![Two-Stage Growth Model: Example
EXAMPLE THE CURRENT DIVIDEND ON AN EQUITY SHARE OF
VERTIGO LIMITED IS RS.2.00. VERTIGO IS EXPECTED TO ENJOY AN
ABOVE-NORMAL GROWTH RATE OF 20 PERCENT FOR A PERIOD OF 6
YEARS. THEREAFTER THE GROWTH RATE WILL FALL AND STABILISE
AT 10 PERCENT. EQUITY INVESTORS REQUIRE A RETURN OF 15
PERCENT. WHAT IS THE INTRINSIC VALUE OF THE EQUITY SHARE OF
VERTIGO ?
THE INPUTS REQUIRED FOR APPLYING THE TWO-STAGE MODEL ARE :
g1 = 20 PERCENT
g2 = 10 PERCENT
n = 6 YEARS
r = 15 YEARS
D1 = D0 (1+g1) = RS.2(1.20) = 2.40
PLUGGING THESE INPUTS IN THE TWO-STAGE MODEL, WE GET THE
INTRINSIC VALUE ESTIMATE AS FOLLOWS :
1.20 6
1 -
1.15 2.40 (1.20)5
(1.10) 1
P0 = 2.40 +
.15 - .20 .15 - .10 (1.15)6
1 - 1.291 2.40 (2.488)(1.10)
= 2.40 + [0.497]
-0.05 .05
= 13.968 + 65.289
= RS.79.597](https://image.slidesharecdn.com/chapter13equityvaluation-230817134151-5743376d/85/Chapter13EquityValuation-ppt-6-320.jpg)
![H Model
ga
gn
H 2H
D0
PO = [(1+gn) + H (ga + gn)]
r - gn
D0 (1+gn) D0 H (ga + gn)
= +
r - gn r - gn
VALUE BASED PREMIUM DUE TO
ON NORMAL ABNORMAL GROWH
GROWTH RATE RATE](https://image.slidesharecdn.com/chapter13equityvaluation-230817134151-5743376d/85/Chapter13EquityValuation-ppt-7-320.jpg)
![Forecasting The Aggregate Stock Market Return
Stock market returns are determined by an interaction of two
factors : investment returns and speculative returns.
• In formal terms :
SMRn = [DYn + EGn] + [(PEn / PE0)1/n – 1]
Investment return Speculative return
where : SMRn = annual stock market return over a period of n years
DYn = annual dividend yield over a period of n years
EGn = annual earnings growth over a period of n years
PEn = price-earnings ratio at the end of n years
PE0 = price-earnings ratio at the beginning of n years.](https://image.slidesharecdn.com/chapter13equityvaluation-230817134151-5743376d/85/Chapter13EquityValuation-ppt-25-320.jpg)
![Illustration
Suppose you want to forecast the annual return from the stock
market over the next five years (n is equal to 5). You come up with
the following estimates. DY5 = 0.025 (2.5 percent), EG5 = 0.125 (12.5
percent), and PE5 = 18. The current PE ratio, PEo, is 15. The forecast
of the annual return from the stock market is determined as follows:
SMR5 = [0.025 + 0.125] + [(18/15)1/5 – 1]
= [0.15] + [0.037]
= 15 percent + 3.7 percent = 18.7 percent
15 percent represents the investment return and 3.7 percent
represents the speculative return.](https://image.slidesharecdn.com/chapter13equityvaluation-230817134151-5743376d/85/Chapter13EquityValuation-ppt-26-320.jpg)
Chapter13EquityValuation.ppt
- 1. Chapter 13 EQUITY VALUATION How to Find Your Bearings
- 2. OUTLINE • Balance Sheet Valuation • Dividend Discount Model • Earnings Multiplier Approach • Earnings – Price Ratio, Expected Return, and Growth • Other Comparative Valuation Ratios • Equity Portfolio Management • Forecasting the Aggregate Stock Market Return
- 3. Balance Sheet Valuation • BOOK VALUE • LIQUIDATION VALUE • REPLACEMENT COST
- 4. Dividend Discount Model • SINGLE PERIOD VALUATION MODEL D1 P1 P0 = + (1+r) (1+r) • MULTI - PERIOD VALUATION MODEL Dt P0 = t=1 (1+r)t • ZERO GROWTH MODEL D P0 = r • CONSTANT GROWTH MODEL D1 P0 = r - g
- 5. Two-Stage Growth Model 1 - 1+g1 n 1+r Pn P0 = D1 + r - g1 (1+r)n WHERE Pn D1 (1+g1)n-1 (1+g2) 1 = (1+r)n r - g2 (1+r)n
- 6. Two-Stage Growth Model: Example EXAMPLE THE CURRENT DIVIDEND ON AN EQUITY SHARE OF VERTIGO LIMITED IS RS.2.00. VERTIGO IS EXPECTED TO ENJOY AN ABOVE-NORMAL GROWTH RATE OF 20 PERCENT FOR A PERIOD OF 6 YEARS. THEREAFTER THE GROWTH RATE WILL FALL AND STABILISE AT 10 PERCENT. EQUITY INVESTORS REQUIRE A RETURN OF 15 PERCENT. WHAT IS THE INTRINSIC VALUE OF THE EQUITY SHARE OF VERTIGO ? THE INPUTS REQUIRED FOR APPLYING THE TWO-STAGE MODEL ARE : g1 = 20 PERCENT g2 = 10 PERCENT n = 6 YEARS r = 15 YEARS D1 = D0 (1+g1) = RS.2(1.20) = 2.40 PLUGGING THESE INPUTS IN THE TWO-STAGE MODEL, WE GET THE INTRINSIC VALUE ESTIMATE AS FOLLOWS : 1.20 6 1 - 1.15 2.40 (1.20)5 (1.10) 1 P0 = 2.40 + .15 - .20 .15 - .10 (1.15)6 1 - 1.291 2.40 (2.488)(1.10) = 2.40 + [0.497] -0.05 .05 = 13.968 + 65.289 = RS.79.597
- 7. H Model ga gn H 2H D0 PO = [(1+gn) + H (ga + gn)] r - gn D0 (1+gn) D0 H (ga + gn) = + r - gn r - gn VALUE BASED PREMIUM DUE TO ON NORMAL ABNORMAL GROWH GROWTH RATE RATE
- 8. Illustration: H Ltd D0 = 1 ga = 25% H = 5 gn = 15% r = 18% 1 (1.15) 1 x 5(.25 - .15) P0 = + 0.18 - 0.15 0.18 - 0.15 = 38.33 + 16.67 = 55.00 IF E = 2 P/E = 27.5
- 9. Impact Of Growth On Price, Returns, and P/E Ratio PRICE DIVIDEND CAPITAL PRICE D1 YIELD GAINS EARNINGS PO = YIELD RATIO r - g (D1 / PO) (P1 - PO) / PO (P / E) RS. 2.00 LOW GROWTH FIRM PO = = RS.13.33 15.0% 5.0% 4.44 0.20 - 0.05 RS. 2.00 NORMALGROWTH PO = = RS.20.00 10.0% 10.0% 6.67 FIRM 0.20 - 0.10 RS. 2.00 SUPERNORMAL PO = = RS.40.00 5.0% 15.0% 13.33 GROWTH FIRM 0.20 - 0.15
- 10. Free Cash Flow Model The enterprise value (EV) according to the free cash flow model is: EV= FCF1 + FCF2 +…+ FCFH + VH (1+WACC) (1+WACC)2 (1+WACC)H (1+WACC)H Present value of the FCF during the explicit forecast period Present value of horizon value
- 11. Earnings Multiplier Approach P0 = m E1 DETERMINANTS OF m (P / E) D1 P0 = r - g E1 (1 - b) = r - ROE x b (1 - b) P0 / E1 = r - ROE x b
- 12. CROSS -SECTION REGRESSION ANALYSIS P / E = 8.2 + 1.5g + 6.7b - .2 g = GROWTH RATE FOR ‘NORMALIZED’ EPS b = PAYOUT RATIO = STD. DEV .. OF % EPS CHANGE • EVERY CONCEIVABLE VARIABLE & COMBINATION OF VAIRABLES .. TRIED.. • ALMOST .. ALL … THESE MODELS .. HIGHLY SUCCESSFUL .. EXPLAINING STOCK PRICES .. AT A POINT .. TIME, BUT LESS SUCCESSFUL … IN SELECTING APPROPRIATE .. STOCKS .. BUY .. SELL. • WHY 1. MARKET TASTES CHANGE • WEIGHTS CHANGE 2. INPUT VALUES CHANGE OVER TIME • DIV … & GROWTH IN EARNINGS 3. THERE ARE FIRM EFFECTS NOT CAPTURED BY THE MODEL
- 13. P / E Benchmark Rules Of Thumb • GROWTH RATE IN EARNINGS 10% 15% 20% 25% 35% 1 1 • = 8.33 NOMINAL INTEREST RATE .12 1 = 5.00 .20 1 1 • = 25 REAL RETURN .04 1 = 16.67 .06 0.5 PAYOUT RATIO • = 16.67 .18 - .15 REQ. RET - GR. RATE
- 14. Growth And P / E Multiple CASE A : NO GROWTH CASE B : 10 PERCENT GROWTH YEAR 0 YEAR 1 YEAR 0 YEAR 1 TOTALASSETS 100 100 100 110 NET WORTH 100 100 100 110 SALES 100 100 100 110 PROFIT AFTER TAX 20 20 20 22 DIVIDENDS 20 20 10 11 RETAINED EARNINGS - - 10 11 CASE A CASE B NO GROWTH GROWTH DISCOUNT DISCOUNT DISCOUNT DISCOUNT DISCOUNT DISCOUNT RATE: 15% RATE: 20% RATE: 25% RATE: 15% RATE: 20% RATE: 25% VALUE 20 / 0.15 20 / 0.20 20 / 0.25 10 / (0.15 10 / (0.20 10 / (0.25 - 0.10) - 0.10) - 0.10) = 133.3 = 100 = 80 = 200 = 100 = 66.7 PRICE- 133.3 / 20 100 / 20 80 / 20 200 /20 100 / 20 66.7 / 20 EARNINGS = 6.67 = 5.0 = 4.0 = 10.0 = 5.0 = 3.33 MULTIPLE
- 15. E / P, Expected Return, And Growth 1 2 ……... E1 = D1 E2 = D2 = 15 = 15 15 r = 15% P0 = = 100 0.15 INVESTMENT .. RS. 15 PER SHARE IN YEAR 1 … EARNS 15% 2.25 NPV PER SHARE = - 15 + = 0 0.15 RATE OF INCREMENTAL PROJECT'S IMPACT ON SHARE PRICE E1/P0 r RETURN CASH FLOW NPV IN SHARE PRICE IN YEAR 0, YEAR 1 IN YEAR 0 P0 0.05 0.75 -10 -8.70 91.30 0.164 0.15 0.10 1.50 -5 -4.35 95.65 0.157 0.15 0.15 2.25 0 0 0 0.15 0.15 0.20 3.00 5 4.35 104.35 0.144 0.15 0.25 3.75 10 8.70 108.70 0.138 0.15
- 16. IN GENERAL, WE CAN THINK OF THE STOCK PRICE AS THE CAPITALISED VALUE OF THE EARNINGS UNDER THE ASSUMPTION OF NO GROWTH PLUS THE PRESENT VALUE OF GROWTH OPPORTUNITIES (PVGO). E1 P0 = + PVGO r MANIPULATING THIS A BIT, WE GET E1 PVGO = r 1 - P0 P0 FROM THIS EQUATION, IT IS CLEAR THAT : EARNINGS-PRICE RATIO IS EQUAL TO r WHEN PVGO IS ZERO. EARNINGS-PRICE RATIO IS LESS THAN r WHEN PVGO IS POSITIVE. EARNINGS-PRICE RATIO IS MORE THAN r WHEN PVGO IS NEGATIVE.
- 17. Price To Book Value Ratio (PBV Ratio) Market price per share at time t PBV ratio = Book value per share at time t The PBV ratio has always drawn the attention of investors. During the 1990s Fama and others suggested that the PBV ratio explained to a significant extent the returns from stocks.
- 18. Determinants Of The PBV Ratio D1 P0 = r – g D1 = E1 (1 – b) = E0 (1 + g) (1 – b) E0 (1 + g) (1 – b) r – g E0 = BV0 x ROE BV0 (ROE) (1 + g) (1 – b) r – g P0 ROE (1 + g) (1 – b) BV0 r - g P0 = P0 = PBV ratio = =
- 19. Price To Sales Ratio (PSR Ratios) • In recent years PSR has received a lot of attention as a valuation tool. The PSR is calculated by dividing the current market value of equity capital by annual sales of the firm. • Portfolios of low PSR stocks tend to outperform portfolios of high PSR stocks. • It makes more sense to look at PSR/Net profit margin as net profit margin is a key driver of PSR.
- 20. Determinants of the PS Ratio PS ratio = Po = NPM (1+g) (1-b) S0 r - g
- 21. Companion Variables and Modified Multiples Let us look at the equations for P/E ratio, PBV ratio, and PS ratio. P/E = (1 - b) r – g PBV = ROE (1 + g) (1 – b) (r – g) PS = NPM (1 + g) (1 – b) r - g Looking at these equations, we find that there is one variable that dominates when it comes to explaining each multiple – it is g for P/E, ROE for PBV, and NPM for PS. This variable – the dominant explanatory variable – is called the companion variable.
- 22. Taking into account the importance of the companion variable, investment practitioners often use modified multiples which are defined below. • P/E to growth multiple, referred to as PEG : P/E g • PBV to ROE, referred to as value ratio : PBV ROE • PS to NPM, referred to as PSM : PS Net profit margin
- 23. Sum of the Parts Method Many companies have subsidiaries or associate companies in which they have significant equity stakes that usually range between 25 percent and 100 percent. To ascertain the intrinsic value per share of such companies the sum of the parts (SOTP) method of valuation is commonly employed. The SOTP method involves the following steps: 1. Determine the value per share attributable to the core business. One way to do is to calculate the earnings per share from the core business and apply a suitable multiple to it. 2. Find the value per share for each of the listed subsidiaries. In computing this value a discount factor of 15 to 20 percent is generally applied to the observed market value of the equity stake in the listed subsidiary. 3. Assess the value per share for each of the unlisted subsidiaries. To do this, the analyst has to first estimate the market value using an earnings multiple or some other basis as there is no observed market value and then apply a a discount factor of 15 to 25 percent to the same. 4. Add the per share values for the core business, for listed subsidiaries, and for unlisted subsidiaries, to get the total value per share.
- 24. Equity Portfolio Management PASSIVE STRATEGY • BUY AND HOLD STRATEGY • INDEXING STRATEGY ACTIVE STRATEGY • MARKET TIMING • SECTOR ROTATION • SECURITY SELECTION • USE OF A SPECIALISED CONCEPT
- 25. Forecasting The Aggregate Stock Market Return Stock market returns are determined by an interaction of two factors : investment returns and speculative returns. • In formal terms : SMRn = [DYn + EGn] + [(PEn / PE0)1/n – 1] Investment return Speculative return where : SMRn = annual stock market return over a period of n years DYn = annual dividend yield over a period of n years EGn = annual earnings growth over a period of n years PEn = price-earnings ratio at the end of n years PE0 = price-earnings ratio at the beginning of n years.
- 26. Illustration Suppose you want to forecast the annual return from the stock market over the next five years (n is equal to 5). You come up with the following estimates. DY5 = 0.025 (2.5 percent), EG5 = 0.125 (12.5 percent), and PE5 = 18. The current PE ratio, PEo, is 15. The forecast of the annual return from the stock market is determined as follows: SMR5 = [0.025 + 0.125] + [(18/15)1/5 – 1] = [0.15] + [0.037] = 15 percent + 3.7 percent = 18.7 percent 15 percent represents the investment return and 3.7 percent represents the speculative return.
- 27. SUMMING UP • While the basic principles of valuation are the same for fixed income securities as well as equity shares, the factors of growth and risk create greater complexity in the case of equity shares. • Three valuation measures derived from the balance sheet are: book value, liquidation value, and replacement cost. • According to the dividend discount model, the value of an equity share is equal to the present value of dividends expected from its ownership. • If the dividend per share grows at a constant rate, the value of the share is : P0 = D1/ (r – g) • A widely practised approach to valuation is the P/E ratio or earnings multiplier approach. The value of a stock, under this approach, is estimated as follows: P0 = E1 x P0/E1
- 28. • In general, we can think of the stock price as the capitalised value of the earnings under the assumption of no growth plus the present value of growth opportunities (PVGo) E1 P0 = + PVGO r • Apart from the price-earnings ratio, price to book value (PBV) ratio and price to sales (PSR) ratio are two other widely used comparative valuation ratios • Two broad approaches are followed in managing an equity portfolio : passive strategy and active strategy. • Stock market returns are determined by an interaction of two factors : investement returns and speculative returns.