Valuation of Debentures

Investment analysis and portfolio management Topic:-Valuation of Debentures and Equity

1

Submitted to:PROF. VIJAY GAWDE

GROUP MEMBERS

Names

Roll No.

Urmi Sampat

26

Harmit Kaur Basra

36

Suraj Bhui

37

2

VALUATION OF DEBENTURES Introduction

Debentures are financial instruments usually issued by companies and government to raise there capital to finance their business without forfeiting control of company ownership. In other words, debentures are simply loans taken by the companies to raise short to medium term loan needed for expenses or for expansions and do not provide the ownership in the company. A debenture is a debt instrument, just like a fixed deposit (FD), usually issued  by a company. You invest a sum, and the company pays you a fixed rate of interest for the  pre-defined period. After the period gets over, you get back your principal amount. However, these types of bonds are not secured by physical asset or collateral. These are unsecured loans as company is not bound to return the principal amount on the maturity and are backed only by the general credit worthiness and reputation of the issuer. Several types of debentures: 

Registered debentures



Bearer debentures



Secured debentures

 

Unsecured or Naked debentures Redeemable debentures



Irredeemable or Perpetual debentures



Convertible debentures and



Non Convertible debentures

Usually convertible debentures are very popular both among the investors and the companies. This is because in case the company goes in profits in future the investors if  they want can convert there debentures into equity shares at some price which will normally be lower than the market price.it guarantees steady income and extra income through their conversion into equity shares.

3

Difference between bonds and debentures

Bonds and debentures are fixed income instruments which are taken by investors looking for regular, fixed income through payment of interest on the principal  purchase. Bonds and debentures are debt instruments with different types of exposure.  In general terms bondholders are secured by access to the underlying asset in case of  default by the issuer. Debentures, on the other hand, are unsecured, and debenture holders do not have recourse to assets in the case of default by the debenture issue. 

Terminologies associated with debt instruments

Face value/par value: this is the value stated on the face of the bond. it represents the amount of borrowing by the firm which specifies to repay after a specific  period of time of maturity. a bond is usually issued at rupees 100 or rupees 1000. 

Coupon rate/interest: a bond carries a specified rate of interest which is called the coupon rate. The amount of annual interest = face or par value x coupon or  interest rate. 

Maturity: a bond is issued for a specific period of time. it is repaid on maturity. Debentures have a maturity date for 7-10 years. Whereas government have for  20-25 years. 



Redemption value: the value which a bond holder gets on maturity is called redemption value. a bond is redeemed at par, premium, discount. Market value: market value is the price at which bond is usually bought or  sold. Market value may be different from the market value or par value. 

4

Cost of debt: It is an interest rate an investor wants to earn by investing  bonds in the company. 

Valuation of redeemable debentures

Investors receive interest at a fixed rate till maturity and a fixed principle repayment at the time of maturity. There are 2 types of cash flows namely: i) ii)

Interest at coupon tare till maturity Redemption value at the time of maturity

Valuation in case interest is received annually

Valuation of bond on which interest is received annually can be done by discounting such annual interest and redemption value to today’s value. Annual interest receivables are an example of annuity with life up to maturity of debenture whereas redemption value receivable at the time of maturity is an example of single cash flow. Formula; Bo or Do = [I(PVIFA kd, n yrs)] + [F(PVIFA kd, n yrs)] Where Bo or Do = intrinsic value or present value of the bond or debenture I = annual amount of interest receivable at coupon rate Kd = cost of debt  N = maturity period F = redemption value to be received at the time of the bond PVIFA kd, n yrs = present value interest factor of annuity at kd rate for n yrs PVIF kd nth year = present value interest factor of single cash flow at kd rate fot n years

5

E.g. 1)Debentures of amber ltd has par value is rupees 100 each and bears a coupon rate of 12% with a maturity period of 4 years the required rate of return on the bond is 10%.what is the value of this debenture? Solution: Do = [I(PVIFA kd, n yrs)] + [F(PVIFA kd, n yrs)] Do is to be found I = 100 x 12% = 12 Kd = 10%  N = 4 yrs F = rupee 100 PVIFA 10%, 4 yrs = 3.168 PVIFA 10%, 4TH yrs = 0.6830 Do = [12 x 3.1698] + [100 x 0.6830] = 38.0376 + 68.30000 = rupees 103.3376 E.g. 2) Redemption at premium: A debenture of rupees 100 face value carries an interest rate of 13% redeemable after 5 years at a premium of 2%.if the required rate return is 15% what is the present value of  the debenture? Solution: Do = [I(PVIFA kd, n yrs)] + [F(PVIFA kd, n yrs)] Do =? I = 100 x 13% = =13 Kd = 15%  N = 5 yrs F = [100 + 2% of 100] = 100 + 2 = rupees 102/PVIFA 15%, 5yrs = 3.3522 6

PVIFA 15%, 5th year = 0.4972 Do = [13 x 3.3522] + [102 x 0.4972] = 43.5786 + 49.72 = rupees 93.2986/*any premium or discount is calculated at face value

E.g. 3) Advice on investment: Debentures of nasal ltd has face value rupees 1000 with a coupon a at 9% redeemable after 5 years at a premium of 6%.the required rate of return is 11%.the current market price of the bond is rupees 995.is the investment at the current market price is advisable? The present value of rupee 1 at 11% discounting rate are 0.9009.0.8116.0.7312, 0.6587 and 0.5935. Will I advice change if the market price of debenture is rupees 945? Solution: Do = [I(PVIFA kd, n yrs)] + [F(PVIFA kd, n yrs)] D0 = ? I = RUPEES 100 x 9% = 90 Kd = 11%  N = 5 yrs F = [1000 + 6% 0f 1000] =1000 + 60 =1060/PVIFA 11% 5yrs = 0.9009 + 0.8116 + 0.7312 + 0.6587 + 0.5935= 3.6959 PVIFA 11% 5TH yr = 0.5935 Do = [90 x 3.6959] + [1060 x 0.5935] = 332.631 + 629.11 7

=Rupees 961.741/-

Valuation incase received semi – annually

Most bonds pay semi annually. It is worked for unit period of 6 months and not one year. Formula; Bo or Do = [I/2(PVIFA kd/2, 2n yrs)] + [F(PVIFA kd/2, 2nth yrs)] Where Bo or Do = intrinsic value or present value of the bond or debenture I = annual amount of interest receivable at coupon rate I/2 = amount to be received every six months Kd = cost of debt  N = maturity period F = redemption value to be received at the time of the bond PVIFA kd/2, “2n yrs” = present value interest factor of annuity at kd/2 rate for 2n yrs PVIF kd/2, “2nth” year = present value interest factor of single cash flow at kd/2 rate for  “2nth” years

E.g. 1) semi – annual interest: Debentures of masher ltd has face value of rupees 1000 and it has a coupon rate of 10% with maturity period of 6 yrs. interest is payable semi annually. if the required rate of  return is 14%.calculate the value of the bond.

8

Solution: Do = [I/2(PVIFA kd/2, 2n yrs)] + [F(PVIFA kd/2, 2nth yrs)] Do =? I = 1000 x 10% = rupees 100 p.a. I/2 = 100/2 = 50 Kd = 14%  N = 6 yrs F = 1000[redeemed at par] Do = [50 (PVIFA 14/2%, 2x6 yrs)] + [1000(PVIFA 14/2%, 2x6th yrs)] = [50(PVIFA7%, 12yrs)] + [1000(PVIFA7%, 12TH yrs)] = [50 x 7.9427] + [1000 x 0.4440] = 397.1343 + 444 = 841.1343 Valuation of irredeemable bonds or debentures Irredeemable debentures are debentures which will never be redeemed by the company or  will be redeemed at the time when company goes into liquidation. Investor will receive interest at fix rate till perpetuity. Formula; Bo or Do = I/kd Where, Bo or Do = intrinsic value or present value of the bond or debenture I = annual amount of interest receivable at coupon rate Kd = cost of debt E.g. 1) eco ltd issued irredeemable debentures having face value of rupees 100 each and a coupon rate of 10%.what is the intrinsic value of debenture if the required rate of return is 12%? Would you recommend purchasing the debenture if it is available at rupees 85 in the market? Solution: Bo or Do = I/kd Do =? 9

I = 100 x 10% = 10 Kd = 12% Do = 10/0.12 = rupees 83.33/-

Current yield

Current yiels looks at the current market price of a debenture instead of its face value and represents the return an investor would expect if he or she purchased the bond and held it for a year. Formula; current yield = annual cash inflows/market price This measure is not an accurate return an investor will receive in all cases because debenture prices keep on changing constantly due to market factors. Yield to maturity

Yield means returns. it means returns an investor will earn if he purchases the bond today at available market price and hold it till maturity. Formula;

YTM = RV- PP/n + 1 the whole upon RV + PP/2

Where YTM = yield to maturity RV = redeemable value PP = purchase price 10

I = annual amount of interest receivable at coupon rate  N = number of years E.g. 1) a government of India bond of rupees 1000 each has a coupon rate of 7.5% per  annum and maturity period is 25 years. if the current market price is rupees 1050 Find YTM. Solution: ; YTM = RV-PP/n + 1 the whole upon RV + PP/2 RV = 1000[since redeemed values is not given] PP = 1050 I = 1000 x 7.5% = 75 n = 25 yrs YTM = 1000-1050/25 + 75 whole upon 1000 + 1050/2 YTM = (-2) + 75/1.025 YTM = 7.12% Valuation of convertibles debentures/bonds A financial instrument that can be converted into different security of the same company under specific conditions is referred to as a convertible security. When converted partially it is refereed to as partly convertible debentures and is the debentures are converted fully into equity shares at the end of maturity it is called fully convertibles debentures Formula of cash inflows involved in case of convertibles bonds; Bo or Do = [I(PVIFA kd%, n yrs)] + [Pn x C(PVIFA kd%, nth yrs)] Where, Bo or Do = intrinsic value or present value of the bond or debenture I = annual amount of interest receivable at coupon rate I/2 = amount to be received every six months Kd = cost of debt  N = number of years Pn = expected market price per equity share at the time of conversion C= the conversion ratio 11

PVIFA kd%, n yrs = present value interest factor of annuity at kd% rate for n yrs PVIF kd%, nth year = present value or discounting factor at kd% for nth years E.g. 1) Amender ltd has issued fully convertible debentures at a face value of rupees 100 with coupon rate of 12% which is to be converted into 5 equity shares of rupees 10 each [at a price of rupees 20] at the end of 5th year. Find out the value of the debentures if the expected rate of return is 18% and the expected market price of one share after 5 years of  rupees 30 each. Solution: Do = [I (PVIFA kd%, n yrs)] + [Pn x C (PVIFA kd%, nth yrs)] Do =? I = 100 x 12% = rupees12 P.A. Kd = 18%  N = 5 yrs C = 5:1 [5 shares for every debentures held] Pn = rupees .30 PVIFA18%, 5yrs = 3.1272 PVIFA 18% 5 th yra = 0.4371 Do = [12 x 3.1272] + [30 x 5 x 0.437 = [37.5264] + [65.5650] = Rupees 103.0914/-

Types of risk that debt instruments carry Default risk 

When a company is not able to pay back the maturity as well as the coupon (interest) amount, you can face the risk of default. However, sovereign papers are risk-free. Keep in mind that the higher the rating of an instrument less is the chance of your  investment facing a default risk. So a debt instrument with an AAA rating will offer a  better protection against default risk compared with a debt instrument of AA rating.  Note that the credit rating is a reflection of the company’s past history of debt 12

 payment and its present financial situation. Neither does it indicate the kind of returns it is capable of providing in the future, nor does it give a guarantee against future default. But it’s a good indicator. Interest rate risk 

Debt instruments are susceptible to interest rate volatility. There is an inverse relationship between interest rates and bond prices. When interest rates move up,  bond prices drop and vice-versa. This volatility affects only those instruments that are listed on the exchange and have a current market price. If you hold a bond till maturity, then an interest rate hike will not affect your returns. It is only when you sell the bond before maturity that interest rate changes can affect your returns. Debt instruments such as fixed deposits don’t suffer from interest rate risk as their  returns are not linked to the market.

Inflation risk 

Inflation plays a cruel joke on debt instruments. Suppose you invest in a debt instrument giving 10% when inflation is 8%. Three years down the line, if inflation rises to, say, 10%, your real rate of return becomes zero. In fact, the longer the tenor of  the bond, the higher is the chance that inflation will affect your real rate of return. Call risk 

This refers to the option available in the hands of the issuer, whereby it has the right to  buy back the bonds issued to investors before the expiry of the tenor. This is the opposite of put option, where the investor has the option to redeem prematurely. Call and put options get activated after a period as specified in the offer document. Usually, when interest rates are expected to fall down in the future, the present bond becomes expensive for the issuer. The company, in this case, exercises its call option, gives the money back to the investor and may issue a fresh bond at the prevailing lower rate of  interest. In this case, you get your principal back. However, all bonds do not come with a call option. 13

Credit rating

A credit rating evaluates the credit worthiness of an issuer of specific types of debt, specifically, debt issued by a business enterprise such as a corporation or a government. It is an evaluation made by a credit rating agency of the debt issuers likelihood of default. Credit ratings are determined by credit ratings agencies. The credit rating represents the credit rating agency's evaluation of qualitative and quantitative information for a company or government; including non-public information obtained by the credit rating agencies analysts. Credit ratings are not based on mathematical formulas. Instead, credit rating agencies use their judgment and experience in determining what public and private information should be considered in giving a rating to a particular company or government. The credit rating is used by individuals and entities that purchase the bonds issued by companies and governments to determine the likelihood that the government will pay its bond obligations. A poor credit rating indicates a credit rating agency's opinion that the company or  government has a high risk of defaulting, based on the agency's analysis of the entity's history and analysis of long term economic prospects. Yield curve Definition of 'Yield Curve'

A line that plots the interest rates, at a set point in time, of bonds having equal credit quality, but differing maturity dates. The most frequently reported yield curve compares the three-month, two-year, five-year and 30-year U.S. Treasury debt. This yield curve is used as a benchmark for other debt in the market, such as mortgage rates or bank lending rates. The curve is also used to predict changes in economic output and growth. The shape of the yield curve is closely scrutinized because it helps to give an idea of  future interest rate change and economic activity. There are three main types of yield curve shapes: normal, inverted and flat (or humped). A normal yield curve (pictured here) is one in which longer maturity bonds have a higher yield compared to shorter14

term bonds due to the risks associated with time. An inverted yield curve is one in which the shorter-term yields are higher than the longer-term yields, which can be a sign of upcoming recession. A flat (or humped) yield curve is one in which the shorterand longer-term yields are very close to each other, which is also a predictor of an economic transition. The slope of the yield curve is also seen as important: the greater  the slope, the greater the gap between short- and long-term rates. Definition of 'Flat Yield Curve'

A yield curve in which there is little difference between short-term and long-term rates for bonds of the same credit quality. This type of yield curve is often seen during transitions between normal and inverted curves. When short- and long-term bonds are offering equivalent yields, there is usually little  benefit in holding the longer-term instruments - that is, the investor does not gain any excess compensation for the risks associated with holding longer-term securities. For  example, a flat yield curve on U.S. Treasury would be one in which the yield on a twoyear bond is 5% and the yield on a 30-year bond is 5.1%.

Definition of 'Inverted Yield Curve'

An interest rate environment in which long-term debt instruments have a lower yield than short-term debt instruments of the same credit quality. This type of yield curve is the rarest of the three main curve types and is considered to be a predictor of economic recession. Partial inversion occurs when only some of the short-term Treasuries (five or 10 years) have higher yields than the 30-year Treasuries do. An inverted yield curve is sometimes referred to as a "negative yield curve".

15

Historically, inversions of the yield curve have preceded many of the U.S. recessions. Due to this historical correlation, the yield curve is often seen as an accurate forecast of  the turning points of the business cycle. A recent example is when the U.S. Treasury yield curve inverted in 2000 just before the U.S. equity markets collapsed. An inverse yield curve predicts lower interest rates in the future as longer-term bonds are being demanded, sending the yields down. Definition of 'Yield Curve Risk'

The risk of experiencing an adverse shift in market interest rates associated with investing in a fixed income instrument. The risk is associated with either a flattening or  steepening of the yield curve, which is a result of changing yields among comparable  bonds with different maturities. When market yields change, this will impact the price of a fixed-income instrument. When market interest rates, or yields, increase, the price of a bond will decrease and vice versa. When the yield curve shifts, the price of the bond, which was initially priced based on the initial yield curve, will change in price. If the yield curve flattens, then the yield spread between long- and short-term interest rates narrows, and the price of the bond will change accordingly. If the bond is a short-term bond maturing in three years and the three-year yield decreases, the price of this bond will increase. If the yield curve steepens, this means that the spread between long- and short-term interest rates increases. Therefore, long-term bond prices will decrease relative to shortterm bonds. Changes in the yield curve are based on bond risk premiums and expectations of future interest rates.

16

VALUATION OF EQUITY Introduction

Equity shares, commonly referred to as ordinary shares also represent the form of  fractional ownership in which a shareholder, as a fractional owner, undertakes the maximum entrepreneurial risk associated with business or a business venture. The holders of such shares are members of the company and have voting rights.

17

Important characteristics of equity shares are as follows:

1. Equity shares (other than non-voting equity shares), have voting rights at all general meting of the company. These votes have the affect of controlling the management of the company.

2. Equity shareholders have the right to share the profits of the company in the form of  dividends (cash) and bonus shares. However even equity shareholders cannot demand declaration of dividend by the company which is left to the discretion of the board of  directors.

3. When the company is wound up, payment towards the equity share capital will be made to the respective shareholders only after payment of the claims of all the creditors and the preference share capital.

Apart from above rights, The Companies Act, 1956 gives various rights to equity shareholders. 4.

From above features, it is clear that as compared to Debentures/Bonds, equity shares involve more risk because of uncertainty of cash inflows. And at the same time, in case of  equity shares the cash inflows are not constant; instead they keep on varying in form of  dividends been declared at different rates every year depending on the profitability of the company and its requirement of funds for expansion and other purposes.

Need for equity valuation

18

Valuation of equity shares is required for many decisions including mergers and acquisition and portfolio management. The price that a buyer/ acquirer is willing to pay need not be same as price in the stock market,, some practical examples for the same are “CitiGroup” intends to acquire the outstanding shares of e-Serve at rs.800 per share as compared to closing price of rs.630 on April 8, 2004 (the financial express, April 13, 2004), other example is Tata steel ltd. Acquiring “Corus group plc” at 608 pence per share which was way higher than the initial offer of 455 pence per share. The reason why many investors are ready to offer higher price for another  company’s share is that they believe that the shares of the company being acquired are under priced. There belief is based on many factors such as, projection of future earnings, comparison of prices and ratios with other companies and with historical ratios, etc. Fundamental analysis assumes that the price in the stock market may not reflect a stock’s real or intrinsic value. It also assumes that price will move towards the intrinsic value in the long run. The aim of the analyst is to identify stocks that are over or under   priced. Stocks that are under priced should be purchased and stocks that are overpriced should be sold or short-sold, another way of identifying whether a stock should be  purchased or not is to estimate the returns over a given future period and compare it with the required return. Fundamental analysis is suitable for those who want to buy and hold a stock; technical analysis may be more suitable for those interested in quick buy and sell decisions.

19

Equity valuation models

There are various approaches to equity valuation. Balance sheet valuation

Under this method it is assumed that the company will go under immediate liquidation and therefore all the assets of the company will be sold and liabilities will be paid off. Accordingly, both assets and liabilities are valued at market value instead of balance sheet values. The net amount left after selling all the assets and paying off all the liabilities and  paying off preference share holders is available to equity share holders and this amount is divided with the number of shares to calculate the value per share. Therefore this method is also known as ‘ asset backing method’, net assets method and intrinsic value method. The procedure to value equity shares under this method is as follows:

Valuation based on yield

Yield means income, accordingly, under this method shares are valued based on income generating capacity of the company. This simple logic behind this valuation principle is that if company is earning more than the general expectation of the investors/prospective investors, they will want to invest money in the company by buying the shares of the company and therefore, value of shares of such company will be higher as compared to other companies in the same industry. Yield method is divided into two different methods, namely: •

dividend yield &

•

earnings yield

Present value of future prices/cash inflows

20

This model of valuation is based on time value of money. Under this model we discount all the future cash inflows expected from the share to today’s value using cost of equity as the discounting factor. This method is also known as ‘capitalization of earnings model’.

Dividend discount model

According to the dividend discount model also known as Gordon’s model conceptually a very sound approach, the value of any equity share is 4equal to the present value of  dividends expected from its ownership plus the present value of the sale price expected when the equity share is sold. For applying the dividend discount model (DDM), we will  be making following assumptions: I) Dividends are paid annually(which is commonly paid by almost all the companies); and II) The first dividend is received one year after the equity share is bought. Here is the basic idea: any stock is ultimately worth no more than what it will provide investors in current and future dividends. Financial theory says that the value of a stock is worth all of the future cash flows expected to be generated by the firm, discounted by an appropriate risk-adjusted rate. According to the DDM, dividends are the cash flows that are returned to the shareholder. (We're going to assume you understand the concepts of  time value of money and discounting. To value a company using the DDM, you calculate the value of dividend payments that you think a stock will throw-off in the years ahead. Here is what the model says:

Where: P= the price at time 0 r= discount rate For simplicity's sake, consider a company with a $1 annual dividend. If you figure the company will pay that dividend indefinitely, you must ask yourself what you are willing to pay for that company. Assume expected return, or, more appropriately in academic 21

 parlance, the required rate of return, is 5%. According to the dividend discount model, the company should be worth $20 ($1.00 / .05).

How do we get to the formula above? It's actually just an application of the formula for   perpetuity :

The obvious shortcoming of the model above is that you'd expect most companies to grow over time. If you think this is the case, then the denominator equals the expected return less the dividend growth rate. This is known as the constant growth DDM or the Gordon model after its creator, Myron Gordon. Let's say you think the company's dividend will grow by 3% annually. The company's value should then be $1 / (.05 - .03) = $50. Here is the formula for valuing a company with a constantly growing dividend, as well as the  proof of the formula:

The classic dividend discount model works best when valuing a mature company that  pays a hefty portion of its earnings as dividends, such as a utility company. The Problem of Forecasting Proponents of the dividend discount model say that only future cash dividends can give you a reliable estimate of a company's intrinsic value. Buying a stock for any other reason - say, paying 20 times the company's earnings today because somebody will pay 30 times tomorrow - is mere speculation. 22

In truth, the dividend discount model requires an enormous amount of speculation in trying to forecast future dividends. Even when you apply it to steady, reliable, dividend paying companies, you still need to make plenty of assumptions about their future. The model is subject to the axiom "garbage in, garbage out", meaning that a model is only as good as the assumptions it is based upon. Furthermore, the inputs that produce valuations are always changing and susceptible to error. The first big assumption that the DDM makes is that dividends are steady, or grow at a constant rate indefinitely. But even for steady, reliable, utility-type stocks, it can be tricky to forecast exactly what the dividend payment will be next year, never mind a dozen years from now. Multi-Stage Dividend Discount Models

To get around the problem posed by unsteady dividends, multi-stage models take the DDM a step closer to reality by assuming that the company will experience differing growth phases. Stock analysts build complex forecast models with many phases of  differing growth to better reflect real prospects. For example, a multi-stage DDM may  predict that a company will have a dividend that grows at 5% for seven years, 3% for the following three years and then at 2% in perpetuity. However, such an approach brings even more assumptions into the model - although it doesn't assume that a dividend will grow at a constant rate, it must guess when and by how much a dividend will change over time. What Should Be Expected?

Another sticking point with the DDM is that no one really knows for certain the appropriate expected rate of return to use. It's not always wise simply to use the long-term interest rate because the appropriateness of this can change. The High-Growth Problem

 No fancy DDM model is able to solve the problem of high-growth stocks. If the company's dividend growth rate exceeds the expected return rate, you cannot calculate a 23

value because you get a negative denominator in the formula. Stocks don't have a negative value. Consider a company with a dividend growing at 20% while the expected return rate is only 5%: in the denominator (r-g) you would have -15% (5%-20%)! In fact, even if the growth rate does not exceed the expected return rate, growth stocks, which don't pay dividends, are even tougher to value using this model. If you hope to value a growth stock with the dividend discount model, your valuation will be based on nothing more than guesses about the company's future profits and dividend policy decisions. Most growth stocks don't pay out dividends. Rather, they re-invest earnings into the company with the hope of providing shareholders with returns by means of a higher share price. Consider Microsoft, which didn't pay a dividend for decades. Given this fact, the model might suggest the company was worthless at that time - which is completely absurd. Remember, only about one-third of all public companies pay dividends. Furthermore, even companies that do offer payouts are allocating less and less of their earnings to shareholders. Conclusion The dividend discount model is by no means the be-all and end-all for valuation. That  being said, learning about the dividend discount model does encourage thinking. It forces investors to evaluate different assumptions about growth and future prospects. If nothing else, the DDM demonstrates the underlying principle that a company is worth the sum of  its discounted future cash flows. (Whether or not dividends are the correct measure of  cash flow is another question.) The challenge is to make the model as applicable to reality as possible, which means using the most reliable assumptions available. Example of the Dividend Discount Valuation Model

ABC Corporation is paying dividends of $2 per share. Investors expect a rate of return of  8% on their investment. Dividends are expected to grow by 5% for one year and then 3% each year thereafter. Applying the discount model using the two formulas above, the value of the investment can be calculated in each period: Year 1. The value of the investment for this time frame is $2.00/1.08 = $1.85. •

24

Year 2. Dividends for this year have grown to $2.10 per share based on the 5% growth rate. The value of the investment for this period of time is expected to be worth $2.10/(1.08)^2 = $1.80 Constant growth value. According to the constant growth equation listed above, the constant growth value of a share of stock is $2.10/(0.08-0.03)= $42. Value of a share of ABC Corporation. The value of a share of stock is calculated by using the two formulas above to calculate the value of the dividends in each period: (2.00)/(1.08) + 2.10/(1.08)^2 + 2.10/(0.08 – 0.03) = $45.65 per share. Compare to a value of a current share of stock. This is the most important part of the model. If a share of stock is trading at less than $45.65 per share, the stock is underpriced and they can profit by purchasing it. If the stock is trading at more than $45.65 per share, they may be able to profit by short selling the security. •

•

Price/earnings model

P/E model is based on the same principle as DDM model is based, i.e. ‘time value of  money’ concept. The only difference is that DMN model uses dividend for valuing the shares, but as compared to this P/E model uses P/E ratio to value the shares. But the answer and conclusion drawn under both the models is same. Example of earning per share (EPS) and price earning ratio (P/E ratio) Ex 1) x. ltd. has earned rs.10 lakhs before tax; it falls under tax bracket of 54%. Preference dividends Rs.60000 per. Annum. Equity share consist of 1 lakh shares of Rs. 10 each fully paid up. Calculate the total earnings for equity shareholders< earnings per  share& P/E ratio if the market price is rs.60 per share and required rate of return of equity shareholders assuming that the equity share is fairly priced. Statement showing earning per share particulars Earning before tax (-)tax@54% Earning after tax (-)preference dividend Earning for equity shareholders (/)total no. of equity shares

Rs. 1000000 540000 460000 60000 400000 100000 25

Earnings per share

4

P/E ratio=MPS/EPS=60/4=15 TIMES Required rate of return=EPS/amount invested per share*100 4/60*100=6.67% OR  1/P/E ratio*100=1/15*100=6.67% i.e. reciprocal of P/E ratio.

 No growth model Growth is driven by two factors i.e. retention ratio/savings (i.e. ‘b’) and the rate (‘r’) at which such savings are invested. For a no growth company retention ratio/ savings is zero i.e. whatever is earned by the company is paid as dividend, therefore for a no growth company, earnings and dividends are always same.

26

BIBLIOGRAPHY

•

Investment analysis and portfolio management- Abhishek Sood

•

www.wikipedia.com

• •

27

28