Equity Valuation Chapter 13 McGraw-Hill/Irwin Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved. Book Value Historical Values recorded on the firm’s financial statements BV Equity = Total Assets – Total Liabilities The values are historical and may not reflect current market conditions/values Limits the informativeness of these values 2 13-2 Valuing Stock: Intrinsic v Price An investors purchasing a share is acquiring the cash flows associated with that share The present value of these cash flows is the Intrinsic Value For now assume intrinsic value is the same as market value, we will relax this assumption later in the semester 3 13-3 Expected HPR When the market price = intrinsic value the E(r) = Div Yield + Capital Gain Div Yield = D1 / P0 Capital Gain = (P1 - P0) / P0 E(r) = D1 / P0 + (P1 - P0) / P0 Also known as the market capitalization rate 4 13-4 Valuing Common Stock The price should reflect the PV of future cash flows So will an investor planning on selling his share in a year be willing to pay today? The investor buying the share next year plans on selling it a year later so he is only willing to pay? 5 13-5 Keep Going This process can be repeated into the future Div1 Div 2 Div H PH P0 ... 1 2 H (1 k ) (1 k ) (1 k ) Using summation: P0 = H Dh / (1 + k)h + PH / (1 + k)H What happens to PH as H approaches infinity? ASIDE: Will an investor’s expected holding period affect the price they are willing to pay today? 6 13-6 Constant Dividend How do you value a stock that will pay a constant dividend? Hint: what does the cash flow stream look similar to? 7 13-7 Constant Dividend Example What is the value of a stock that is expected to pay a constant dividend of $2 per share? The required rate of return is 10% 8 13-8 Constant Dividend Example What is the market capitalization rate of a stock that is selling for $60, that is expected to pay a constant dividend of $2 per share? 9 13-9 When Dividends Grow Now lets assume that the firm and its dividend will grow at g forever Dividends now: Div 1 Div 0 (1 g ) D iv 2 D iv 1 (1 g ) D iv 0 (1 g ) 2 D iv 3 D iv 2 (1 g ) D iv 0 (1 g ) 3 10 13-10 DDM with Constant Growth V0 = D1 / (k-g) V0 = {D0*(1+g) }/ (k-g) Is a stock more or less valuable when dividends grow? 11 13-11 Growing Dividend Example Geneva steel just paid a dividend of $2.10. Dividend payments are expected to grow at a constant rate of 6%. The appropriate discount rate is 12%. What is the price of Geneva stock? 12 13-12 Firm Life Cycles Firms generally grow faster when they are young, then growth slows as the firm matures Two-Stage DDM (Multistage Growth Models) Allow dividends to grow at different rates as firm matures 13 13-13 Differential Growth Rates Dividends will grow at g1 for T years and g2 thereafter Step 1: An T-year annuity growing at rate g1 PA C1 (1 g1 ) 1 k g1 (1 k ) { } T Step 2: A growing perpetuity at rate g2 PN = DivN+1 / (k-g2) Step 3: PB = PN / (1+k)T Step 4: P0 = PA + PB 14 Non-Constant Growth Example (Given) Websurfers Inc, a new internet firm is expected to do very well during its initial growth period. Investors expect its dividends to grow at 25% for the next 3 years. Obviously one cannot expect such extraordinary growth to continue forever, and it is expected that dividends will grow at 5% after year 3 in perpetuity. Its current dividend is $1/share. Required rate of return on the stock = 10%. Calculate what the current price should be. 15 13-15 Websurfer Inc, Example (Given) 1*1.25 1*1.25 = 1.25 0 1 1*1.252 =1.56 2 1*1.253 = 1.95 1*1.253*1.05 = 2.05 3 4 1.PA=[(1.25)/(0.10-0.25)]*[1-{1.25/1.10}3] = 3 *1.052 = 2.15 5 3.90 2.PN ={2.05}/(0.10-0.05) = 41.00 3.PB =41.00/(1.103) = 30.80 4.P0 = PA + PB = 3.90+ 30.80 = $34.70 16 13-16 A Differential Growth Example A common stock just paid a dividend of $2. The dividend is expected to grow at 8% for 3 years, then it will grow at 4% in perpetuity. R=12% What is the stock’s intrinsic value? PA = 2. PN = 3. PB = 4. P0 = PA + PB = 1. 17 13-17 Problem 1 (Given) A firm is expected to grow at 25% for the next 3 years. Its growth is expected to decline to 15% for the following 4 years. It is then expected to grow at 5% in perpetuity. Find the current share price if the current dividend is $1 and the discount rate is 10%. 18 13-18 Problem 1 (Given) A firm is expected to grow at 25% for the next 3 years. Its growth is expected to decline to 15% for the following 4 years. It is then expected to grow at 5% in perpetuity. Find the current share price if the current dividend is $1 and the discount rate is 10%. PA=[(1.25)/(0.10-0.25)]*[1-{1.25/1.10}3]=3.89 PN1 ={1*1.253*1.15}/(0.10-0.15)]* [1-{1.15/1.10}4]=8.76 PB =8.76/(1.103) = 6.58 PN2 ={1*1.253*1.154*1.05}/(0.10-0.05)] = 71.80 PC =71.80/(1.107) = 36.83 P0 = PA + PB + Pc = 3.89+6.58+36.83 = $47.30 19 13-19 Problem 2 (Given) Consider a firm whose dividend growth is expected to decline gradually. For the next two years, the growth is expected to be 20%. In the following years, it is expected to grow at 18%, 13% and 10%. From year 6 onwards, dividends are expected to grow at 5% for perpetuity. Assume the current dividend is $1 and the required rate of return is 10%. What is the current price? 20 13-20 Problem 2: Phase 1 – Years 1-5 (Given) DIV1 = 1.00 * 1.20 = 1.20 DIV2 = 1.20 * 1.20 = 1.44 DIV3 = 1.44 * 1.18 = 1.70 DIV4 = 1.70 * 1.13 = 1.92 DIV5 = 1.92 * 1.10 = 2.11 PA = 1.2/1.1 + 1.44/1.12 + 1.70/1.13 + 1.92/1.14 + 2.11/1.15 = 6.18 21 13-21 Problem 2 Phase 2 – Years 6- (Given) DIV6 = 2.11 * 1.05 = 2.22 PN = DIV6 / (r-g) = 2.22/(0.10-0.05) = 44.4 PB = 44.4 * 1/1.15 = 27.57 Current Price = 6.18 + 27.57 = $33.75 22 13-22 What to do with Cash Once a firm has paid everyone, it has two chooses with what to do with any remaining money Give it to shareholders Who can invest it themselves Reinvest it in the company Growth the firm When should the firm give the cash to investors? Reinvest? 23 13-23 How Fast Can a Firm Grow? The firm’s growth is determined by how much it re-invests (plowback ratio) & the return on its re-investment Plowback (b)how much of every dollar is re-invest Earnings Retention Ratio REMEMBER: Plowback + Payout = 1 Return on investment is the firm’s ROE g = plowback ratio * ROE 24 13-24 Calculating Growth Rates (g) Consider two firms with earnings of $5 & k=12.5% Cash Cow pays out all earnings as dividends CC’s growth rate is _______ CC’s share price is _______ Growth Prospects wants to grow → Div Payout = 40% & ROE is 15% GP’s growth rate is _______ GP’s share price is _______ 25 13-25 Alternative Growth Valuation Price is composed of: The value of the current operations (100% Div Payout) EPS1 / k Growth opportunities PVGO P0 = EPS1 / k + PVGO 26 13-26 Who cares about PVGO? For what type of stock is the PVGO more important? Growth or Value stocks 27 13-27 PVGO Example A firm reinvests 60% of its earnings in projects with ROE of 10%, capitalization rate is 15%. Expected year-end dividend is $2/share, paid out of earnings of $5/share. Compute the firm’s share price? What is the per share value of the firm’s current assets? What is the per share PVGO? 28 Price-Earnings Ratio The price-earnings ratio is calculated as the current stock price divided by annual EPS. Wall Street Journal uses last 4 quarter’s earnings The Price per share P/E ratio EPS Many analysts use this to determine how the market feels about a company 29 13-29 Price-Earnings Ratio Breakdown P0 = EPS1 / k + PVGO ↓ P0 1 PVGO 1 E E1 k k P/E can be thought of as a ratio of growth options to current assets 30 Price-Earnings Ratio and Growth When PVGO=0, P0=E1 / k. The stock is valued like a constant perpetuity. P/E rises dramatically with PVGO. High P/E indicates that the firm has ample growth opportunities. 31 Price Earnings Ratio 2nd Breakdown P0 = Div1 / (k –g) Div1: is E1 * (1+b) g is ROE * b P0 = {E1 * (1+b) }/ {k –(ROE * b)} P0 1 b 1 b E1 k ( ROE * b) k g 32 13-32 Price-Earnings Ratio Implications P0 1 b 1 b E1 k ( ROE * b) k g Since riskier stocks have higher k (rates of returns) this implies they will also have lower P-E multiples P/E increases: As ROE increases As plowback increases IF ROE>k 33 ROE & Plowback on Growth and the P/E Ratio, k=12% 34 13-34 Issues With P/E Analysis Uses accounting earnings Earnings Management Choices on GAAP Inflation Reported earnings fluctuate around the business cycle 35 Figure 13.4 Earnings Growth for Two Companies Earnings per share (1995 = 1.0) 6.0 5.0 Con Ed Intel 4.0 3.0 2.0 1.0 0.0 1995 1997 1999 2001 2003 2005 2007 2009 2011 36 13-36 Figure 13.5 Price-Earnings Ratios 60 Con Ed Intel 50 P/E ratio 40 30 20 10 0 1995 1997 1999 2001 2003 2005 2007 2009 2011 37 13-37 Industrial P/E Ratios Aerospace/defense Integrated oil & gas Money center banks Health care plans Computer systems Telecom services Industrial metals Electric utilities Home improvement Pharmaceuticals Chemical products Application software Asset management Food products Restaurants Auto manufacturers Trucking Heavy construction Business software Biotech 8.5 10.2 11.0 11.8 13.2 14.7 14.9 15.6 16.5 17.2 17.4 17.5 17.5 21.1 21.4 25.3 28.0 32.4 34.7 57.8 0 10 20 30 40 50 60 P/E ratio 38 13-38 Other Comparative Valuation Ratios Price-to-book: Indicates how aggressively the market values the firm Price-to-cash-flow: Cash flow less affected by accounting decisions than earnings Price-to-sales: For start-ups with no earnings 39 13-39 Free Cash Flow to the Firm Value the firm by discounting its free cash flows by WACC Free cash flow to the firm, FCFF, equals: After tax EBIT Plus depreciation Minus capital expenditures Minus increase in net working capital FCFF= EBIT(1-tc) + Dep - Cap Ex - Inc. NWC 40 Using FCFF to Value the Firm FCFF= EBIT(1-tc) + Dep - Cap Ex Inc. NWC FCFFt 1 Pt WACC g 41 13-41 Free Cash Flow to Equityholders Two ways to determine the value of Equity Firm Value minus Debt 2. Discounting free cash flows to equity by cost of equity 1. Free cash flow to equity, FCFE, equals: FCFF Minus Interest Expense After Tax Plus Increase in Net Debt FCFE= FCFF – Int Exp * (1-tc) + Inc. net Debt 42 Finding the Value of Equity Equity = Firm Value – Debt Or FCFE= FCFF – Int Exp * (1-tc) + Inc. net Debt FCFEt 1 Equity t kE g 43 13-43 Stock Value Represents: Present value of expected future dividends, Present value of free cash flow, Present value of average future earnings under a no-growth policy plus the present value of growth opportunities 44 13-44 Free Cash Flow to the Firm Eagle Products’ EBIT is $400, its tax rate is 30%, depreciation is $16, capital expenditures are $56, and the planned increase in net working capital is $25. What is the free cash flow to the firm? 45 13-45 MoMi Corp’s operating cash flows before interest and taxes was $2M last year MoMi expects this to grow by 5% per year forever To make this happen, MoMi will have to invest 20% of pretax cash flow each year. Depreciation last year was $200K and is expected to grow at the same rate as OCF Market capitalization rate for unleveraged CF is 12% WACC Firm has $4M in debt outstanding The tax rate is 35% What is the value of MoMi? What is the value of MoMi’s equity? 46 13-46 FCFE Example Acme reports free cash flow to the firm of $205 million. The interest expense to the firm is $22 million. If the tax rate is 35% and the net debt of the firm increased by $25 million, what is the approximate market value of equity if the FCFE grows at 2% and the cost of equity is 11%? 47 13-47 Different Models Different Values In practice Values from these models differ Analysts are always forced to make simplifying assumptions Problems with DCF Calculations are sensitive to small changes in inputs Growth opportunities and growth rates are hard to pin down 48 13-48