of future inflows can be calculated as = \u20b9 150 \u00d7 PVIFA(14%5) + \u20b9 1,000 \u00d7 PVIF(14%>5) \n= \u20b9 150 \u00d7 3.4331 + \u20b9 1,000 \u00d7 0.5194 \n= \u20b9 514.96 + \u20b9 519.40 = \u20b9 1,034.36 \nThe current market value (Rs. 1,025.86) is less than the intrinsic value (Rs. 1,034.36) of the bond. Therefore, the bond is underpriced. So, Mr. A should buy the bond.<\/p>\n (ii) Calculation of Current Yield (CY): \nCurrent yield = Annual Interest\/Price = \u20b9 150\/\u20b9 1,025.86 \n= 14.6296<\/p>\n (iii) Calculation of Yield to Maturity (YTM): \nSince, the coupon rate is 15% and bond is redeemable at par, therefore the price of the bond at 15% YTM will be Rs. 1,000.<\/p>\n \n\n\nYelid<\/td>\n | Value (Rs)<\/td>\n<\/tr>\n | \n15%<\/td>\n | 1,000<\/td>\n<\/tr>\n | \n14%<\/td>\n | 1,034.36<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n YTM at Rs, 1025.86 can be calculated using interpolation as per the manner given below. \nBy interpolation, the YTM is \n= 14% + \\(\\frac{34.36-25.86}{34.36}\\) \u00d7 (15% – 14%) \n= 14% + \\(\\frac{8.5}{34.36}\\)% \n= 14.24796<\/p>\n Question 5. \nA bond is held for a period of 45 days. The current discount yield is 6 per cent per annum. It is expected that current yield will increase by 200 basis points and current market price will come down by Rs. 2.50. \nCalculate \n(i) Face Value of the Bond \n(ii) Bond Equivalent yield. [May 2017] [4 Marks] \nAnswer: \n(i) Let the Face value of bond be Re. 1 \n \nThe difference in bond price due to 200 basis increase in interest rates is a decrease of Re. 0.0025. Therefore, by applying unitary method, if the actual difference is Rs. 2.50 the face value of the bond will be \\(\\frac{2.5}{0.0025}\\) \u00d7 1 = Rs. 1,000 \nFace Value of the Bond = Rs. 1,000<\/p>\n (ii) Bond Equivalent yield \n<\/p>\n Question 6. \nBright Computers Limited is planning to issue a debenture series with a face value of \u20b9 1,000 each for a term of 10 years with the following coupon rates:<\/p>\n \n\n\nYears<\/td>\n | Rates<\/td>\n<\/tr>\n | \n1-4<\/td>\n | 8%<\/td>\n<\/tr>\n | \n5-8<\/td>\n | 9%<\/td>\n<\/tr>\n | \n9-10<\/td>\n | 13%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n The current market rate on similar debenture is 15% p.a. The company proposes to price the issue in such a way that a yield of 16% compounded rate of return is received by the investors. The redeemable price of the debenture will be at 10% premium on maturity. What should be the issue price of debenture? \nPV @ 16% for 1 to 10 years are: .862, .743, .641, .552, .476, .410, .354, .305, .263, .227 respectively. [May 2016] [5 Marks] \nAnswer: \nThe issue price of the debentures will be the sum of present value of interest payments during 10 years and present value of redemption of debenture. \nInterest (first 4 Years) = Rs. 1,000 @ 8% = Rs. 80 \nInterest (Next 4 Years) = Rs. 1,000 @ 9% = Rs. 90 \nInterest (Next 2 Years) = Rs. 1,000 @ 13% = Rs. 130 \nRedemption Value (10th Year) = Rs. 1,100 \nMaturity = 10 Years YTM = 16%<\/p>\n The cash inflows of the interest part are not constant throughout the period and the present value factors are given in the question. Therefore, it would be better to solve in the following tabular form.<\/p>\n \n\n\nYears<\/td>\n | Cash outflow (Rs.)<\/td>\n | PVF @ 16%<\/td>\n | PV<\/td>\n<\/tr>\n | \n1<\/td>\n | 80<\/td>\n | 0.862<\/td>\n | 68.96<\/td>\n<\/tr>\n | \n2<\/td>\n | 80<\/td>\n | 0.743<\/td>\n | 59.44<\/td>\n<\/tr>\n | \n3<\/td>\n | 80<\/td>\n | 0.641<\/td>\n | 51.28<\/td>\n<\/tr>\n | \n4<\/td>\n | 80<\/td>\n | 0.552<\/td>\n | 44.16<\/td>\n<\/tr>\n | \n5<\/td>\n | 90<\/td>\n | 0.476<\/td>\n | 42.84<\/td>\n<\/tr>\n | \n6<\/td>\n | 90<\/td>\n | 0.410<\/td>\n | 36.90<\/td>\n<\/tr>\n | \n7<\/td>\n | 90<\/td>\n | 0.354<\/td>\n | 31.86<\/td>\n<\/tr>\n | \n8<\/td>\n | 90<\/td>\n | 0.305<\/td>\n | 27.45<\/td>\n<\/tr>\n | \n9<\/td>\n | 130<\/td>\n | 0.263<\/td>\n | 34.19<\/td>\n<\/tr>\n | \n10<\/td>\n | 130<\/td>\n | 0.227<\/td>\n | 29.51<\/td>\n<\/tr>\n | \n10<\/td>\n | 1,100 (RV)<\/td>\n | 0.227<\/td>\n | 249.70<\/td>\n<\/tr>\n | \n<\/td>\n | <\/td>\n | <\/td>\n | 676.29<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n The company should issue the debentures at a price at \u20b9 6\/6.29.<\/p>\n <\/p>\n Question 7. \nConsider two bonds, one with 5 years to maturity and the other with 20 years to maturity. Both the bonds have a face value of \u20b9 1,000 and coupon rate of 8% (with annual interest payments) and both are selling at par. \n(i) Assume that the yields of both the bonds fall to 6%, whether the price of bond will increase or decrease? \n(ii) What percentage of this increase\/decrease comes from a change in the present value of bond\u2019s principal amount and what percentage of this increase\/decrease comes from a change in the present value of bond\u2019s interest payments? [May 2009] [8 Marks] \nAnswer: \n(i) The price of bond and yield are inversely related. Since the yield falls to 6%, the price of bonds will increase. The increase in price of the bond with higher maturity period will be higher.<\/p>\n If yield falls to 6%<\/p>\n \n\n\nPrice of 5 years bond<\/td>\n<\/tr>\n | \n= \u20b9 80 \u00d7 PVIFA(6% 5) + \u20b9 1,000 \u00d7 pvif(6% 5) \n= (\u20b9 80 \u00d7 4.2124) + (\u20b9 1,000 \u00d7 0.7473) \n= 336.99 + 747.30 \n= \u20b9 1,084.29<\/td>\n | Increase in price \nRs. 84.29<\/td>\n<\/tr>\n | \nPrice of 20 years bond<\/td>\n<\/tr>\n | \n= \u20b9 80 \u00d7 pvifa(6%20) + \u20b9 1,000 \u00d7 PVIF(6%20) \n= (\u20b9 80 \u00d7 11.4699) + (\u20b9 1,000 \u00d7 0.3118) \n= 917.59 + 311.80 \n= \u20b9 1,229.39<\/td>\n | Increase in price \nRs. 229.39<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n(ii) Price increase in Bond: \n(a) Due to change in the present value of bond\u2019s principal amount:<\/p>\n \n\n\nPrice of 5 years bond<\/td>\n<\/tr>\n | \n= Principal \u00d7 [PVIF(6%,5)<\/sub> – PVIF(8%,5)<\/sub>] \n= 1,000 \u00d7 [0.7473 – 0.6806] \n= Rs. 66.70<\/td>\nPercentage Increase \n\\( \\frac{\\text { Rs. } 66.70}{\\text { Rs. } 84.29} \\) \u00d7 100 = 79.13%<\/td>\n<\/tr>\n | \nPrice of 20 years bond<\/td>\n | <\/td>\n<\/tr>\n | \n= Principal \u00d7 [PVIF(6%,5)<\/sub> – PVIF(8%,5)<\/sub>] \n= 1,000 \u00d7 [0.3118 – 0.2145] \n= Rs. 97.30<\/td>\nPercentage Increase \n\\( \\frac{\\text { Rs. } 97.30}{\\text { Rs. } 229.39} \\) \u00d7 100 = 42.42%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n(b) Due to change in the present value of bond\u2019s Interest amount:<\/p>\n \n\n\nPrice of 5 years bond<\/td>\n<\/tr>\n | \n= Interest \u00d7 [PVIF(6%,5)<\/sub> – PVIF(8%,5)<\/sub>] \n= 80 \u00d7 [4.2124 – 3.9927] \n= Rs. 17.59<\/td>\nPercentage Increase \n\\( \\frac{\\text { Rs. } 17.59}{\\text { Rs. 84.29 }} \\) \u00d7 100 = 20.87%<\/td>\n<\/tr>\n | \n= Interest \u00d7 [PVIF(6%,5)<\/sub> – PVIF(8%,5)<\/sub>] \n= 80 \u00d7 [11.4699 – 9.8181] \n= Rs. 132.14<\/td>\nPercentage Increase \n\\( \\frac{\\text { Rs. } 132.14}{\\text { Rs. } 229.39} \\) \u00d7 100 = 57.58%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nTutorial Note: \nThe segment of increase in the price of the bond due to interest part is higher mease of bond with higher maturity.<\/p>\n Question 8. \nPet feed pic has outstanding, a high yield Bond with the following features:<\/p>\n \n\n\nFace value<\/td>\n | \u00a310,000<\/td>\n<\/tr>\n | \nCoupon<\/td>\n | 10%<\/td>\n<\/tr>\n | \nMaturity period<\/td>\n | 6 years<\/td>\n<\/tr>\n | \nSpecial feature<\/td>\n | Company can extend the life of Bond to 12 years.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n (a) If an investor expects that interest will be 8%, six years from now then how much he should pay for this bond now. \n(b) Now suppose, on the basis of that expectation, he invests in the Bond, \nbut interest rate turns out to be 12%, six years from now, then what will be his potential loss\/gain if company extends the life of bond another 6 years [RTP Nov. 2018] \nAnswer: \n(a) If the current interest rate is 896, the company will not extend the duration of Bond and the maximum amount the investor would be ready to pay will be: \n= \u00a3 1,000 PVIFA (8%, 6) + \u00a310,000 PVIF (8%,6) \n= \u00a31,000 \u00d7 4.623 + \u00a310,000 \u00d7 0.630 \n= \u00a34,623 + \u00a3 6,300 \n= \u00a310,923<\/p>\n (b) If the current interest rate is 1296, the companies will extend the duration of Bond. After six year the value of Bond will be =\u00a3 1,000 PVIFA (1296,6) + \u00a310,000 PVIF (1296,6) \n= \u00a31,000 \u00d7 4.111 + \u00a310,000 \u00d7 0.507 \n= \u00a3 4,111 + \u00a3 5,070 \n= \u00a3 9,181 \nPotential gain = \u00a39,181 – \u00a310.923 = -\u00a31,742 \nThus, potential loss will be \u00a31,742<\/p>\n Question 9. \nOn 31st March 2013, the following information about bond is available: \n \ni. If 10 year yield is 7.5% p.a., what price the Zero coupon Bond would fetch on 31st March 2013? \nii. What will be the annualized yield if the T-Bill is traded @ Rs. 98,500? \niii. If 10.71% GOI 2023 Bond having yield to maturity is 8% what price would it fetch on April 1, 2013 (after coupon payment on 31st March)? \niv. If 10% GOI 2018 Bond having yield to maturity is 8%, what price would it fetch on April 1, 2013 (after coupon payment on 31st March)? [May 2015][8 Marks] \nAnswer: \n(i) Price of Zero coupon bond on 31.3.2013: \n= 10,000 PVIF (7.5%, 10) \n= 10,000 \u00d7 0.4852 \n= Rs. 4,852<\/p>\n (ii) Annualized yield on T-Bill = \\(\\frac{F-P}{P} \\times \\frac{365}{M}\\) \u00d7 100 \n\\(\\frac{1,00,000-98,500}{98,500} \\times \\frac{365}{81}\\) \u00d7 100 = 6.<\/p>\n (iii) 10.71 PVIFA (8%, 10) + 100 PVIF (8%, 10) \n= 10.71 \u00d7 6.7101 + 100 \u00d7 0.4632 \n= 71.87 + 46.32 \n= Rs. 118.19<\/p>\n (iv) 5 PVIFA (496,10) + 100 PVIF (4%, 10) \n= 5 \u00d7 8.111 + 100 \u00d7 0.6756 \n= 40.56 + 67.56 \n= Rs.108.12<\/p>\n <\/p>\n Question 10. \nConsider a bond selling at its par value of \u20b9 1,000, with 6 years to maturity and a 7% coupon rate (with annual interest payment). \n(a) What is bond\u2019s duration? [May 2009] [6 Marks] \n(b) If the YTM of the bond in (a) above increases to 10%, how it affects the bond\u2019s duration? And why? [3 Marks] \nAnswer: \n(i) Determination of Duration of the Bond: \nThe following steps are to be taken: \nStep 1: Calculation of YTM (Yield to maturity). \nSince, the coupon rate is 7\u00b0-6 and bond is redeemable at par, and the price of the bond is Rs. 1,000 i.e. the bond is selling at par therefore the YTM ‘ will be 7%.<\/p>\n Step 2 : Calculation of Duration. \nThe duration of a bond is the weighted average of the time it takes to return the investor\u2019s money. The present values of cash flows are to be taken as weights (w).<\/p>\n Year Cash flows(Rs.) PVIF@ PV of cash flows (?) Weighted Time \n<\/p>\n Duration = \\(\\frac{\\text { Weighted Time }}{\\text { Purchase Price }}=\\frac{\\sum a d}{\\sum d}=\\frac{\\text { Rs. } 5,100}{\\text { Rs.1,000 }}\\) = 5.10 Years<\/p>\n Alternative Method for determination of Duration:<\/p>\n \n\n\nFormula method<\/td>\n | Where,<\/td>\n<\/tr>\n | \nDuration = \\( \\frac{1+y}{y-}-\\frac{(1+y)+\\text { Period }(c-y)}{c\\left[(1+y)^{\\text {Period }}-1\\right]+y} \\)<\/p>\n <\/td>\n | y = Yield to maturity \nc = Coupon rate<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nDuration = \\(\\frac{1+0.07}{0.07}-\\frac{(1+0.07)+6(0.07-0.07)}{0.07\\left[(1+0.07)^6-1\\right]+0.07}\\) \n= \\(\\frac{1.07}{0.07}-\\frac{1.07}{0.10505}\\) \n= 15.2857 – 10.1855 = 5.10 Years (approx.)<\/p>\n (ii) Effect of increase in YTM on duration of the Bond: \nThe calculations are similar to first part except changes in Present value factors. \n \nDuration = \\(\\frac{\\text { Weighted Time }}{\\text { Purchase Price }}=\\frac{\\sum a d}{\\sum d}=\\frac{\\text { Rs. } 4369.751}{\\text { Rs. } 869.364}\\) = 5.025 Years<\/p>\n Alternative Method for determination of Duration:<\/p>\n \n\n\nFormula method<\/td>\n | Where<\/td>\n<\/tr>\n | \nDuration = \\( \\frac{1+y}{y}-\\frac{(1+y)+\\operatorname{Period}(c-y)}{c\\left[(1+y)^{\\text {Period }}-1\\right]+y} \\)<\/td>\n | y = Yield to maturity \nc = Coupon rate<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nDuration = \\(\\frac{1+0.1}{0.1}-\\frac{(1+0.1)+6(0.07-0.1)}{0.07\\left[(1+0.1)^6-1\\right]+0.1}\\) \n= \\(\\frac{1.1}{0.1}-\\frac{.92}{0.154}\\) \n= 11 – 5.975 = 5.025 Years (approx.) \nThe duration of bond decreases, reason being the receipt of slightly higher portion of one\u2019s investment on the same intervals as the present value or purchase price is less.<\/p>\n Question 11. \nMr. A will need \u20b9 1,00,000 after two years for which he wants to make one time necessary investment now. He has a choice of two types of bonds. Their details are as below:<\/p>\n \n\n\n<\/td>\n | Bond X<\/td>\n | Bond Y<\/td>\n<\/tr>\n | \nFace value<\/td>\n | \u20b9 1,000<\/td>\n | \u20b9 1,000<\/td>\n<\/tr>\n | \nCoupon<\/td>\n | 7% payable annually<\/td>\n | 8% payable annually<\/td>\n<\/tr>\n | \nYears to maturity<\/td>\n | 1<\/td>\n | 4<\/td>\n<\/tr>\n | \nCurrent price<\/td>\n | \u20b9 972.73<\/td>\n | \u20b9 936.52<\/td>\n<\/tr>\n | \nCurrent yield<\/td>\n | 10%<\/td>\n | 10%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n Advice Mr. A whether he should invest all his money in one type of bond or he should buy both the bonds and, if so, in which quantity? \nAssume that there will not be any call risk or default risk. [Nov. 2015] [6 Marks] \nAnswer: \nStep 1: Determination of duration of the bonds available for investment. \nDuration of the bond X: \nSince the year to maturity of Bond X is one year, therefore all the cash flows will be at the end of 1st year only. Hence, the duration will be 1 year.<\/p>\n Duration of the bond Y: \n \nDuration = \\(\\frac{\\text { Weighted Time }}{\\text { Purchase Price }}=\\frac{\\sum a d}{\\sum d}=\\frac{\\text { Rs. } 3,335.824}{\\text { Rs. } 936.584}\\) = 3.5617 Years<\/p>\n Step 2 : Determination of investment to be made today to meet obligation after 2 years: \n= Amount of obligation \u00d7 PVIF(10% 2)<\/sub> \n= Rs. 1,00,000 \u00d7 0.8264 \n= Rs. 82,640<\/p>\nStep 3 : Determination of proportion of investment in Bond X & Bond Y \nThe duration of both the bonds is different and the duration of liabilities is 2 years. Our objective is to match the duration of the liability with the duration of investment in bonds. Therefore, the weighted average of duration of bonds should be equal to 2 years. \nLet x1<\/sub> be the investment in Bond X and therefore investment in Bond Y shall be (1 – x1<\/sub>). The proportion of investment in these two bonds shall be computed as follows: \nRequired duration= [x1<\/sub> \u00d7 Duration of Bond X] + [(1 – x1<\/sub>) \u00d7 Duration of Bond Y] \n2 = x1<\/sub>(1) + (1 – x1<\/sub>) 3.5617 \nx1<\/sub> = 0.6096 = 61% (appx.) \nTherefore, 61 % investment should be made in Bond X and balance 39% in Bond Y.<\/p>\nStep 4 : Investments in Bond X and Bond Y \n \nMr. A must invest in both the bonds in above manner and remain invested for 2 years. Since the duration of Bond X is one year, therefore he should reinvest at the end of first year.<\/p>\n Question 12. \nThe following data are available for three bonds A, B and C. These bonds are used by a bond portfolio manager to fund an outflow scheduled in 6 years. Current yield is 9%. All bonds have face value of Rs. 100 each and will be redeemed at par. Interest is payable annually.<\/p>\n \n\n\nBond<\/td>\n | Maturity (years)<\/td>\n | Coupon rate<\/td>\n<\/tr>\n | \nA<\/td>\n | 10<\/td>\n | 10%<\/td>\n<\/tr>\n | \nB<\/td>\n | 8<\/td>\n | 11%<\/td>\n<\/tr>\n | \nC<\/td>\n | 5<\/td>\n | 9%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n (i) Calculate the duration of each bond. \n(ii) The bond portfolio manager has been asked to keep 45% of the portfolio money in Bond A. Calculate the percentage amount to be invested in bonds B and C that need to be purchased to immunize the portfolio. \n(iii) After the portfolio has been formulated, an interest rate change occurs, increasing the yield to 11%. The new duration of these bonds are: Bond A = 7.15 years, Bond B = 6.03 years and Bond C= 4.27 years. \nIs the portfolio still immunized? Why or why not? \n(iv) Determine the new percentage of B and C that are needed to immunize the portfolio. Bond A remaining at 45% of the portfolio. \nPresent values be used as follows: [Nov. 2018] [12 Marks] \n \nAnswer: \n(i) Determination of duration of the bonds available for investment. \n(a) Bond A: \n \nDuration = \\(\\frac{\\text { Weighted Time }}{\\text { Purchase Price }}=\\frac{\\sum a d}{\\sum d}=\\frac{\\mathbf{R s . 7 3 6 0 . 2 4}}{\\text { Rs.106.404 }}\\) = 6.863 Years<\/p>\n (b) Bond B: \n \nDuration = \\(\\frac{\\text { Weighted Time }}{\\text { Purchase Price }}=\\frac{\\sum a d}{\\sum d}=\\frac{\\text { Rs. } \\mathbf{6 4 8 . 2 2}}{\\text { Rs. } \\mathbf{1 1 1 . 0 7 4}}\\) = 5.8359 Years<\/p>\n (c) Bond C: \n \nDuration = \\(\\frac{\\text { Weighted Time }}{\\text { Purchase Price }}=\\frac{\\sum a d}{\\sum d}=\\frac{\\mathrm{R s . 4 2 4}}{\\mathrm{R s . 1 0 0}}\\) = 4.24 Years (approx.)<\/p>\n \n\n\nFormula method<\/td>\n | Where<\/td>\n<\/tr>\n | \nDuration = \\( \\frac{1+y}{y}-\\frac{(1+y)+\\text { Period }(c-y)}{c\\left[(1+y)^{\\text {Periad }}-1\\right]+y} \\)<\/td>\n | y = Yield to maturity \nc = Coupon rate<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/p>\n (ii) Determination of proportion of investment in Bond B & Bond C given that 45% is invested in Bond A \nThe duration of the bonds is different and the duration of liabilities is 6 years. Our objective is to match the duration of the liability with the duration of investment in bonds. Therefore, the weighted average of duration of bonds should be equal to 6 years. \nLet x1<\/sub> be the investment in Bond B and therefore investment in Bond C shall be (1 – 0.45 – x1<\/sub>) as 45% is invested in Bond A. The proportion of investment in these two bonds shall be computed as follows:<\/p>\nRequired duration \n= [0.45 \u00d7 Duration of Bond A]+ [x1<\/sub> x Duration of BondB] + [(0.55 – x1<\/sub>) \u00d7 Duration of Bond C] = 6 \n0.45 \u00d7 6.863 + x1<\/sub>(5.8354)+ (0.55 – x1<\/sub>) 4.24 = 6 \n3.08835 + 5.8354x1<\/sub> + 2.332 – 4.24x1<\/sub> = 6 \n5.42035 + 1.5954 x1<\/sub> = 6 \n1.5954 x1<\/sub> =0.57965 \nx1<\/sub> = 0.3633 = 36% (approx.)<\/p>\nTherefore, 45% investment should be made in Bond A, 36% investment should be made in Bond B and balance 19% in Bond C. \nWeighted Duration = WA<\/sub> (DA<\/sub>) + WB<\/sub> (DB<\/sub>) + WC<\/sub> (DC<\/sub>) \n= 0.45(6.863) + 0.36(5.8354) + 0.19(4.24) \n= 6 Yrs. App.<\/p>\n(iii) Weighted Duration of the portfolio, if the Yield changes to 11% and the new duration of the three Bonds are given as under:<\/p>\n \n\n\nBond<\/td>\n | Duration<\/td>\n<\/tr>\n | \nA<\/td>\n | 7.15<\/td>\n<\/tr>\n | \nB<\/td>\n | 6.03<\/td>\n<\/tr>\n | \nC<\/td>\n | 4.27<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n Weighted Duration = WA<\/sub> (DA<\/sub>) + WB<\/sub> (DB<\/sub>) + WC<\/sub> (DC<\/sub> ) \n= 0.45(7.15) + 0.36(6.03) + 0.19(4.27) \n= 6.1996 \nThe Liability is not immunized as the duration of Bond A with highest maturity and highest weight has increased thereby increasing the duration of the portfolio and since it is slightly beyond 6 years the liability is not immunized.<\/p>\n(iv) New percentage ofB and C: Let x1<\/sub> be the investment in Bond B and there-fore investment in Bond C shall be (1- 0.45 – x1<\/sub>) as 45% is invested in Bond A. The proportion of investment in these two bonds shall be computed as follows: \nRequired duration \n= [0.45x Duration of Bond A]+ [x1<\/sub> \u00d7 Duration of Bond B] + [(0.55 – x1<\/sub>) \u00d7 Duration of Bond C] = 6 \n= 0.45 \u00d7 7.15 + x1<\/sub>(6.03)+ (0.55 – x1<\/sub>) 4.27 \n= 6 3.2175 + 6.03x1<\/sub> + 2.3485 – 4.27x1<\/sub> \n= 6 5.566 + 1.76x = 6 1.76x1<\/sub> = 0.434 \nx = 0.2466 = 24.66% \nTherefore, 45% investment should be made in Bond A, 24.66% investment should be made in Bond B and balance 30.34% in Bond C. \nWeighted Duration = WA<\/sub> (DA<\/sub>) + WB<\/sub> (DB<\/sub>) + WC<\/sub> (DC<\/sub>) \n= 0.45(7.15) + 0.2466(6.03) + 0.3034(4.27) \n= 6 Yrs.<\/p>\n<\/p>\n Question 13. \nThe following data is available for a bond:<\/p>\n \n\n\nFace value<\/td>\n | \u20b9 1,000<\/td>\n<\/tr>\n | \nCoupon Rate<\/td>\n | 11%<\/td>\n<\/tr>\n | \nYears to Maturity<\/td>\n | 6<\/td>\n<\/tr>\n | \nRedemption Value<\/td>\n | \u20b9 1,000<\/td>\n<\/tr>\n | \nYield to Maturity<\/td>\n | 15%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n (Round-off your answers to 3 decimals) \nCalculate the following in respect of the bond: \n(i) Current Market Price. \n(ii) Duration of the Bond. \n(iii) Volatility of the Bond. \n(iv) Expected market price if increase in required yield is by 100 basis points, \n(v) Expected market price if decrease in required yield is by 75 basis points. [Nov. 2015] [5 Marks] \nAnswer: \n(i) Current Market Price = \\(\\frac{\\text { Coupon Interest }}{\\text { Yield } \\%}\\) \n= \\(\\frac{110}{15 \\%}\\) \n= \u20b9 733.33<\/p>\n (ii) Determination of Duration of the Bond: \nThe following steps are to be taken: \nStep 1 Calculation of YTM (Yield to maturity). \nIt is given in the question as 1596 \nStep 2 Calculation of Duration. \nThe duration of a bond is the weighted average of the time it takes to return the investor\u2019s money. The present values of cash flows are to be taken as weights (w). \n \nDuration = \\(\\frac{\\text { Weighted Time }}{\\text { Purchase Price }}=\\frac{\\sum a d}{\\sum d}=\\frac{\\text { Rs. } 3883.10}{\\text { Rs. } 848.59}\\)4.576 Yrs. \nAlternative Method for determination of Duration:<\/p>\n \n\n\nFormula method<\/td>\n | Where,<\/td>\n<\/tr>\n | \nDuration = \\( \\frac{1+y}{y}=\\frac{(1+y)+\\text { Period }(c-y)}{c\\left[(1+y)^{\\text {Period }}-1\\right]+y} \\)<\/td>\n | y = Yield to maturity \nc = Coupon rate<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nDuration = \\(\\frac{1+0.15}{0.15}-\\frac{(1+0.15)+6(0.11-0.15)}{0.11\\left[(1+0.15)^6-1\\right]+0.15}\\) \n= \\(\\frac{1.15}{0.15}-\\frac{0.91}{02944}\\) \n= 7.6667 – 3.091 = 4.576 Years (approx.)<\/p>\n (iii) Volatility of the Bond \n \nThe negative sign indicates that the price will be inversely related to the change in interest rates and the number 3.979 indicates the magnitude of the sensitivity. This means that for every 100 basis points i.e. 1% rise in interest rates the price of the bond will fall approximately by 3.979% and vice versa.<\/p>\n (iv) Expected Market price if increase in requiredyield is by 100 basis points \n= (-) 3.979 \u00d7 \\(\\frac{100}{100}\\) = -3.979% \n848. 59 \u00d7 3.979% = \u20b9 33.77 \n= Then Market Price will fall by Rs. 33.77 and it will be = 848.59 – 33.77 \n= \u20b9 814.82<\/p>\n (v) Expected Market Price if Decrease in requiredyield is by 75 basis points \n(-) 3.979 \u00d7 \\(\\frac{100}{100}\\) = 2.984% \n= 848.59 \u00d7 2.984% = 25.32 \n= Therefore Market Price will rise by Rs. 25.32 and it will be = 848.59 + 25.32 = ? 873.91<\/p>\n Question 14. \nXL Ispat Ltd. has made an issue of 14 per cent non-convertible debentures on January 1, 2007. These debentures have a face value of ? 100 and is currently traded in the market at a price of \u20b9 90. \nInterest on these NCD will be paid through post-dated cheques dated June 30 and December 31. Interest payments for the first 3 years will be paid in advance though post-dated cheques while for the last 2 years, post-dated cheques will be issued at the third year. The bond is redeemable at par on December 31, 2011 at the end of 5 years. \nRequired: \n(i) Estimated the current yield at the YTM of the bond. \n(ii) Calculate the duration of the NCD. \n(iii) Assuming that intermediate coupon payments are, not available for reinvestment calculate the realized yield on the NCD. [Nov. 2008] [6 Marks] \nAnswer: \n(i) Current yield: \n= (Coupon Interest\/Market Price) \u00d7 100= (14\/90) \u00d7 100 = 15.55%<\/p>\n (ii) Determination of Duration of the Bond: \nThe following steps are to be taken: \nStep 1: Calculation of YTM (Yield to maturity). \nYTM in this case shall be calculated by interpolation. Since, the coupon rate is 1% half yearly and bond is redeemable at par, and the price of the bond is Rs. 90 i.e. the bond is selling below par therefore the YTM will be more than 1% half yearly and as per the current yield also it is 15.55% p.a so the first trial is assumed at 7.5%. \nHalf yearly Interest (I) = Rs. 100 \u00d7 = Rs. 7 \nRedemption Value (RV) = Rs. 100 \nMaturity Period (n)= 5 Years =10 half years<\/p>\n Accordingly, Present value of future inflows can be calculated as \n= \u20b9 7 (PVIFA(7.5%, 10)<\/sub>) + \u20b9 100 \u00d7 PVIF(7.5%,10)<\/sub> \n= \u20b9 7 \u00d7 6.8641 + \u20b9 100 \u00d7 0. 4852 \n= \u20b9 48.0487 + 48.52 \n= \u20b9 96.568<\/p>\nAlternative Method \n \nSince the present value is required to be brought down, the next trial should be at higher rate of interest. Taking 9%, the present value will be: \n= \u20b9 7 \u00d7 PVIFA(9% 10)<\/sub> + \u20b9 100 \u00d7 PVIF(9% 10)<\/sub> \n= \u20b9 7 \u00d7 6.418 + \u20b9 100 \u00d7 0.4224 \n= \u20b9 44.93 + 42.24 \n= \u20b9 87.17<\/p>\nCalculation of Yield to Maturity (YTM):<\/p>\n \n\n\nYield<\/td>\n | Value (Rs.)<\/td>\n<\/tr>\n | \n7.5%<\/td>\n | 96.57<\/td>\n<\/tr>\n | \n9u<\/sup>o<\/td>\n87.17<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n YTM at Rs. 90 can be calculated using interpolation as pei the manner given below \nBy interpolation, the YTM is \n= 7.5% + \\(\\frac{96.57-90}{96.57-87.17}\\) \u00d7 (9% – 7.5%) \n= 7.5% + \\(\\frac{6.57}{9.4}\\) \u00d7 (1.5%) \n= 8.548% semi annual \nTherefore, annualized ytm = 8.548% \u00d7 2=17.10% app.<\/p>\n Step 2: Calculation of Duration. \nThe duration of a bond is the weighted average of the time it takes to return the investor\u2019s money. The present values of cash flows are to be taken as weights (w). \n \n= 3.682 yrs.<\/p>\n Alternative Method for determination of Duration:<\/p>\n \n\n\nFormula Method<\/td>\n | Where,<\/td>\n<\/tr>\n | \nDuration = \\( \\frac{1+y}{y}-\\frac{(1+y)+\\text { Period }(c-y)}{c\\left[(1+y)^{\\text {Period }}-1\\right]+y} \\)<\/td>\n | Y = Yelid to maturity \nc = Coupon rate<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nDuration = \\(\\frac{1+0.0855}{0.0855}-\\frac{(1+0.0855)+10(0.07-0.0855)}{0.07\\left[(1+0.0855)^{10}-1\\right]+0.0855}\\) \n= \\(\\frac{1.0855}{0.0855}-\\frac{0.9305}{0.1745}\\) \n= 12.696 – 5.332= 7.364 half Years (approx.) = \\(\\frac{7.364}{2}\\) = 3.682 year<\/p>\n (i) If the interest received is not reinvested then realized yield can be calcu-lated as follows: \nHalf yearly Interest (I) = Rs. 100 \u00d7 \\(\\frac{7}{100}\\) = Rs. 7<\/p>\n (ii) Redemption Value (RV) = Rs. 100<\/p>\n (iii) Maturity Period (n) = 5 Years =10 half years<\/p>\n (iv) Total amount from interest = 7 \u00d7 10 = Rs. 70 \nTotal realized Value = Rs. 170 \nRealized Yield. 170 = 90 (1 + r)5 \nSolving for r: \nr = 13.5696<\/p>\n Question 15. \nThe Nominal value of 12% bonds issued by a company is Rs.100. The bonds are redeemable at Rs. 105 at the end of year 5. Coupons are paid annually. \nDetermine the duration and convexity of the bond at required annual yield rate of 10%. [Practice question] \nAnswer: \n(i) Determination of duration and convexity of the bond: \n<\/p>\n <\/p>\n Question 16. \nThe following is the yield structure of AAA rated debenture: \nPeriod-Yield (%) \n3 months-8.5%. \n6 months-9.25 \n1 year-10.50 \n2 years-11.25 \n3 years and above-12.00 \n(i) Based on the expectation theory calculate the implicit one-year forward rates in year 2 and year 3. \n(ii) If the interest rate increases by 50 basis points, w hat 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 \u20b9 1,000. [Nov. 2008] [4 Marks] \nAnswer: \n(i) Implicit 1 year forward rates for year 2 and year 3 \n<\/p>\n (ii) If fairly priced at \u20b9 1,000 and rate of interest increases to 12.596, the percentage change will be as follows: \n<\/p>\n Question 17. \nConsider the following data for Government Securities: \n \nCalculate the forward interest rates. [May 2010] [8 Marks] \nAnswer: \nTo get forward interest rates, \n(i) For 1 year, the one year Government Security. \n\u20b9 91,000 = \u20b9 1,00,000\/(1 + r) \nr = 0.099 \nr = 9.9%<\/p>\n (ii) The two years Government Security \n\u20b9 99,000 = (\u20b9 10,500\/1.099) + (\u20b9 1,10,500\/(1.099) (1+r)) \nr = 0.124 \nr = 12.4%<\/p>\n (iii) The three years Government Security \n\u20b9 99,500 = (11,000\/1.099) + [(\u20b9 11,000\/1.099) (1.124)] + [(\u20b9 1,11,000\/1.099) (1.124(1 +r)] \nr = 0.115 \nr = 11.5%<\/p>\n (iv) The four years Government Security \n\u20b9 99,000 = (\u20b9 11,500\/1.099) + [(\u20b9 11,500\/1.099) (1.124)] + [(\u20b9? 11,500\/1.099) (1.124) (1.115)] + [(\u20b9 1,11,500\/1.099) (1.124) (1.115) (1 + r)] \nr = 0.128 \nr = 12.8%<\/p>\n Question 18. \nSonic Ltd. issued 8% 5 year bonds of Rs. 1,000 each having a maturity of 3 year. The present rate of interest is 12% for one year tenure. It is expected that forward rate of interest for one year tenure is going to fall by 75 basis points and further by 50 basis points for next year. This bond has a beta value of 1.02 and is more popular in the market due to less credit risk. \nCalculate: \n(i) Intrinsic value of bond. \n(ii) Expected price of bond in the market. [Nov. 2013] [Nov. 2018 old syllabus] [5 Marks] \nAnswer: \nThe following information is available :<\/p>\n \n\n\nFace Value<\/td>\n | 1000<\/td>\n<\/tr>\n | \nCoupon rate<\/td>\n | 8%<\/td>\n<\/tr>\n | \nRemaining Life<\/td>\n | 3 Years<\/td>\n<\/tr>\n | \nPresent rate of Interest<\/td>\n | 12%<\/td>\n<\/tr>\n | \nForward rate after one year<\/td>\n | 11.25% (12 – 0.75)<\/td>\n<\/tr>\n | \nForward rate after 2 years<\/td>\n | 10.75% (11.25 – 0.50)<\/td>\n<\/tr>\n | \nBeta<\/td>\n | 1.02<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n (i) Intrinsic Value of the Bond: \n<\/p>\n The intrinsic value of the Bond is Rs. 918.27<\/p>\n (ii) Expected Price of the Bond: \n= Intrinsic value \u00d7 Beta \n= 918.27 \u00d7 1.02 \n= Rs. 936.64<\/p>\n Question 19. \nSabanam Ltd. has issued convertible debenture with coupon rate 11%. Each debenture has an option to convert to 16 equity shares at any time until the date of maturity. Debentures will be redeemed at Rs.100 on maturity after 5 years. An investor generally requires a rate of return of 8% p.a. on a 5 year security. As an advisor, when will you advise the investor to exercise conversion for given market prices of the equity share of (i) Rs. 5 (ii) Rs. 6 and (iii) Rs. 7.10. [May 2018 New syllabus] [8 Marks]<\/p>\n \n\n\nCumulative PV factor for 8% for 5 year<\/td>\n | 3.993<\/td>\n<\/tr>\n | \nP.V factor for 8% for year 5<\/td>\n | 0.681<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n Answer: \nThe value of Debentures if conversion option is not exercised: \nArtnual Interest (I) = Rs. 100 \u00d7 \\(\\frac{11}{100}\\) = Rs. 11 \nRedemption Value (RV) = Rs. 100 \nMaturity Period (n) = 5 Years<\/p>\n Accordingly, Present value of future inflows can be calculated as \n= Rs. 11 PVIFA(8%5)<\/sub> + Rs. 100 PVIF(8% 5)<\/sub> \n= Rs. 11 3.993 + Rs. 100 0.681 \n= Rs. 43.923 + 68.10 \n= Rs. 112.023<\/p>\nThe value of Shares if conversion option is exercised at various prices:<\/p>\n \n\n\nS. No.<\/td>\n | If the price of the share is<\/td>\n | Com ersion Value<\/td>\n<\/tr>\n | \n(i)<\/td>\n | R.s. 5<\/td>\n | Rs. 80 (5 \u00d7 16)<\/td>\n<\/tr>\n | \n(ii)<\/td>\n | Rs. 6<\/td>\n | Rs. 96 (6 \u00d7 16)<\/td>\n<\/tr>\n | \n(iii)<\/td>\n | Rs. 7.10<\/td>\n | Rs. 113.60(7.1 \u00d7 16)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n Conclusion: Conversion value is more than straight value of the bond only at the price of Rs. 7.10, therefore the conversion option is exercisable only if the share price is Rs. 7.10.<\/p>\n <\/p>\n Question 20. \nPineapple Ltd. has Issued fully convertible 12 per cent debentures of \u20b9 5,000 face value, convertible into 10 equity shares. The current market price of the debentures is \u20b9 5,400. The present market price of equity shares is \u20b9 430. \nCalculate: \n(i) The conversion value [3 Marks] \n(ii) The conversion percentage premium [Nov. 2011] [3 Marks] \nAnswer:The following information is given in the question: \nFace Value of the Debenture : Rs. 5,000 \nCoupon Rate : 12% \nConversion Ratio: 10 Equity Shares for 1 Debenture \nMarket Price of the Debenture Rs. 5,400 \nMarket Price of Equity Share Rs. 430<\/p>\n (i) Calculation of Conversion Value per Debenture: \nConversion Value of Debenture = Value of Shares received per debenture \n= Market Price per share \u00d7 Conversion Ratio \n= 430 \u00d7 10 \n= Rs. 4,300<\/p>\n (ii) Calculation of Conversion Percentage premium: \nMarket Conversion Price = \\(\\frac{\\text { Market Price of the Debenture }}{\\text { Conversion Ratio }}\\) \n= \\(\\frac{R s .5,400}{10}\\) = Rs. 540<\/p>\n Conversion Premium per Share = Market Conversion Price – Market Price per Share \n= Rs. 540 – Rs. 430 \n= Rs. 110<\/p>\n Conversion Premium per Share = \\(\\frac{\\text { Conversion Premium per Share }}{\\text { Market Price per Share }}\\) \n= \\(\\frac{R s .110}{430}\\) \u00d7 100 \n= 25.58%<\/p>\n Question 21. \nThe data given below relates to a convertible bond:<\/p>\n \n\n\nFace Value<\/td>\n | \u20b9 250<\/td>\n<\/tr>\n | \nCoupon rates<\/td>\n | 12%<\/td>\n<\/tr>\n | \nNo. of shares per bond<\/td>\n | 20<\/td>\n<\/tr>\n | \nMarket price of share<\/td>\n | \u20b9 12<\/td>\n<\/tr>\n | \nStraight value of bond<\/td>\n | \u20b9 235<\/td>\n<\/tr>\n | \nMarket price of convertible bond<\/td>\n | \u20b9265<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n Calculate: \n(i) Stock value of bond. \n(ii) The percentage of downside risk. \n(iii) The conversion premium \n(iv) The conversion parity price of the stock. [Nov. 2008] [8 Marks] \nAnswer: \nThe following information is given in the question: \nFace Value of the Bond : Rs. 250 \nCoupon Rate : 12% \nConversion Ratio : 20 \nEquity Shares for 1 Bond \nMarket Price of the Convertible Bond : Rs. 265 \nMarket Price of Equity Share : Rs. 12 \nStraight Value of Bond : Rs. 235 \n(i) Calculation of Stock Value or Conversion Value of Bond: \nConversion Value of Bond = Value of Shares received per Bond \n= Market Price per share \u00d7 Conversion Ratio \n= 12 \u00d7 20 = Rs. 240<\/p>\n (ii) Percentage of Down side Risk \nMarket Price of the Bond = \\(\\frac{\\text { Market Price of the Bond-Straight Value of the Bond }}{\\text { Straight Value of the Bond }} \\) \u00d7 100 \n= \\(\\frac{R s .265-235}{235}\\) \u00d7 100 \n= 12.77%<\/p>\n (iii) Calculation of Conversion Percentage premium: \nMarket Conversion Price = \\(=\\frac{\\text { Market Price of the Bond }}{\\text { Conversion Ratio }}\\) \u00d7 100 \n= \\(\\frac{R s .265}{20}\\) = Rs. 13.25<\/p>\n Conversion Premium per Share = Market Conversion Price – Market Price per Share \n= Rs. 13.25 – Rs. 12 \n= Rs. 1.25<\/p>\n Conversion Percentage Premium = \\(\\frac{\\text { Conversion Premium per Share }}{\\text { Market Price per Share }}\\) \n= \\(\\frac{R s .1 .25}{12}\\) \u00d7 100 \n= 10.42%<\/p>\n (iv) The Conversion Parity Price Or the Market Conversion Price \nMarket Conversion Price = \\(\\frac{\\text { Market Price of the Bond }}{\\text { Conversion Ratio }}\\) \n= \\(\\frac{R s .265}{20}\\) = Rs. 13.25<\/p>\n <\/p>\n Question 22. \nThe following is the data related to 9% fully convertible (into equity shares) debentures issued by Delta Ltd. at Rs.1000<\/p>\n \n\n\nMarket price of 9% Debenture Rs.<\/td>\n | 1,000<\/td>\n<\/tr>\n | \nConversion Ratio (No. of shares)<\/td>\n | 25<\/td>\n<\/tr>\n | \nStraight value of 9% Debentures<\/td>\n | 800<\/td>\n<\/tr>\n | \nMarket price of Equity share on the date of conversion Rs.<\/td>\n | 30<\/td>\n<\/tr>\n | \nExpected Dividend per share Rs.<\/td>\n | 1<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n Calculate: \n(\u0430) Conversion value of Debenture; \n(b) Market conversion Price; \n(c) Conversion premium per share; \n(d) Ratio of conversion premium; \n(e) Premium over straight value of Debenture; \n(f) Favourable income differential per share and \n(g) Premium pay back period \nAnswer: \nThe following information is given in the question:<\/p>\n Face Value of the Debenture : Rs. 1,000 \nMarket price of the debenture : Rs. 1,000 \nCoupon Rate : 9% \nConversion Ratio : 25 Equity Shares for 1 debenture \nExpected dividend per share : Re. 1 \nMarket Price of Equity Share : Rs. 30 \nStraight Value of 9% debenture : Rs. 800<\/p>\n (a) Calculation of Stock Value or Conversion Value of Debenture: \nMarket Price of one equity share \u00d7 Conversion ratio = 30 \u00d7 25 \n= Rs. 750.<\/p>\n (b) Market Price of the debenture = \\(\\frac{\\text { Market Price of the debenture }}{\\text { Conversion Ratio }}\\) \n= \\(\\frac{\\text { Rs. } 1000}{25}\\) = Rs. 40<\/p>\n (c) Calculation of Conversion premium: \nConversion Premium per Share = Market Conversion Price – Market Price per Share \n= Rs. 40 – Rs. 30 \n= Rs. 10<\/p>\n (d) Ratio of conversion Premium \n\\(\\frac{\\text { Premium per share }}{\\text { Price of the share }} \\) \u00d7 100 \n= \\(\\frac{\\text { Rs. } 10}{30}\\) \u00d7 100 \n= 33.33%<\/p>\n (e) Premium over straight value of debenture \nMarket Conversion Price of the Share- Straight Price of the share based on straight value of bond i.e. Rs. 800\/25 = 32 \n= Rs. 8 per share \n= \\(\\frac{\\text { Rs. } 8}{32}\\) \u00d7 100 = 25% \nOr \n\\(\\frac{\\text { Market Price of the debenture }}{\\text { Straight value of debenture }}\\) – 1 = (\\(\\frac{R s .1000}{800}\\) – 1) \u00d7 100 = 25%<\/p>\n (f) Favourable income differential per Share: \n\\(\\frac{\\text { Coupon interest from debenture }- \\text { Conversion ratio } \\times \\text { Expected dividend per share }}{\\text { Conversion ratio }}\\) \u00d7 100 \n= \\(\\frac{90-25 \\times 1}{25}\\) = Rs. 2.6<\/p>\n (g) Premium pay back period \n\\(\\frac{\\text { Conversion premium per share }}{\\text { Favourable income differential per share }}=\\frac{\\text { Rs.10 }}{\\text { Rs.2.6 }}\\) = 3.846 years<\/p>\n Question 23. \nThe following is the data related to 8.5% fully convertible (into equity shares) debentures issued by JAC Ltd. at Rs.1000<\/p>\n \n\n\nMarket price of 9% Debenture Rs.<\/td>\n | 900<\/td>\n<\/tr>\n | \nConversion Ratio (No. of shares)<\/td>\n | 30<\/td>\n<\/tr>\n | \nStraight value of 9% Debentures<\/td>\n | 700<\/td>\n<\/tr>\n | \nMarket price of Equity share on the date of conversion Rs.<\/td>\n | 25<\/td>\n<\/tr>\n | \nExpected Dividend per share Re.<\/td>\n | 2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n Calculated: \n(a) Conversion value of Debenture; \n(b) Market conversion Price; \n(c) Conversion premium per share; \n(d) Ratio of conversion premium; \n(e) Premium over straight value of Debenture \n(f) Favourable income differential per share; and \n(g) Premium pay back period [Mock Test August 2018] [8 Marks] \nAnswer: \nThe following information is given in the question: \nFace Value of the Debenture : Rs. 1,000 \nMarket price of the debenture : Rs. 900 \nCoupon Rate Conversion Ratio : 8.5% \nExpected dividend per share : 30 \nEquity Shares for 1 debenture : Re. 1 \nMarket Price of Equity Share : Rs. 25 \nStraight Value of 9% debenture : Rs. 700 \n(a) Calculation of Stock Value or Conversion Value of Debenture: \nMarket Price of one equity share \u00d7 Conversion ratio = 25 \u00d7 30 = Rs. 750.<\/p>\n (b) Market Conversion Price = \\(\\frac{\\text { Market Price of the debenture }}{\\text { Conversion Ratio }}\\) \n= \\(\\frac{\\text { Rs. } 900}{30}\\) = Rs. 30<\/p>\n (c) Calculation of Conversion premium: \nConversion Premium per Share = Market Conversion Price – Market Price per Share \n= Rs. 30 – Rs. 25 = Rs. 5<\/p>\n (d) Ratio of conversion Premium \n\\(\\frac{\\text { Premium per share }}{\\text { Price of the share }}\\) \u00d7 100 = \\(\\frac{\\text { Rs. } 5}{25}\\) \u00d7 100 = 20%<\/p>\n (e) Premium over straight value of debenture \nMarket Conversion Price of the Share – Straight Price of the share based on straight value of bond i.e. Rs. 700\/30 = 23.33 \nRs. 30 – Rs. 23.33 = Rs. 6.67 per share \n= \\(\\frac{R s .6 .67}{23.33}\\) \u00d7 100 = 28.60% approx.<\/p>\n Or \\(\\frac{\\text { Market Price of the debenture }}{\\text { Straight value of debenture }}\\) – 1 = [\\(\\frac{R s .900}{700}\\) – 1] \u00d7 100 = 28.57%<\/p>\n (f) Favourable income differential per share: \n\\(\\frac{\\text { Coupon interest from debenture }- \\text { Conversion ratio } \\times \\text { Expected dividend per share }}{\\text { Conversion ratio }}\\) \u00d7 100<\/p>\n (g) Premium pay back period \n\\(\\frac{\\text { Conversion premium per share }}{\\text { Favourable income differential per share }}=\\frac{\\text { Rs. } 5}{\\text { Rs. } 1.833}\\) = 2.73 vears<\/p>\n <\/p>\n Question 24. \nGUI Ltd., AAA rated company has issued fully convertible bonds on the following terms, a year ago: \nFace value of bond : \u20b9 1,000 \nCoupon (interest rate) : 8.5% \nTime to Maturity (remaining) : 3 years \nInterest Payment : Annual at the end of year \nPrincipal Repayment : At the end of bond maturity \nConversion ratio (No. of shares per bond) : 25 \nCurrent market price per share : \u20b9 45 \nMarket price of convertible bond : \u20b9 1, 175 \nAAA rated company can issue plain vanilla bonds without corn ersion option at an interest rate of 9.5%. \nRequired: \nCalculate as of today: \n(i) Straight Value of bond. \n(ii) Conversion Value of the bond. \n(iii) Conversion Premium. \n(iv) Percentage of downside risk, \n(v) Conversion Parity Price. \n \n[May 2014] [4 + 1 + 1 + 1 + 1 = 8 Marks] \nAnswer: \nThe following information is given in the question: \nFace Value of the Bond : Rs. 1, 000 \nCoupon Rate : 85% \nConversion Ratio : 25 Equity Shares for 1 bond \nMarket Price of the Convertible : Rs. 1, 175 \nBond Market Price of Equity Share : Rs. 45 \nRemaining life of Bond ie. Maturity : 3yrs \nInterest payments : Anuual \nRedemption at maturity : At par \nThis question is different from previous as the straight value of Bond is required to be calculated and therefore maturity period and redemption price is also given in the question. \n(i) Calculation of Straight Value of Bond \nThe present value of future inflows (comprising both interest as well as redemption value) discounted at 9.5% is the straight value of the Bond. \nAnnual Interest (I) = Rs. 1000 \u00d7 \\(\\frac{8.5}{100}\\) = Rs. 85 \nRedemption Value (RV) = Rs. 1000 \nMaturity Period (n) = 3 Years<\/p>\n Accordingly, Present value of future inflows can be calculated as \n= \u20b9 85 \u00d7 PVIFA (9.5%,3) + \u20b9 1000 \u00d7 PVIF (9.5%,3) \n= \u20b9 85 \u00d7 2.5089 + \u20b9 1000 \u00d7 0.7617 \n= \u20b9 213.26 + 761.7 = \u20b9 974.96<\/p>\n (ii) Calculation of Stock Value or Conversion Value of Bond: \nConversion Value of Bond = Value of Shares received per Bond \n= Market Price per share \u00d7 Conversion Ratio \n= 25 \u00d7 45 \n= Rs. 1125<\/p>\n (iii) Calculation of Conversion premium: \nMarket Conversion Price = \\(\\frac{\\text { Market Price of the Bond }}{\\text { Conversion Ratio }}\\) \n= \\(\\frac{\\mathrm{Rs} .1175}{25}\\) = Rs. 47<\/p>\n Conversion Premium per Share = Market Conversion Price – Market Price per Share \n= Rs. 47 – Rs. 45 \n= Rs. 2<\/p>\n (iv) Percentage of Down side Risk \n\\(\\frac{\\text { Market Price of the Bond }- \\text { Straight Value of the Bond }}{\\text { Straight Value of the Bond }}\\) \u00d7 100 \n= \\(\\frac{\\text { Rs. } 1175-974.96}{974.96}\\) \u00d7 100 = 20.52%<\/p>\n (v) The Conversion Parity Price or the Market Conversion Price \nMarket Conversion Price = \\(\\frac{\\text { Market Price of the Bond }}{\\text { Conversion Ratio }}\\) \n= \\(\\frac{\\text { Rs. } 1175}{25}\\) = Rs. 47<\/p>\n Question 25. \nA Ltd. has issued convertible bonds, which carries a coupon rate of 14%. Each bond is convertible into 20 equity shares of the company A Ltd. The prevailing interest rate for similar credit rating bond is 8%. The convertible bond has 5 years maturity. It is redeemable at part at ? 100. \n \nYou are required to estimate: \n(Calculations be made up-to 3 decimal places) \n(i) current market price of the bond, assuming it being equal to its funda-mental value; \n(ii) Minimum market price of equity share at which bond holder should exercise conversion option; and \n(iii) duration of the bond. \nAnswer: \nThe following information is given in the question: \nFace Value of the Bond : Rs. 100 \nCoupon Rate : 14% \nConversion Ratio : 20 Equity Shares for 1 Bond \nRemaining life of Bond i.e. Maturity : 5 yrs. \nInterest payments : Annual \nRedemption at maturity : At Par<\/p>\n (i) Calculation of Current Market Price or the Straight Value of Bond \nThe present value of future inflows (comprising both interest as well as redemption value; discounted at 8% is the market price or the straight value of the Bond. \nAnnual Interest (I) = Rs. 100 \u00d7 \\(\\frac{14}{100}\\) = Rs. 14 \nRedemption Value (RV) = Rs. 100 \nMaturity Period (n) = 5 Years \nAccordingly, Present value of future inflows can be calculated as \n= \u20b9 14 \u00d7 PVIFA (896,5) + \u20b9 1000 \u00d7 PVIF (8%,5) \n= \u20b9 14 \u00d7 3.993 + \u20b9 100 \u00d7 0.681 \n= \u20b9 55.902 + 68.1 \n= \u20b9 124.002 = Rs. 124 (Approx.)<\/p>\n Alternatively: \nCurrent Market Price of Bond \n \n\u20b9 124<\/p>\n (ii) Minimum Price at which Bond holder should exercise Conversion: \nIt should be the Market conversion price which is calculated as below: \n\\(\\frac{\\text { Market Price of the Bond }}{\\text { Conversion ratio }}=\\frac{124.002}{20 \\text { shares }}\\) = \u20b9 6.20 Per Share<\/p>\n (iii) Duration of Bond (Formula method) \nFormula method \nDuration = \\(\\frac{1+y}{y}-\\frac{(1+y)+\\text { Period }(c-y)}{c\\left[(1+y)^{\\text {Period }}-1\\right]+y}\\)<\/p>\n Where, \ny = Yield to maturity \nc = Coupon rate<\/p>\n Duration = \\(\\frac{1+0.08}{0.08}-\\frac{(1+0.08)+5(0.14-0.08)}{0.14\\left[(1+0.08)^5-1\\right]+0.08}\\) \n= \\(\\frac{1.08}{0.08}-\\frac{1.38}{0.1457}\\) \n= 13.5 – 9.472 = 4.028 Years (approx)<\/p>\n <\/p>\n Question 26. \nXYZ company has current earnings of 13 per share with 5,00,000 shares outstanding. The company plans to issue 40,000, 7% convertible preference shares of \u20b9 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 \u20b9 21 per share. \n(i) What is preference shares\u2019 conversion value? \n(ii) What is conversion premium? \n(iii) Assuming that total earnings remain the same, calculate the effect of the Issue on the basic earning per share (a) before conversion (b) after conversion. \n(iv) If profits after tax increases by \u20b9 1 million what will be the basic EPS \n(a) before conversion and (b) on a fully diluted basis? [Nov. 2009] [8 Marks] \nAnswer: \nThe following information is given in the question: \nFace Value of the Share : Rs. 50 1% \nRate of Preference Share : 7% \nConversion Ratio : 2 Equity Shares for 1 Preference Share \nMarket Price of the Preference Share : Rs. 50 \nMarket Price of Equity Share : Rs. 21 \nNo. of Equity Shares Outstanding : 5,0, 000 \nEPS : Rs. 3 per Share \nTotal number of convertible preference shares to be issued : 40,000<\/p>\n (i) Calculation of Conversion Value of Preference Shares: \nConversion Value of Pref. Share = Value of equity Shares received per Pref. Share \n= Market Price per Equity share \u00d7 Conversion Ratio \n= Rs. 21 \u00d7 2 = Rs. 42<\/p>\n (it) Calculation of Conversion Percentage premiunv \nMarket Conversion Price = \\(\\frac{\\text { Market Price of the Pref. Share }}{\\text { Conversion Ratio }}\\) \n= \\(\\frac{R s .50}{2}\\) = Rs. 25 \nConversion Premium per Share = Market Conversion Price – Market Price per Share \n= Rs. 25 – Rs. 21 = Rs. 4 \nConversion Percentage Permium = \\(\\frac{\\text { Conversion Premium per Share }}{\\text { Market Price per Share }}\\) \n= \\(\\frac{R s .4}{21}\\) \u00d7 100 \n= 19.05%<\/p>\n (iii) Statement of EPS before Conversion<\/p>\n \n\n\nParticulars<\/td>\n | Amount (\u20b9)<\/td>\n<\/tr>\n | \nTotal earning [3 \u00d7 5,00,000]<\/td>\n | 15,00,000<\/td>\n<\/tr>\n | \n(-) Preference dividend (40,000 \u00d7 50 \u00d7 1%)<\/td>\n | (1,40,000)<\/td>\n<\/tr>\n | \nEarnings for Equity Shareholders<\/td>\n | 13,60,000<\/td>\n<\/tr>\n | \nNo. of Equity Shares<\/td>\n | 5,00,000<\/td>\n<\/tr>\n | \nEPS<\/td>\n | 2.72<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n Statement of EPS After Conversion<\/p>\n \n\n\nParticulars<\/td>\n | Amount (\u20b9)<\/td>\n<\/tr>\n | \nTotal earning<\/p>\n No. of Equity shares [5,00,000 + (40,000 \u00d7 2)]<\/td>\n | 15,00,000 5,80,000<\/td>\n<\/tr>\n | \nEPS<\/td>\n | 2.586<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n (iv) If Profits increase by 10 Lakhs \nStatement of EPS before Conversion<\/p>\n \n\n\nParticulars<\/td>\n | Amount (\u20b9)<\/td>\n<\/tr>\n | \nTotal earning [(3 \u00d7 5,00,000) + 10,00,000] \n(-) Preference dividend \nEarnings for Equity Shareholder \nNo. of Equity Shares<\/td>\n | 25,00,000<\/p>\n (1,40,000)<\/td>\n<\/tr>\n | \n23,60,000 \n5,00,000<\/td>\n<\/tr>\n | \nEPS<\/td>\n | 4.72<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n Statement of EPS after Conversion<\/p>\n \n\n\nParticulars<\/td>\n | Amount (\u20b9)<\/td>\n<\/tr>\n | \nTotal earning<\/p>\n No. of Equity Shares [5,00,000 + (40,000 \u00d7 2)]<\/td>\n | 25,00,000<\/p>\n 5,80,000<\/td>\n<\/tr>\n | \nEPS<\/td>\n | 4.31<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n Question 27. \nP Ltd. has current earnings of \u20b9 6 per share with 10,00,000 shares outstanding. The company plans to issue 80,000,8% convertible preference shares of \u20b9 100 each at par. The preference shares are convertible into 2 equity shares for each preference share held. The equity share has a current market price of \u20b9 42 per share. Calculate: \n(i) What is preference share\u2019s conversion value? \n(ii) What is conversion premium? \n(iii) Assuming that total earnings remain the same, calculate the effect of the issue on the basic earnings per share (A) before conversion (B), after conversion. \n(iv) If profits after tax Increases by \u20b9 20 Lakhs what will be the basic EPS, (A) before conversion and (B) on a fully diluted basis? [May 2017] [8 Marks] \nAnswer: \nThe following information is given in the question: \nFace Value of the Share : Rs. 100 \nRate of Preference Dividend : 8% \nConversion Ratio : 2 2 Equity Shares for 1 Preference Share \nMarket Price of the Preference Share : Rs. 100 \nMarket Price of Equity Share : Rs. 42 \nNo. of Equity Shares Outstanding : 10,00,000 \nEPS : Rs. 6 per shares \nTotal number of convertible preference shares to be issued : 80,000<\/p>\n (i) Calculation of Conversion Value of Preference Shares: \nConversion Value of Pref. Share = Value of equity Shares received per Pref. Share \n= Market Price per Equity share \u00d7 Conversion Ratio \n= Rs. 42 \u00d7 2 = Rs. 84<\/p>\n (ii) Calculation of Conversion Percentage premium: \nMarket Conversion Price = \\(\\frac{\\text { Market Price of the Pref. Share }}{\\text { Conversion Ratio }}\\) \n= \\(\\frac{\\mathrm{Rs} \\cdot 100}{2}\\) = Rs. 50 \nConversion Premium per Share = Market Conversion Price – Market Price per Share \n= Rs. 50 – Rs. 42 = Rs. 8 \nConversion Premium Premium = \\(=\\frac{\\text { Conversion Premium per Share }}{\\text { Market Price per Share }}\\) \n= \\(\\frac{\\text { Rs. } 8}{42}\\) = 19.05%<\/p>\n (iii) Statement of EPS before Conversion<\/p>\n \n\n\nParticulars<\/td>\n | Amount (\u20b9)<\/td>\n<\/tr>\n | \nTotal earning [6 X 10,00,0001 (-) \nPreference dividend (80,000 \u00d7 100 \u00d7 8%)Earnings for Equity Shareholders \nNo. of Equity Shares<\/td>\n | 60,00,000 \n(6,40,000)<\/span><\/td>\n<\/tr>\n\n53,60,000 \n10,00,000<\/td>\n<\/tr>\n | \n<\/td>\n | 5.36<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n Statement of EPS after Conversion<\/p>\n \n\n\nParticulars<\/td>\n | Amount (\u20b9)<\/td>\n<\/tr>\n | \nTotal earning \nNo. of Equity shares (10,00,000 + (80,000 \u00d7 2)]<\/td>\n | 60,00,000 \n11,60,000<\/td>\n<\/tr>\n | \nEPS<\/td>\n | 5.17<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n (iv) If Profits increase by 20 Lakhs \nStatement of EPS before Conversion<\/p>\n \n\n\nParticulars<\/td>\n | Amount (\u20b9)<\/td>\n<\/tr>\n | \nTotal earning [6 \u00d7 10,00,0001 + 20,00,000] \n(-) Preference dividend (80,000 \u00d7 100 \u00d7 8%)Earnings for Equity Shareholder \nNo. of Equity Shares<\/td>\n | 80,00,000 \n(6,40,000)<\/td>\n<\/tr>\n | \n73,63,000 \n10,00,000<\/td>\n<\/tr>\n | \nEPS<\/td>\n | 7.36<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n Statement of EPS after Conversion<\/p>\n \n\n\nParticulars<\/td>\n | Amount (\u20b9)<\/td>\n<\/tr>\n | \nTotal earning \nNo. of Equity Shares [10,00,000 + (80,000 \u00d7 2)]<\/td>\n | 80,00,000 \n11,60,000<\/td>\n<\/tr>\n | \nEPS<\/td>\n | 6.90<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n <\/p>\n Question 28. \nABC Ltd. has \u20b9 300 million, 12 per cent bonds outstanding with six years remaining to maturity. Since interest rates are falling, ABC Ltd. is contemplating of refunding these bonds with a \u20b9 300 million issue of 6 year bonds carrying a coupon rate of 10 per cent. Issue cost of the new bonds will be \u20b9 6 million and the call premium is 4 per cent. \u20b9 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. [May 2009] [6 Marks] \nAnswer: \n1. Calculation of initial outlay:<\/p>\n \n\n\n<\/td>\n | \u20b9 (million)<\/td>\n<\/tr>\n | \na. Face value<\/td>\n | 300<\/td>\n<\/tr>\n | \nAdd: Call premium<\/td>\n | 12<\/td>\n<\/tr>\n | \nCost of calling old bonds<\/td>\n | 312<\/td>\n<\/tr>\n | \nb. Gross proceed of new issue<\/td>\n | 300<\/td>\n<\/tr>\n | \nLess: Issue costs<\/td>\n | 6<\/td>\n<\/tr>\n | \nNet proceeds of new issue<\/td>\n | 294<\/td>\n<\/tr>\n | \nc. Tax savings on call premium and unamortized cost 0.30 (12 + 9)<\/td>\n | 6.3<\/td>\n<\/tr>\n | \nInitial outlay = \u20b9 312 million – \u20b9 294 million – \u20b9 6.3 million<\/p>\n = \u20b9 11.7 million<\/td>\n | 6.3<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n 2. Calculations of net present value of refunding the bond:<\/p>\n \n\n\nSaving in annual interest expenses<\/td>\n | 7 (million)<\/td>\n<\/tr>\n | \n[300 \u00d7 (0.12-0.10)]<\/p>\n Less: Tax saving on interest and amortization<\/td>\n | 6.00<\/td>\n<\/tr>\n | \n0.30 \u00d7 [6 + (9 – 6)\/6]<\/td>\n | 1.95<\/td>\n<\/tr>\n | \nAnnual net cash saving<\/td>\n | 4.05<\/td>\n<\/tr>\n | \nPVIFA (7% 6 years)<\/td>\n | 4.766<\/td>\n<\/tr>\n | \nPresent value of net annual cash saving<\/td>\n | = \u20b9 19.30 million<\/td>\n<\/tr>\n | \nLess: Initial outlay<\/td>\n | = \u20b9 11.70 million<\/td>\n<\/tr>\n | \nNet present value of refunding the bond \nDecision: The bonds should be refunded.<\/td>\n | \u20b9 7.60 million<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n Question 29. \nM\/s. Earth Limited has 11% bond worth of \u20b9 2 crores outstanding with 10 years remaining to maturity. \nThe company is contemplating the issue of a \u20b9 2 crores 10 years bond carrying the coupon rate of 9% and use the proceeds to liquidate the old bonds. \nThe unamortized portion of issue cost on the old bonds is \u20b9 3 lakhs which can be written off no sooner the old bonds are called. The company is paying 30% tax and it\u2019s after tax cost of debt is 7%. Should Earth Limited liquidate the old bonds? \nYou may assume that the issue cost of the new bonds with be \u20b9 2.5 lakhs and the call premium is 5%. [May 2013] [6 Marks] \nAnswer: \n1. Computation of initial outlay:<\/p>\n \n\n\n<\/td>\n | <\/td>\n | (\u20b9 lakhs)<\/td>\n<\/tr>\n | \n(a)<\/td>\n | Face value<\/td>\n | 200.00<\/td>\n<\/tr>\n | \n<\/td>\n | Add: Call premium<\/td>\n | 10.00<\/td>\n<\/tr>\n | \n<\/td>\n | Cost of calling old bonds<\/td>\n | 210.00<\/td>\n<\/tr>\n | \n(b)<\/td>\n | Gross proceed of new issue<\/td>\n | 200.00<\/td>\n<\/tr>\n | \n<\/td>\n | Less: Issue costs<\/td>\n | 2.50<\/td>\n<\/tr>\n | \n<\/td>\n | Net proceeds of new issue<\/td>\n | 197.50<\/td>\n<\/tr>\n | \n(c)<\/td>\n | Tax savings on call premium and unamortized costs 0.30 (10 + 3)<\/td>\n | 3.90 lakhs<\/td>\n<\/tr>\n | \n<\/td>\n | Therefore, Initial outlay = \u20b9 \u00a0210 lakhs – \u20b9 \u00a0197.50 lakhs – \u20b9 \u00a03.90 lakhs<\/td>\n | <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n 2. Computation of net present value of refunding the bond:<\/p>\n \n\n\n<\/td>\n | \u20b9 lakhs<\/td>\n<\/tr>\n | \nSaving in annual interest expenses[\u20b9 200 (0.11 – 0.09)]<\/td>\n | 4.000<\/td>\n<\/tr>\n | \nLess: Tax saving on interest and amortization 0.30 [4 + (3 – 2.5)\/10]<\/td>\n | \u00a01.215<\/td>\n<\/tr>\n | \nAnnual net cash saving<\/td>\n | 2.785<\/td>\n<\/tr>\n | \nPVIFA (7%, 10 years)<\/td>\n | 7.024<\/td>\n<\/tr>\n | \nPresent value of net annual cash saving<\/td>\n | \u20b9 19.56 lakhs<\/td>\n<\/tr>\n | \nLess: Initial outlay<\/td>\n | \u20b9 8.60 lakhs<\/td>\n<\/tr>\n | \nNet present value of refunding the bond<\/td>\n | \u20b9 10.96 lakhs<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n Decision, Since the NPV of refunding the bond is favourable, the bonds should be refunded.<\/p>\n Question 30. \nTangent Limited is considering calling Rs. 3 crores of 30 years, Rs. 1000 bond issued 5 years ago with a coupon interest rate of 14 per cent. The bonds have a call price of Rs. 1,150 and had initially collected proceeds of Rs. 2.91 crores since a discount of Rs. 30 per bond was offered. The initial floating cost was Rs. 3,90,000. The company intends to sell Rs. 3 crores of 12 per cent coupon rate, 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. 4,25,000. The company is paying 40% tax and its after tax cost of debt is 8 per cent. As the new bonds must first be sold and then their proceeds to be Used to retire the old bonds, the company expects a two months period of overlapping interest during which interest must be paid on both the old and the new bonds. You are required to evaluate the bond retiring decision. [PVIFA8%,25<\/sub> = 10.675] [Nov. 2018] [8 Marks] \nAnswer: \n1. Computation of initial outlay:<\/p>\n\n\n\n<\/td>\n | (Rs. in lakhs)<\/td>\n<\/tr>\n | \n(a) Face value<\/td>\n | 300.00<\/td>\n<\/tr>\n | \nAdd: Call premium<\/td>\n | 45.00<\/td>\n<\/tr>\n | \nCost of calling old bonds<\/td>\n | 345.00<\/td>\n<\/tr>\n | \n(b) Gross proceed of new issue<\/td>\n | 300.00<\/td>\n<\/tr>\n | \nLess: Issue costs<\/td>\n | 4.25<\/td>\n<\/tr>\n | \nNet proceeds of new issue<\/td>\n | 295.75<\/td>\n<\/tr>\n | \n(c) Tax savings on call premium and unamortized costs 0.40 (45+10.75)(W.N.)<\/td>\n | 22.30<\/td>\n<\/tr>\n | \n(d) Overlapping Interest after tax (300 \u00d7 0.14 \u00d7 \\(\\frac{2}{12}\\)) (1-0.4)<\/td>\n | = 4.2<\/td>\n<\/tr>\n | \nTherefore, Initial outlay = \u20b9 345 + 4.2 – (\u20b9 295.75 + 22.30) 31.15<\/td>\n | <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n 2. Annual cash flow savings: (Rs. in Lakhs) \n(a) Old bond<\/p>\n \n\n\n(i) Interest cost after tax (300 \u00d7 0.14)(1 – 0.4)<\/td>\n | 25.20<\/td>\n<\/tr>\n | \n(ii) Tax saving on amortization of discount (9,00,000\/30) (0.40)<\/td>\n | 0.12<\/td>\n<\/tr>\n | \n(iii) Tax saving on amortization of floatation costs (390000\/30)(0.40)<\/td>\n | 0.052<\/td>\n<\/tr>\n | \nAnnual cost<\/td>\n | 25.028<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n (b) New bond<\/p>\n | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |