PART-2 IP

Key Features of a Bond  Credit instrument- A debt securities is a type of loan. Debenture holder is a creditor of the company.  Par value – Face Value and Issue Price: Each bond carries a face value which may be for example; Rs1000.This is the nominal value of bond. It is used for accounting purpose and coupon is calculated on face value. Corporate bond may be issued at a discount, at par or at a premium with reference to its face value. The price at which a bond is issued to investor is known as its issue price.  Maturity date – Fixed maturity date, when the bonds must be re paid or redeemed.  Issue date – when the bond was issued.  Coupon Rate: These bonds carry a coupon rate which may be fixed rate (for example 12%) or a floating rate linked to some base rate. For example, a floater bond may have coupon such as “5 year G-Sec rate + 2%”. Where 5 year G-sec rate is base rate and keeps on changing as the rates of central government securities change while 2% is the spread which remains fixed for the entire tenure of the bond. Coupon payments are made to investors periodically for example coupon may be paid quarterly, semi-annually or annually.  Face value and redemption value- Mostly same but different in some cases.  Yield to maturity - rate of return earned on a bond held until maturity. It is the annual percentage rate of return that will be earned if the bond is purchased today at current price and is held till maturity.  Face Value: Rs 1000/-  Issue Price: Rs 1000/- (issued at par) Coupon: 12% (fixed coupon)  Issue Date: 1stjan’ 2010 Maturity Date: 31st Dec’ 2020 Maturity Period: 10 years  Coupon Frequency: Semi-annual June & Dec. Redemption Value: Rs 1000/- (at par)  Call option: not available Put option: not available

Regular Income Capital appreciation For Ex: 10% bond, 1000 face value, redeeming at premium of 5%, issued at par maturing after 5 years. Coupon is paid semi annually. Calculate the yield earned by investor if the bond is kept till maturity. Set end FV= 1050 N = 10 P/y=2 PV=1000 I= Solve PMt=50 C/y=2 What is the YTM on a 10-year, 10% annual coupon, Rs 1,000 par value bond, selling for Rs 1052?  Must find the rd that solves this model. VB  INT  ... INT  M (1 rd )1 (1 rd )N (1 rd )N Rs1052  100  ... 100  1,000 (1 rd )1 (1 rd )10 (1 rd )10 Using a financial calculator to solve for the YTM  Solving for I/YR, the YTM of this bond is 9.18%.

Find YTM, if the bond price is Rs 1,134.20 Solving for I/YR, the YTM of this bond is 7.08%. Current yield: The current yield relates the coupon interest rate with the current market price of the bond. Current yield (CY) = ������������������������������������ ������������������������������������ ������������������������������������������ ������������������������������������������ ������������������������������  For Example:  The future value of a 13% bond is Rs 100.An investor buys the bond from the market for Rs 90/ or Rs 100. his current yield is: 13/ 90* 100= 14.40% 13/100*100= 13% Current yield ignores the prospective capital gain or loss which the bond holder may have in future. It ignores the re investment of interest income for remaining life of bond.

PERPETUAL BONDS  Perpetual bonds, also called consols, has an indefinite life and therefore, it has no maturity value. Perpetual bonds or debentures are rarely found in practice.  Suppose that a 10 per cent Rs 1,000 bond will pay Rs 100 annual interest into perpetuity. What would be its value of the bond if the market yield or interest rate were 15 per cent?  The value of the bond is determined as follows: MACULAY DURATION  Find duration of a bond With 8% coupon rate, 10% YTM, Face value is Rs1000 redeemable after 3 yrs. Duration Calculation 8% Bond Time Payment PV of CF Weight C1 X C4 years (10%) 1 80 72.727 0.0765 0.0765 2 80 66.116 0.069 0.1392 3 1080 811.42 0.8539 2.5617 Sum 950.263 1 2.7774 Macaulay’s duration  Duration  Characteristics of Macaulay’s duration  Coupon payments at periodical intervals are determining factor in computing duration of a bond.  The duration of a coupon bond will always be less than its maturity term  Coupon and duration are inversely related.

Duration of the Bond  Let’s consider two bonds with 5 years maturity. The 8.5% coupon bond of Rs.1000/-face value has the YTM of 10% and the 11.5% coupon has the YTM of 10.6%. Duration of Bonds 8.50 % Bond Year Cash PV at Proportion Proportion of Flow 10% of Bond Bond price X Price 1 85 77.27 time 2 85 70.25 0.082 3 85 63.86 0.074 0.082 4 85 58.06 0.068 0.149 5 1085 673.7 0.062 0.203 0.714 0.246 943.14 3.572 1 4.252 8.50 % Bond PV at Proportion Proportion of 10.6 % of Bond Bond price X Year Cash price Flow 103.98 time 94.01 0.101 1 115 0.091 0.101 2 115 85 0.082 0.182 3 115 76.86 0.074 0.247 4 115 673.75 0.652 0.297 5 1115 1033.6 3.259 1 4.086

Properties of Duration  All the bonds which pays the periodic coupon , the duration is less than the maturity since the investor recovers a part of his investment every year. When due weight age is given to the recoveries made in the intermediate periods, the bonds duration will be shorter than the term of maturity.  A bond’s duration will be equal to its term to maturity if and only if it is ZCB. When no intermediate recoveries are made by the investor , the duration will equal the term to maturity.  The duration of perpetual bonds is equal to (1+r)/r, where r= yield to maturity of the bond i.e.  10% yield , duration of a perpetuity that pays Rs.100 forever is  Longer the coupon – paying bond’s term to maturity , greater the difference between its term to maturity and duration.  Duration of a level annuity is :  Duration = 1+ yield -- No. of payments Yield ( 1+ yield) ^ No. of payments – 1 Example  A 15 years annual annuity with a yield of 10% will have a duration of  (1.10) / (.10) – 15 / (1.10)^15 -1 = 6.28 years  Another example,  A 10 years annual annuity has a yield of 9%, what is the duration  (1.09) / 0.09 – 10 / (1.09)^10 – 1 = 4.798 years

Realized Yield • While calculating the YTM, we assume that all the future cash flows are reinvested at the same rate… • But, actually it may not be so…! • So, we have to calculate the Realized Yield. • Example: Find out the realized yield of a 15% coupon bearing bond with a par value of Rs.1000, maturing after 5 years and currently selling at Rs.850/-. The reinvestment rate applicable to the future value cash flow of the bond is 16%. • Solution thru CMPD… Step 1 Set: End , n=5 , I=16, PV= 0 , PMT = - 150 , P/Y=1, C/Y=1 Solve FV = 1031.57/- Step 2 Set: End , n=5 , PV= -850 , PMT = 0 , FV = 1031.57 1000 = 2031.57 P/Y=1, C/Y=1 Solve i = 19% Realized Yield = 19% Valuing Money Market Securities • The Yield of T- bill / short term money market is calculated as • i = ( FV / PV) – 1 X ( 365/n) • Where n = no. of days • Example: If a security has 90 days remaining before the maturity, the appropriate current selling price is Rs.102473.22 and maturity amount is Rs1,05,000/- • i = ( FV / PV) – 1 X ( 365/n) • I = (105000/102473.22) -1 X ( 365/90) • I = 10% …Answer • Another Example: A Rs.100000 T bill is selling at Rs 98000 today. It will mature in 60 days. What is the annual yield? • Solution: Formula for Yield is • i = ( FV / PV) – 1 X ( 365/n) • I = (100000/98000) -1 X ( 365/60) • I = ( 1.02040) – 1 X ( 365/60) • I = 0.020408 X ( 365/60) • I = 12.41% .. Answer

Intrinsic Value and Market Price  The intrinsic value (IV) is the “true” value, according to a model.  The market value (MV) is the consensus value of all market participants IV > MV Buy IV < MV Sell or Short Sell IV = MV Hold or Fairly Priced Dividend Discount Models (DDM) V0  D1  D2  D3  ... 1 k 1 k 2 1 k 3  V0 =current value; Dt=dividend at time t; k = required rate of return  The DDM says the stock price should equal the present value of all expected future dividends into perpetuity.  Value of a share of common stock is the present value of all future dividends n DPSt  Value per share of stock=  ---------- t=1 (1+r)t  What if the stock is not held for an infinite period?  One year holding period  Multiple year holding periods  Dividend every year will be the same  Investor anticipates to receive the same amount dividend per year forever Zero Growth Model  Dividend every year will be the same  Investor anticipates to receive the same amount dividend per year forever D  V = ------------- Ke

Constant Growth Model DDM Implications 1. Assumptions: 2. The growth rate “g” is constant and compounded annually. 3. Growth rate ‘g’ is less than the required rate of return of the equity investors 4. Growth rate “g” is subjective estimate of the investor. Constant Growth DDM V0  D0 1 g   D1 kg kg g=dividend growth rate Example Constant Growth DDM  A stock just paid an annual dividend of Rs 3/share. The dividend is expected to grow at 8% indefinitely, and the market capitalization rate is 14%.

Price to Earnings ratio  P/E is short for the ratio of a company's share price to its per-share earnings. As the name implies, to calculate the P/E, you simply take the current stock price of a company and divide by its earnings per share (EPS)  (Earnings per share (EPS) is calculated as a company's profit divided by the outstanding shares of its common stock.

 A stock's P/E tells us how much investors are willing to pay per rupee of earnings. For this reason it's also called the \"multiple\" of a stock. In other words, a P/E ratio of 20 suggests that investors in the stock are willing to pay Rs20 for every Rs1 of earnings that the company generates. However, this is a far too simplistic way of viewing the P/E because it fails to take into account the company's growth prospects.

Strategies for Portfolio revision  Active strategy  Passive strategy Active strategy  Active revision strategy involves substantial adjustments to the portfolio.  It is essentially carrying out portfolio analysis and selection all over again.  It is based on an analysis of the fundamental and technical factors.  Practitioners of this strategy believe that they can develop better estimates of risk & return of securities.  High transaction costs.  Lot of Time, skill & resources required in implementing the strategy. Passive revision strategy  Passive revision strategy involves only minor adjustment to the portfolio over time.  Adjustment to the portfolio is carried out according to certain pre determined rules and procedures.  Practitioners of this strategy believe in market efficiency and find little incentive for actively trading and revision of portfolio. Different Passive strategy 1. Buy & hold (leave the portfolio alone)-Drifting asset allocation Rebalancing of the portfolio 2. Constant mix policy-Balanced Asset allocation 3. Portfolio insurance policy- CPPI Policy Leave the Portfolio Alone  A buy and hold strategy means that the portfolio manager hangs on to its original investments  The initial portfolio is left undisturbed. No rebalancing is done. For example: if the initial portfolio has a stock mix of 50:50 and after six months, stock-bond mix happens to be 70:50, the portfolio mix is allowed to be drift. Rebalance the Portfolio  Rebalancing a portfolio involves revision and reviewing the portfolio composition.(stock bond mix) Constant Mix Strategy

 The constant mix strategy:  It calls for maintaining the proportion of stocks and bonds in line with their target value. For example: if the desired mix of stocks & bonds is 50:50, the constant mix policy calls for rebalancing the portfolio when share prices fluctuate from time to time or when the relative value of components change so that the target proportion is maintained. Constant Mix Strategy (cont’d) Example A portfolio has a market value of 20 lakhs. The investment policy statement requires a target asset allocation of 50 percent stock and 50 percent bonds. The initial portfolio value and the portfolio value after one quarter are shown on the next slide. Portfolio Value Actual Allocation Stock Bonds 100 1,00,000 50%/50% 50,000 50,000 80 90,000 44%/55% 40,000 50,000 What amount of stock should the portfolio manager buy to rebalance this portfolio? What amount of bonds should he sell? Solution: In order to maintain, 50: 50 ratio of stock & bond mix, Rs 5,000 worth bonds to be sold and Rs 5000 worth stocks should be purchased. Constant Proportion Portfolio Insurance  A constant proportion portfolio insurance (CPPI) strategy requires the manager to invest a percentage of the portfolio in stocks: Amount in stocks = Multiplier × (Portfolio value – Floor value)  A method of portfolio insurance in which the investor sets a floor on the value of his or her portfolio, then structures asset allocation around that decision. The two asset classes used in CPPI are a risky asset and a riskless asset .  The percentage allocated to each depends on the \"cushion\" value, defined as (current portfolio value – floor value), and a multiplier coefficient, where a higher number denotes a more aggressive strategy. The investor will make a beginning investment in the risky asset equal to the value of (Multiplier) x (Portfolio value- floor value) and will invest the remainder in the riskless asset. As the portfolio value changes over time, the investor will rebalance according to the same strategy.

Consider a hypothetical portfolio of 100,000, of which the investor decides 90,000 is the absolute floor. If the portfolio falls to 90,000 in value, the investor would move all assets to riskless asset. The value of the multiplier is based on the investor's risk profile, Multiplier values between 3 and 6 are very common. A portfolio has a market value of 1 lakh. The investment policy statement specifies a floor value of 75,000 and a multiplier of 2. What is the amount that should be invested in stocks according to the CPPI strategy? Amount in stocks = 2.0 × (1,00,000 – 75,000) = 50,000 Risk adjusted Returns • In determining the various returns earned by a portfolio, a higher return by itself is not necessarily indicative of superior performance. Alternately, a lower return is not indicative of inferior performance. • There are three major composite equity portfolio measures that combine risk and return to give quantifiable risk-adjusted numbers. These composite performance measures are • The Treynor index, • The Sharpe index, and • The Jensen index. • Investors can use these measures together to determine whether a portfolio or fund manager actually beat the market. • In order to determine the risk-adjusted returns of investment portfolios, several eminent authors have worked since 1960s to develop composite performance indices to evaluate a portfolio by comparing alternative portfolios within a particular risk class. The most important and widely used measures of performance are: • The Treynor Measure • The Sharpe Measure • Jenson Model The Treynor Measure • Developed by Jack Treynor, this pe1r9formance measure evaluates funds on the basis of Treynor's Index. • This Index is a ratio of return generated by the fund over and above risk free rate of return (generally taken to be the return on securities backed by the government, as there is no credit risk associated), during a given period and systematic risk associated with it (beta). It can be represented as • Treynor's Index (Ti) = (Ri - Rf)/Bi. • Where, Ri represents ‘Return on Fund’ or ‘Portfolio Return’ • Rf is ‘Risk Free Rate of Return’ and • Bi is ‘Beta of the fund’ or ‘Portfolio Beta’.

• All risk-averse investors would like to maximize this value. While a high and positive Treynor's Index shows a superior risk-adjusted performance of a fund, a low and negative Treynor's Index is an indication of unfavorable performance. Developed by Jack treynor Reward to volatility. It is the ratio of the reward to the volatility of return as measured by portfolio beta. The Sharpe Measure Performance of a fund is evaluated on the basis of Sharpe Ratio, which is a ratio of returns generated by the fund over and above risk free rate of return and the total risk associated with it. Developed by William sharpe Called as reward to variability. It is the ratio of the reward or risk premium to the variability of return. (risk measured by standard deviation). • It is the total risk of the fund that the investors are concerned about. So, the model evaluates funds on the basis of reward per unit of total risk. it can be written as: • Sharpe Index (Si) = (Ri - Rf)/Si • Where, Si is ‘Standard Deviation of the Fund’. • While a high and positive Sharpe Ratio shows a superior risk- Comparison of Sharpe and Treynor • Sharpe and Treynor measures are similar in a way, since they both divide the risk premium by a numerical risk measure. • The total risk is appropriate when we are evaluating the risk return relationship for well-diversified portfolios. On the other hand, the systematic risk is the relevant measure of risk when we are evaluating less than fully diversified portfolios or individual stocks. • For a well-diversified portfolio the total risk is equal to systematic risk. Rankings based on total risk (Sharpe measure) and systematic risk (Treynor measure) should be identical for a well-diversified portfolio, as the total risk is reduced to systematic risk. • Therefore, a poorly diversified fund that ranks higher on Treynor measure, compared with another fund that is highly diversified, will rank lower on Sharpe Measure. Jenson Model • Jenson's model proposes another r2is2k adjusted performance measure.

• This measure was developed by Michael Jenson and is sometimes referred to as the Differential Return Method. • This measure involves evaluation of the returns that the fund has generated vs. the returns actually expected out of the fund given the level of its systematic risk. The surplus between the two returns is called Alpha, which measures the performance of a fund compared with the actual returns over the period. • Required return of a fund at a given level of risk (Bi) can be calculated as: Ri = Rp - Rf + Bi (Rm - Rf) Where, Rm is ‘Average Market Return’ during the given period. After calculating it, alpha can be obtained by subtracting required return from the actual return of the fund. Developed by Michael Jensen This ratio attempts to measure the differential between the actual return earned on a portfolio and the return expected from the portfolio given its level of risk. The differential return gives an indication of the portfolio manager’s predictive ability or managerial skill. • Higher alpha represen2t3s superior performance of the fund and vice versa. • Limitation of this model is that it considers only systematic risk not the entire risk associated with the fund and an ordinary investor can not mitigate unsystematic risk, as his knowledge of market is primitive. E(R) = Risk free return+ beta of portfolio (Return from market- risk free return). Differential return = Return of portfolio - Expected return. Question • Consider the following information for 3 mutual funds, Particulars Mean Returns ( %) Std. deviation(%) Beta A 12 18 1.1 B 10 15 0.9 C 13 20 1.2 Market Index 11 17 1 The mean risk –free rate was 6 percent. Calculate: the Treynor measure, Shrape Measure and Jensen Measure for the three mutual funds and the market index.

Treynor Measure • Treynor Measure: Rp - Rf βp • Fund A: 12- 6 = 5.45 1.1 • Fund B: 10-6 = 4.44 0.9 • Fund C: 13-6 = 5.83 1.2 • Market Index: 11-6 = 5.00 1.0 Sharpe Measure • Shrape Measure: Rp - Rf αp • Fund A: 12-6 = 0.333 18 • Fund B: 10- 6 = 0.267 15 • Fund C: 13- 6 = 0.350 20 • Market Index: 11- 6 = 0.294 17 Jenson Measure Rp – [Rf + βp (Rm – Rf)] • Jensen Measure: 12- [6 + 1.1(5)] = 0.5 10- [ 6+ 0.9(5)] = -0.5 • Fund A: 13- [6 + 1.2(5)] = 1.0 • Fund B: 0 (By definition) • Fund C: • Market Index:

Q1. Mr. X wants to invest on a yearly basis to achieve his goals for his children's higher education. You have recommended him to invest in Debt and Equity in the ratio of 20:80. If he starts investing today, what approximate amount should he set aside every year to achieve his said goals? Assume the client has two children aged 5 years and 2 years and the fund for higher education is required at their respective age of 21 years. The present cost for higher education for both the children is ₹ 3,00,000 each which would be growing at an average annual inflation of 4% p.a. The rate of return on Debt and Equity investments are expected to be 9% p.a. and 15% p.a. respectively. a) ₹ 9,000 and ₹8,000 respectively b) ₹10,000 and ₹7,000 respectively c) ₹8,000 and ₹7,000 respectively d) ₹10,000 and ₹8,000 respectively Sol. Calculation of FV of education expenses of the younger child: N = 16, I = 4, PV = 3,00,000, FV = (?) = 5,61,894. Assume the monthly investment is 100 of which 20 get invested in Debt and 80 is invested in Equity. FV of the Debt Investment would be: Set = Begin, N = 16, I = 9, PMT = 20, FV = (?) = 719.47. FV of the Equity Investment would be: Set = Begin, N = 16, I = 15, PMT = 80, FV = (?) = 5126.01. The total FV = 719.47 + 5126.01 = 5845.48. Hence the monthly investment required would be: (100/5845.48) * 561894 = (?) = 9612.50. Repeat the entire process for the older child to get the monthly investment at 6931.42. Q2. A businessman wants to achieve the goal of marriage of his daughter after 10 years. The funds required would be ₹ 25 lakh at then costs. He wants to invest monthly for the goal. You suggest an asset allocation strategy where he should invest monthly in equity and debt in ratio 65:35 for 9 years, and shift the entire accumulated amount in these funds to liquid fund in the last year. If the returns expected from equity, debt and liquid funds in this period are 12 % p.a., 9 % p.a. and 5 % p.a., respectively, what approximate amount per month is required to be allocated to equity and debt schemes? a) ₹ 12,679 &₹ 8,453 b) ₹ 9,485 &₹ 6,323 c) ₹ 8,601 &₹ 4,631 d) ₹ 12,075 &₹ 8,050 Sol. Discount the FV at the end of 10 years for 1 year to calculate the FV at the end of 9 years:

N = 1, I = 5, FV = 2500000, PV = (?) = 2380952. Assume the monthly investment is 100 of which 65 gets invested in Equity and 35 is invested in Debt. FV of the Equity Investment would be: Set = Begin, N = 9*12, I = APR of 12%/12, PMT = -65, FV = (?) = 12261. FV of the Debt Investment would be: Set = Begin, N = 9*12, I = APR of 9%/12, PMT = -35, FV = (?) = 5732. The total FV = 12261 + 5732 = 17993. Hence the monthly investment required would be: (100/17993) * 2380952 = (?) = 13233 of which 8601 (65%) would be invested in Equity and 4631 (35%) would be invested in Debt. Q3. Your client started investing ₹ 12,000 per month a year ago in an asset allocation of 30:70 in equity and debt to achieve a goal in 6 years from now by accumulating ₹ 10 lakh. You realize that he would be requiring ₹ 15 lakh for the same goal. You expect equity and debt to give returns of 11.75% p.a. and 8.25% p.a., respectively in the entire period of investment. You assess changing asset allocation to 65:35 in equity and debt by investing ₹ 2,000 additional per month to see how closer he can reach to his goal. You find that ______. a) Approximate surplus of ₹ 2,13,707 b) Approximate shortfall of ₹ 1,68,091 c) Approximate surplus of ₹ 6,47,691 d) Approximate surplus of ₹ 1,47,69 Sol. The monthly investment is 12000 of which 30% i.e. 3600 gets invested in Equity and 70% i.e. 8400 gets invested in Debt. Accumulation in a year's time would be – Equity: Set = Begin, N = 1*12, I = APR of 11.75%/12, PMT = -3600, FV = (?) = 45906. . Accumulation in a year's time would be – Debt: Set = Begin, N = 1*12, I = APR of 8.25%/12, PMT = -8400, FV = (?) = 105250. Revised investment per month is now 12000+ 2000 = 14000 of which 65% i.e. 9100 get invested in Equity and 35% i.e. 4900 gets invested in Debt. FV of the Equity Investment after 6 years would be: Set = Begin, N = 6*12, I = APR of 11.75/12, PV = -45906, PMT = -9100, FV = (?) = 1025095. FV of the Debt Investment after 6 years would be:

Set = Begin, N = 6*12, I = APR of 8.25/12, PV = -105250, PMT = -4900, FV = (?) = 622596. The total FV = 1025095 + 622596 = 1647691. Hence the surplus would be: 1647691 – 1500000 = 147691. Q4. Your client starts investing immediately for 10 years annually ₹ 60,000 in the ratio of 80:20 in equity and debt products. You expect return from equity and debt to be 11.75% p.a. and 8.25% p.a. during this period. To protect the wealth, he rebalances the portfolio in 40:60 ratio of equity and debt after 10 years and invests in the same ratio annually ₹ 60,000 for the next 5 years. The return expected from equity and debt in this period subsides to 9% p.a. and 7% p.a., respectively. What rate of return is expected on his total investments? How would this return fare when seen from average inflation of 6% during the entire period? a) 6.96% p.a.; real return of 0.91% p.a. b) 7.57% p.a.; real return of 1.48% p.a. c) 7.24% p.a.; real return of 1.17% p.a. d) 9.52% p.a.; real return of 3.32% p.a. Sol. The annual investment for the first 10 years is 60000 of which 80% i.e. 48000 gets invested in Equity and 20% i.e. 12000 gets invested in Debt. Accumulation at the end of 10 years would be – Equity: Set = Begin, N = 10, I = 11.75%, PMT = -48000, FV = (?) = 930010. . Accumulation at the end of 10 years would be – Debt: Set = Begin, N = 10, I = 8.25%, PMT = -12000, FV = (?) = 190429. The total FV = 930010 + 190429 = 1120439. The asset allocation for the subsequent 5 years is reshuffled to 40% in Equity & 60% in Debt for both the accumulated fund as well as ongoing investments. Revised investment per annum is now 24000 (40%) in Equity and 36000 (60%) in Debt. FV of the Equity Investment after 5 years would be: Set = Begin, N = 5, I = 9, PV = -448176 (40% of accumulated fund), PMT = -24000, FV = (?) = 846134. FV of the Debt Investment after 5 years would be:

Set = Begin, N = 5, I = 7, PV = -672263 (60% of accumulated fund), PMT = -36000, FV = (?) = 1164403. The total FV = 846134 + 1164403 = 2010536. The rate of return on the entire investment horizon would be: Set = Begin, N = 15, PMT = -60000, FV = 2010536, I = (?) = 9.52%. The real return on the investments would be: [{(1 + 9.52%) / (1 + 6%)} – 1] *100 = 3.32%. Q5. Dividend one year hence on a stock is expected to be ₹12. Thereafter the dividend is expected to grow @ 12% for 2 years, @ 10% for another 2 years and @ 5% thereafter. If the investor expects a return of 15% the current price of the security will be? a) ₹142.15 b) ₹140.10 c) ₹147.15 d) ₹144.10 Sol. Future Dividends are expected be as follows 12/13.44/15.053/16.558/18.214 and growing @ 5% p.a. thereafter. Use formula for Constant Growth of Dividend under Infinite period of holding: PV = (18.214*1.05) / (0.15 – 0.05) = 191.246. Use CASH: Cash Flows: 12/13.44/15.053/16.558/18.214 +191.246, ESC, NPV = (?) = 144.10 Q6. Mr. A is of 35 years with spouse and a kid of an age 5 yrs. His strategic asset allocation is 50:35:15 in equity, debt and liquid. He is able to invest ₹ 1.5 lakh p.a. immediately to work various life goal. At age 40 he rebalances the portfolio and changes the allocation to 40:50:10 in equity, debt and liquid asset with annual investment going up to 2.5 lakh for 5 more years. At age 45, for next 10 year he adapts the conservative wealth protection allocation 25:70:05 in equity, debt & liquid asset with 3 lakh pa investments. The per annum return expected in this stage are; from equity: 12%, 11% & 10% from debt: 9%, 8% & 7%, from liquid asset: 6.5%, 5.5% & 4.5%. What amount could he accumulate by his age 55 years? a) ₹ 97.21 lakhs b) ₹ 66.65 lakhs c) ₹ 117.91 lakhs d) ₹ 113.9 lakhs Sol. For the first 5 years we would invest Equity:Debt:Liquid ratio of 50:35:15. Value of equity portfolio after 5 years would be ₹ 533639 (Set: Begin, N = 5, I% = 12, PV = NA, PMT = 150000*0.5, FV = (?) = Solve). Value of the debt portfolio after 5 years would be ₹ 342475(Set: Begin, N = 5, I% = 9, PV = NA, PMT = -150000*0.35, FV = (?) = Solve).

Value of the liquid portfolio after 5 years would be ₹ 136434(Set: Begin, N = 5, I% = 6.5, PV = NA, PMT = 150000*0.15, FV = (?) = Solve). The value of equity, debt and liquid portfolio after 5 years would be ₹ 1012548. For the next 5 years we would invest Equity:Debt:Liquid ratio of 40:50:10. Value of equity portfolio after next 5 years would be ₹ 1373767 (Set: Begin, N = 5, I% = 11, PV = -1012548*0.4, PMT = -250000*0.4, FV = (?) = Solve). Value of the debt portfolio after next 5 years would be ₹ 1535874(Set: Begin, N = 5, I% = 8, PV = -1012548*0.5, PMT = 250000*0.5, FV = (?) = Solve). Value of the liquid portfolio after next 5 years would be ₹ 279537(Set: Begin, N = 5, I% = 5.5, PV = -1012548*0.1, PMT = -250000*0.1, FV = (?) = Solve). The value of equity, debt and liquid portfolio after next 5 years would be ₹ 3189178. For the last 10 years we would invest Equity: Debt: Liquid ratio of 25:70:05. Value of equity portfolio after last 10 years would be ₹ 3382814 (Set: Begin, N = 10, I% = 10, PV = -3189178*0.25, PMT = -300000*0.25, FV = (?) = Solve). Value of the debt portfolio after last 10 years would be ₹ 7496073 (Set: Begin, N = 10, I% = 7, PV = -3189178*0.70, PMT = -300000*0.70, FV = (?) = Solve). Value of the liquid portfolio after last 10 years would be ₹ 440252 (Set: Begin, N = 10, I% = 4.5, PV = -3189178*0.05, PMT = -300000*0.05, FV = (?) = Solve). The value of equity, debt and liquid portfolio after last 10 years at the age of 55 would be ₹ 1,13,19,139.59. Option (d) is the closest option. Q7. A company has recently paid a dividend of₹2 per share which is expected to grow at the rate of 15% p.a. for the next 3 years and then at thereafter at the rate of 10% p.a. What will be the fair price of the share if the required return is 12% p.a.? a) ₹167.30 b) ₹125.41 c) ₹110.00 d) ₹166.67 Sol. Future Dividends are expected be as follows 2.3/2.645/3.042 and growing @ 10% p.a. thereafter. Use formula for Constant Growth of Dividend under Infinite period of holding: PV = (3.042*1.10) / (0.12 – 0.10) = 167.30. Use CASH: Cash Flows: 2.3/2.645/3.042+167.30, ESC, NPV = (?) = 125.41