Business Finance Lecture 8

Lecture 8: Equity Valuation Share valuation Difficulties ! • With equity, not even the promised cash ßows are certain in advance ! • Life of investment is uncertain because an equity can theoretically last forever (no maturity)! • Difficult to measure the expected return the market requires ! Share prices are highly volatile ! FTSE 100 Index Data Source: Yahoo! FTSE100,Close, Index,1996-2016 7,500.00 7,000.00 6,500.00 6,000.00 5,500.00 5,000.00 4,500.00 4,000.00 Apr,10,,1996 Aug,29,,1996 Jan,17,,1997 Jun,10,,1997 Oct,27,,1997 Mar,17,,1998 Aug,6,,1998 Dec,23,,1998 May,19,,1999 Oct,6,,1999 Feb,25,,2000 Jul,18,,2000 Dec,4,,2000 Apr,26,,2001 Sep,14,,2001 Feb,4,,2002 Jun,27,,2002 Nov,13,,2002 Apr,3,,2003 Aug,26,,2003 Jan,14,,2004 Jun,4,,2004 Oct,21,,2004 Mar,11,,2005 Aug,2,,2005 Dec,19,,2005 May,12,,2006 Sep,29,,2006 Feb,19,,2007 Jul,11,,2007 Nov,27,,2007 Apr,18,,2008 Sep,8,,2008 Jan,27,,2009 Jun,19,,2009 Nov,10,,2009 Mar,31,,2010 Aug,25,,2010 Jan,14,,2011 Jun,8,,2011 Oct,25,,2011 Mar,14,,2012 Aug,6,,2012 Dec,21,,2012 May,16,,2013 Oct,4,,2013 Feb,24,,2014 Jul,16,,2014 Dec,2,,2014 Apr,27,,2015 Sep,15,,2015 Feb,4,,2016 Jun,27,,2016 Nov,11,,2016 3,500.00 3,000.00 The present value of equity ! In general, the price today of a share of equity, P0, is the present value of all of its future dividends, D1, D2, D3,É:! Where R is the investor required return (dividend yield, dividend payout, capital gain). ! Proof that share value = PV of future dividends ! First, look one period ahead: ! 0 1 Div$1 Price$1 PV$=$? Pt = Div t +1 Pt +1 + 1+ r 1 + r   The value of the share today (P0) is: ! P0 = Div1 P + 1 1+ r 1+ r ! The value the share one year from today (P1) is: ! P1 = Div 2 P + 2 1 + r 1+ r ! Substitute P1 into the formula for P0: ! P0 = Div1 Div2 P2 + + 2 1+ r (1 + r ) (1 + r )2 Continue adding a period and substituting the result into the original equation, to obtain: ! Conclusion: the value of a share is the present value of all future dividends. It does NOT matter when you intend to sell the share. ! ! Three scenarios ! Scenario 1: Constant dividend (zero growth) The case of zero growth is one weÕve already seen. A share of equity in a company with a constant dividend is much like a preference share. For a zero-growth share of equity, this implies that: ! D1 = D2 = D3 = D = constant (assuming that the dividend is constant, and there is no change). ! Zero growth: dividends are expected to be the same forever. ! Approach: because the dividend is always the same and there is no growth, the share price can be viewed as an ordinary perpetuity with a cash ßow equal to D every period.!   If the dividend is expected to be constant and the required rate of return is R, the present value of future dividend cash ßows is: ! P0 = D D D D D + + + + +L (1 + R)1 (1 + R)2 (1 + R)3 (1 + R)4 (1 + R)5 P0 = D R Lecture example 1 ! A company pays a dividend of $2 per share per year. If investors require a 10% return, what is a share price? ! D&=&2 0 1 D&=&2 D&=&2 2 3 Answer:! P = D/r! = $2/0.10! = $20 ! Scenario 2: Constant growth in dividend (constant growth) Constant growth: dividends are expected to grow forever at a constant rate (g).! D3 ………. 3 ………. D2 D0 0 D1 1 2 ! Approach: we would use the growing perpetuity formula, because dividends grow forever at a constant rate.! Assume the dividends grow at constant growth rate of g and required rate of return is R. Then the share price will be: ! When D1 is unknown, we use: ) P)0 = D0 ´ (1 + g ) ) ) R- g otherwise, we use: !P0 = D1 R- g Note: g cannot be > R ! You have to use the dividend at time T + 1 when looking at the present value today. You should always assume that C are the cash ßows in 1 yearÕs time. ! Lecture example 2 ! The required rate of return on the stock of J&P PLC is 8.8%. You expect that the current dividend of £0.50 will grow at a steady rate of 6% per year. A dividend of £0.50 has just been paid. !   Required: a) Calculate the stock value for J&P PLC.! b) The current market price of J&P PLC stock is £23. Is the stock fairly valued, undervalued or overvalued? ! Answers: D0 will be the dividend just paid, and g will be the constant growth rate: D0 = 0.50 ! R = 0.088 ! g = 0.06! a) P0 = D0 (1+g) / (R-g) ! = (£0.50 x 1.06) / (0.088-0.06)! = £18.93! b) The intrinsic value (price at which the share should be selling for) for J&P, £18.93 < market price of £23. So, stock is overvalued according to the constant growth model. ! ! Summary:! P0 = D0 ´ (1 + g ) D1 = R -g R -g Relationship of price, P, with growth rate and required rate of return: ! ) Growth rate! g Required rate of return! Constant growth model Ñ R => P0 => P0 ation modelÕ ! Advantages ! • The dividend valuation model is often useful for valuing stable-growth, dividend-paying companies ! • It is often useful for valuing broad-based equity indexes ! • The model features simplicity and clarity; it is useful for understanding the relationship among value and growth, required rate of return, and pay-out ratio ! • It provides an approach to estimating the expected rate of return given efficient prices (for stable-growth, dividend-paying companies) ! Scenario 3: Non-constant growth in dividend (differential growth) Differential growth: dividends have different growth rates in different time periods. ! The main reason for considering this case is to allow for ÔsupernormalÕ growth rates over some Þnite length of time. To avoid the problem of having to forecast and discount an   inÞnite number of dividends, we shall require that the dividends start growing at a constant rate at some time in the future. ! Examples: • No dividend for the Þrst few years (Type I) ! • Non-constant growth in the Þrst few years and then constant growth later on in perpetuity (Type II) ! • Growth rate 1 for the Þrst few years and then a different growth rate 2 for remaining years in perpetuity (Type III) ! ' Valuation approach: split the problem into sections according to the growth rate in different time periods. ! Lecture example 3 (Non-constant growth in dividend Ñ Type I) ! A company is not expected to pay a dividend until three yearsÕ time. The dividend will then be EUR 2.50 and increase each year by 5%. If the required return is 10%, what is the share price today?! ! PV (growing perpetuity) Step 1: Draw a timeline Step 2: Calculate the price at time 3 (valuing the perpetuity) g = 5%! D3 = 2.50 ! R = 10%! P3 = D3 x (1 + g) / (R Ñ g)! = 2.50 x 1.05 / (0.10 Ð 0.05)! = € 52.50! Step 3: Calculate the present value of the price at time 0 PV = FV / (1+r)t P0 = € 52.50 / 1.103 = € 39.44! Lecture example 4 (Non-constant growth in dividend Ñ Type II) ! A company pays dividends of EUR 1 in one year, EUR 2 in two years and EUR 2.50 in three yearsÕ time. Dividends are then expected to grow at a constant rate of 5% from then on in perpetuity. If the required return is 10%, what is the share price today? ! ! Step 1: Draw a timeline PV (growing perpetuity)   For this problem, the constant growth starts at time 3. This means that we can use our constant growth model to determine the share price at time 3, P3. The most common mistake in this situation is to incorrectly identify the start of the constant growth phase and, as a result, calculate the future share price at the wrong time.! Step 2: Calculate the price at time 2 As always, the share price is the present value of all the future dividends. To calculate this present value, we Þrst have to compute the present value of the share price 3 years down the road, just as we did before.! P3 = D3 x (1 + g) / (R Ñ g)! = (2.50 x 1.05) / (0.10 Ð 0.05)! = € 52.50 (as in example 3)! Step 3: Calculate the price at time 0, working out the present value of each cash ßow separately, including the present value of the price at time 3. !0 = $1 $2 $3 !3 ! + + + 1 2 3 ( 1 + ( )3 (1 + ( ) (1 + ( ) (1 + ( ) !0 = 1 2 2.50 52.50 + + + = €+43.88! 1.10 1.102 1.103 1.103 When there are two growth rates, the idea is that the dividend will grow at a rate of g1 for for t years and then grow at a rate of g2 thereafter forever. ! !0 = 1 + (1 . $1 !. × *1 − + ! - /+ & − (1 (1 + &). 1+& Notice that the Þrst term in our expression is the present value of a growing annuity. In this Þrst stage, g1 can be greater than R. The second part is the present value of the share price once the second stage begins at time t. We can calculate Pt as follows: ! Dt +1 D0 ´ (1 + g 1 )t ´ (1 + g 2 ) Pt = = R - g2 R - g2 Lecture example 5 ! Royal Hotel SA just paid a dividend of €2.35 per share. The dividends are expected to grow at 26% a year for the next eight years and then level off to an 8% annual growth rate indeÞnitely. If the required return is 15%, what is the share price today?! Step 1: Calculate the price at time: Pt = Dt+1 D ´ (1 + g1 ) t ´ (1 + g2 ) = 0 R - g2 R - g2   So:! !" # $%&'( ) *+ , -%$./" ) *+ , -%-"/( # $&-%&&( -%+' 0 -%-" Step 2: Calculate the price today, including P8 just calculated: !" # % , (% . $% !. ) *% ' + ! - /, & ' (% 0% , &1. %,& Where D1 = D0 x (1 + g) ! ! So: ! !" # $%&' ( )* + "%$,$&"%&& * + "%$, 2 # *"4%$25 ( /* . 0 1 3+ )* + "%*'-2 "%*' . "%$, * + "%*' The two-stage model:! • This is very useful because many scenarios exist in which a company can achieve a supernormal growth rate for a few years, after which time the growth rate falls to a more sustainable level.! • For example, a company may achieve supernormal growth due to a patent, Þrst mover advantage, or another reason that provides a temporary lead in a speciÞc marketplace. Later, earnings growth must decline to a level thats more consistent with competition and the growth in the overall economy. ! • Using a two-stage model, we can model the extraordinary growth for a few years, and the normal growth thereafter. ! Calculating implied growth Non-constant growth in dividend ! The dividend growth rate inßuences the estimated value of a stock using the constant growth model. Thus, differences between estimated values of a stock and its actual market value might be explained by different growth rate assumptions. ! Lecture example 6 ! The required rate of return for the stock of BBA PLC is 12.2%. The current dividend is $2. What dividend growth rate would be required to justify a $40 price? ! Answer: P0 = D0 x (1 + g) / (R Ñ g) R = 0.122! D0 = $2! P0 = $40 ! So, 40 = [2 x (1 + g)] / (0.122 Ñ g)! 40 x (0.122 Ð g) = 2 + 2g!   4.88 Ð 40g = 2 + 2g! 2.88 = 42g ! g = 2.88 / 42! = 0.0686! = 6.86%! Components of shareholder return When shareholders receive cash: ! • The company pays dividends ! • You sell your shares either to another investor in the market or back to the company ! As with bonds, the price of a share is the present value of these expected cash ßows. ! Dividend' Yield Capital' Gains' Yield Total' Return Dividend yield Ñ an equityÕs expected cash dividend divided by its current price. ! Capital gains yield Ñ the dividend growth rate, or the rate at which the value of an investment grows. ! R ="Dividend"yield"+"Capital"gains"yield R ="D1/P0 +"g Proof: P0"="D1/(R)– g) So,)P0"x"(R)– g))=)D1 So,)P0"x"R)– P0"x"g)=)D1 So,)P0"x"R)=)D1"+)P0"x"g So,)R =)D1/P0"+) g) Strengths of the Gordon Growth Model ! • The Gordon growth model is often useful for valuing stable-growth, dividend-paying companies ! • It is often useful for valuing broad-based equity indexes ! • The model features simplicity and clarity; it is useful for understanding the relationship among value and growth, required rate of return, and pay-out ratio ! • It provides an approach to estimating the expected rate of return given efficient prices (for stable-growth, dividend-paying companies)! Understanding stock markets and preference shares Comparing ordinary and preference shares ! Ordinary equity Ñ this is equity without priority for dividends or in bankruptcy. !   Preference shares Ñ equity with dividend priority over ordinary shares, normally with a Þxed dividend rate, sometimes without voting rights. ! Ordinary equity is equity that has no special preference either in receiving dividends or in bankruptcy. Preference shares differ from ordinary equity because they have preference over ordinary equity in the payment of dividends, and in the distribution of corporation assets in the event of liquidation. Preference just means that the holders of the preference shares must receive a dividend before holders of ordinary shares are entitled to anything.! Other features of preference shares • Holders of preference shares sometimes have no voting privileges ! • Preference shares have a stated liquidating value (e.g. 100 per share) and the cash dividend is described as a percentage of stated value ! • Dividends payable on preference shares are either cumulative or non-cumulative, most are cumulative, (i.e. if not paid in a particular year, they will be carried forward) ! • Are preference shares equity or debt?! Market terms ! Primary market Ñ the market in which new securities are originally sold to investors. ! Secondary market Ñ the market in which previously issued securities are traded among investors. ! Dealer Ñ an agent who buys and sells securities from inventory. ! Broker Ñ an agent who arranges security transactions among investors.! Thus, when we speak of used car dealers and real estate brokers, we recognise that the used car dealer maintains an inventory, whereas the real estate broker does not. ! Summary  