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Problem - 1• ABC currently pays a dividend of Rs 3 pershare which is expected to grow at anannual rate of 14% for 3 years and 11%for the next 3 years after which it will growat 4% per annum forever. What amountshould be paid for the stock if the rate ofreturn required by the equity investors is16%.
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Solution - 1Year Dividend Formula Dividend PV of Dividend (@16%)1 3*1.14 3.42 2.952 3*1.14*1.14 3.9 2.93 3*1.14*1.14*1.14 4.44 2.854 3*1.14*1.14*1.14*1.11 4.93 2.725 3*1.14*1.14*1.14*1.11*1.11 5.47 2.66 3*1.14*1.14*1.14*1.11*1.11*1.11 6.07 2.49Total Present Value of Dividend fornext 6 Years16.51
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Solution – 1 (Contd.)Dividend at the end of Year 7 6.07 * 1.04 6.31Market Price at the end of year 6 6.31/(0.16-0.04) 52.58Present Value of Market Price at the end of Year 6 at 16% 52.58/(1.16)621.58Total Value of the Stock 16.51+21.58 38.09
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Problem - 2• The shares of ABC are currently priced atRs.25. The Risk Free Rate of Return is8% and the market return is 20%. With thecompany having paid Rs.2 as the currentdividend and the company having agrowth rate of 8%, what is the value of theshare if its Beta is 0.7
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Solution – 2Expected Rate of Return 8 + 0.7 (20-8) 16.4Dividend for the Next Year 2 * 1.08 2.16Value of the Stock given the growth and Rate of Return 2.16/(0.164-0.08) 25.71Current Share Price in the Market 25Conclusion MarginallyUnderpriced
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Problem - 3• The profit after Tax for a firm is Rs.20,000.The dividend payout ratio is 50%. If thegrowth rate of earnings is 4% and thescrip trades at 2.5 times its EPS in themarket, what is the required rate of returnby equity share holders if the number ofoutstanding shares is 5000.
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Solution – 3EPS 20000/5000 4Market Price of the Share 2.5*4 10Dividend Payout Ratio 50%Dividend Paid Out 4*50% 2Dividend for Next period 2 * 1.04 2.08Required Rate of Return 2.08/10 + 0.04 24.8%
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Problem - 4• An Automobile Companyrecently paid a dividend ofRs.3 per share and it is a fairlyrisky company with a cost ofequity of 25%. A summary ofDividends and Earnings pershare is given to the right• Any new investment isexpected to yield a returncomparable to the cost ofequity. What is the estimationof growth rate based ondividends?Year Dividends Earnings2007 3 5.52006 2.8 4.52005 2.7 52004 2.4 42003 2.3 3.5
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Problem - 5• The Standard Deviation of XYZ stock is24% and its correlation coefficient with themarket portfolio is 0.5. The expectedreturn on the market is 16% with astandard deviation of 20%. If the risk freerate of return is 6% find the required rateof return on XYZ stock
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Solution – 5Beta Cov (A,M)/Var(M)Other formula for Beta using Correlation coefficient r r*SD(A)/SD(M)Beta from the problem 0.5*0.24/0.2 0.6Rate of Return 6 + 0.6 (16-6) 12%
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Problem - 6• A Financial institution issues two types ofbonds with one and three years maturityrespectively. The first pays Rs.10,000 ayear hence is now selling for Rs.8,929.The second which pays Rs.100 next year,Rs.100 after two years and Rs.1,100 atthe end of third year is now offered atRs.997.18. Find the implied interest ratesof these two bonds.
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Solution – 6Present value for Bond 1 10000/(1+k)Given present value 8929K for Bond 1 10000/8929 – 1 12%Given Present value for Bond 2 997.18Calculated present value from future returns 100/(1+k) + 100/(1+k)2+ 1100/(1+k)3Doing a Trial and Error the value of K for Bond 2 is 10.1%
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Problem - 7• A bond with a face value of Rs.100provides 12% annual return and paysRs.105 at the time of maturity which is 10years from now. If the investors requiredrate of return is 13%, at what price shouldthe company issue the bond?
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Solution – 7Interest every year 12No of years of Interest 10Present value of all the interests for the next 10 years 12/1.13 + 12/1.132+ ----------+12/1.1310Maturity value paid out 105Present value of the maturity amount 105/1.1310Total Present value of the Bond 96.087
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Problem - 8• A company is offering a bond with theissue price Rs.100, coupon rate of 12%with maturity period of 5 years. If the bondis to be redeemed at par and the investorfaces a 30% tax on income and 10%capital gains tax. Find the effective yield tomaturity for the investor
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Solution – 8Interest every year 12No of years of Interest 5Tax on the Interest every year 30% = 3.6Effective Interest after tax every year 8.4Present value of all the interests for the next 5 years (A) 8.4/(1+i) + 8.4/(1+i)2+ ----------+8.4/(1+i)5Maturity value paid out 100Present value of the maturity amount (B) 100/(1+i)5Total Present value of the Bond A+BSolving A+B = 100By Trial and Error method i = 8.4%
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Problem - 9• A company is contemplating a debenture issueon the following terms.• Face Value = Rs.100 per debenture• Coupon rates: Years 1-2 (5% p.a), Years 3-4(13% p.a), Years 5-7 (16% p.a)• Current market rate of interest on similardebentures is 15% p.a. The company proposesto price the issue so as to yield a compoundedreturn of 16% p.a to the investors. Find the issueprice assuming redemption on debenture at apremium of 10%.
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Solution - 9Year Coupon PV Formula PV of Dividend (@16%)1 5 5/1.16 4.312 5 5/1.1623.713 13 13/1.1638.334 13 13/1.1647.175 16 16/1.1657.616 16 16/1.1666.567 16 16/1.1675.66TotalPresentValue ofCouponsfor next 7Years43.35
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Solution – 9 (Contd.)Redemption Amount at the end of Year 7 100*1.1 110PV of the redemption amount 110/1.16738.94Present Value of Debenture 38.94+43.35 82.29
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Problem - 10• A bond of face value Rs.1,000 is currentlyquoting in the market at Rs.1,062. The couponrate of the bond is 14% payable semi annually.The remaining maturity of the bond is 5 yearsand the principal is repayable at two equalinstallments at the end of 4thand 5thyear fromnow. The yield to maturity of the bond is 12.16%.What would be the new price of the bond if theYTM for similar type of bonds increases by 2%?
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Solution – 10Increase in Market Rate (YTM) 2%New YTM 12.16 + 2 14.16%Interest payable until 4 years (8 Installments) 70PV of those 8 Installments 70/(1.0708) + 70/(1.0708)2+----------+ 70/(1.0708)8Principal paid at the end of 4thyear 500PV of that Principal 500/ /(1.0708)8Interest payable in 4.5thYear (9thInstallment) 35PV of that Interest =35/ /(1.0708)9Principal paid at the end of 5thyear + 10thInstallment Interest 500 + 35 = 535PV of that Principal + Interest 535/ /(1.0708)10Total Present value of the Bond 995.29
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Bond Valuation – Key Facts• Whenever the Expected Rate of Return, rd, is equal to the coupon rate, a fixed-rate bond will sell at its par value.• Interest rates do change over time, but the coupon rate remains fixed afterthe bond has been issued. Whenever the Expected Rate of Return rises abovethe coupon rate, a fixed-rate bond’s price will fall below its par value. Such abond is called a discount bond.• Whenever the Expected Rate of Return falls below the coupon rate, a fixed-ratebond’s price will rise above its par value. Such a bond is called a premiumbond.• Thus, an increase in interest rates will cause the prices of outstanding bonds tofall, whereas a decrease in rates will cause bond prices to rise.• For bonds with similar coupons, the differential sensitivity to changes ininterest rates always holds true—the longer the maturity of the bond, themore its price changes in response to a given change in interest rates.
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Problem – 11 – A quick Recap• If you buy a stock for a price P0 = Rs.23, and if you expect thestock to pay a dividend D1 = Rs.1.24 one year from now and togrow at a constant rate g = 8% in the future, what is theexpected rate of return on such a stock?
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Problem - 12• The bond of Zeta Industries with a parvalue of Rs.500 is currently traded atRs.435. The coupon Rate is 12% and ithas a maturity period of 7 years. What isthe yield to maturity?
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Problem 13• Consider the following three firms with different growthrates– Firm A with a growth rate of 0%– Firm B with a growth rate of 6%– Firm C a super normal growth rate of 10%• The expected EPS and DPS of each of the above firmsare Rs 5 and Rs 4 respectively. Required rate of returnfrom Equity is 16%• Find the Current Stock Price, Dividend Yield, CapitalGain Yield and P/E Ratio
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