University:
Massachusetts Institute of Technology
Course:
15.501/516 | Accounting
Academic year:

2023
Views:

385

Pages:

26
Author:

Vivian Hester

Today Firm valuation • Dividend discount model • Cashflows, profitability, and growth Reading • Brealey and Myers, Chapter 4 Firm valuation The WSJ reports that FleetBoston has a DY of 4.6% and a P/E ratio of 16, IBM has a DY of 0.8% and a P/E ratio of 27, and Intel has a DY of 0.3% and a P/E ratio of 46. What explains the differences? What do the financial ratios tell us about the prospects of each firm? Your firm has the opportunity to acquire a smaller competitor. You forecast that the target will earn $78 million this year, $90 million next year, and $98 million in the following year. The target reinvests 75% of its earnings and long-term growth is expected to be 6% for the foreseeable future. Is the growth rate adequate given its payout policy? How much would you be willing to pay for the firm? S&P price-earnings ratio, 1871 – 1999 35 28 21 14 7 0 1871 1887 1903 1919 1935 1951 1967 1983 1999 Firm valuation Similar to projects DCF analysis Forecast cashflows (inflation, working capital, taxes, …) Discount at the opportunity cost of capital Additional issues Assets or equity value? Is growth sustainable? How does growth affect cashflow? Firms have no end date. Do we have to forecast cashflows forever? Balance sheet view of the firm Assets Liabilities and Equity Current Liabilities Current Assets Cash flows from assets Long-Term Debt Fixed Assets 1. Tangible fixed assets 2. Intangible fixed assets Total value Shareholders’ Equity = Total value Cash flows to debt and equity Approach 1 Asset value PV of assets = FCFH Term. value FCF1 FCF2 ... + + + + 2 H 1 + r (1 + r) (1 + r) (1 + r)H Free cashflow Cash generated by the assets after all reinvestment FCF = EBIT (1 – τ) + depreciation – ∆NWC – CAPX Terminal value Firm value at the end of the forecast horizon Equity Equity value = Assets – Debt Approach 2 Equity value Div1 Div 2 DivH Term. value PV of equity = + + ... + + 2 H 1 + r (1 + r) (1 + r) (1 + r)H Equity is a claim to future dividends Divt = expected dividend Terminal value Equity value at the end of the forecast horizon Assets Asset value = Equity + Debt Most useful if payout policy is stable Not for high growth firms Approach 3 Equity value PV of equity = stock price (Look in the WSJ!) Why does this approach make sense? If the market is efficient, stock price is the best estimate of value Why shouldn’t we always use it? Private companies (no stock price) Private information Acquisitions create value not yet reflected in stock prices (?) Sometimes the market gets it wrong But, typically not a bad benchmark Takeover announcements Stock price of target firm Capital gains vs. dividends What about capital gains? Buy stock today ⇒ future cashflow of Div1 + P1 P0 = E[Div1] + E[P1] 1+ r E[Div 2 ] + E[P2 ] P1 = 1+ r Substitute P1 into first formula: P0 = E[Div 1 ] E[Div 2 ] E[P2 ] + + 2 1+ r (1 + r) (1 + r)2 If prices are rational, then repeating for P2, P3, …, gives the dividend discount formula Approach 2 – Dividends Equity value PV of equity = Div1 Div 2 Div H Term. value + + + ... + 1+ r (1 + r)2 (1 + r)H (1 + r)H Special cases No growth Mature firms, few new investment opportunities Ex. Kodak, AT&T Sustainable growth Firms with moderate growth that is expected to persist Ex. IBM, Procter and Gamble Case 1: No growth No net investment Reinvestment covers depreciation Firm pays out all its earnings: Divt = EPSt Equity value, dividends, earnings aren’t expected to grow Div0 = E[Divt] = E[Div2] = … Price = Div 0 Div 0 Div 0 Div 0 + + + L 2 3 4 1+ r (1 + r) (1 + r) (1 + r) Price = Div0 EPS0 = r r Example It’s 2001 and you’re attempting to value AT&T’s equity. The longdistance market is mature and new competition makes growth difficult. In fact, AT&T has experienced little growth over the last few years, which you believe will continue. Dividends Year 1996 1997 1998 1999 2000 DPS 0.88 0.88 0.88 0.88 0.88 No growth formula: If r = 7%: price = 0.88 / 0.07 = $12.57 If r = 5%: price = 0.88 / 0.05 = $17.60 (actual price = $17.25) AT&T earnings and dividends $3.0 EPS DPS $2.0 $1.0 $0.0 1985 -$1.0 -$2.0 1987 1989 1991 1993 1995 1997 1999 Case 2: Sustainable growth Growth opportunities Positive net investment (reinvestment > depreciation) Firm pays out only a portion of its earnings (Divt < EPSt) Equity, dividends, earnings are all expected to grow Exp[Div]: Div0×(1+g), Div0×(1+g)2, … Div 0 (1+ g) Div 0 (1 + g)2 Div 0 (1 + g)3 + Price = + L + 2 3 1+ r (1 + r) (1 + r) Price = Div1 Div0 × (1 + g) = r −g r −g Example Firms in the S&P 500 are expected to pay, collectively, around $20 in dividends next year. Dividends have grown 5.57% annually since 1950. If the historical pattern continues, what is the value of index if the discount rate is 8%? Constant growth Value = 20 20.0 21.11 22.29 + + + ... = 0.08 − 0.0557 (1.08) (1.08)2 (1.08)3 = 823.05 Current index level = 989.28 Forecasting growth How quickly will the firm grow? Payout ratio = DPS / EPS Plowback ratio = 1 – payout ratio = retained earnings / EPS If growth is financed internally: ∆Equityt-1 to t = retained earnings = EPS × plowback ratio Growth rate = ∆Equityt-1 to t / Equityt-1 EPS × plowback = Equity = ROE × plowback Growth rate = g = ROE × plowback ratio Forecasting growth Observations Growth is faster if ROE is high Growth is faster if plowback is high Growth ≠ good investments If margins and payout are constant, equity, dividends, and earnings all grow at the same rate EPSt = ROE × equityt-1 ⇒ EPS growth = equity growth DPSt = payout × EPSt DPS growth = EPS growth ⇒ Example Since 1950, firms in the S&P 500 have, on average, paid out 50.4% of their earnings as dividends. They have also been profitable, with an ROE of 11.7% annually. If these trends continue, how quickly will the firms grow? What will happen to growth if the payout ratio drops to 30% (including repurchases)? Growth = plowback × ROE If payout 50.4% Growth = (1 – 0.504) × 11.7 = 5.8% (historical = 5.6%) If payout 30% Growth = (1 – 0.300) × 11.7 = 8.2% (if ROE doesn’t change) Example By 2003, AT&T’s situation had changed. Demand for long-distance and broadband is expanding. AT&T decides to reinvest half its earnings, equal to $1.50 / share in 2002. Analysts forecast that AT&T would earn an ROE of 15% on its investments. If investors required a 10% rate of return, what is the value of AT&T’s stock at the end of 2002? What information do we need? ROE = 15% g = 7.5% Plowback ratio = 50% EPS2002 = 1.50 Div2002 = 0.75 Example, cont. Equity value Div2002 = 0.75 → Div2003 = 0.75 × 1.075 = 0.806 Price = $0.806 / (0.10 – 0.075) = $32.24 Growth opportunities increase AT&T’s stock price from $15.00 to $32.24, or 215%. AT&T EPS Div Plowback Growth Price No growth $1.50 $1.50 0% 0% $15.00 Growth $1.50 $0.75 50% 7.5% $32.24 AT&T, forecasted dividends $4 No growth Growth = 7.5% $3 $2 $1 $0 0 2 4 6 8 10 12 Years in the future 14 16 18 20 Example, cont. Suppose that AT&T could earn only 6% ROE on its investments. What would be AT&T’s stock price? ROE = 6% Plowback ratio = 50% EPS2002 = 1.50 g = 3% Div2002 = 0.75 Stock price Div2002 = 0.75 → Div2003 = 0.75 × 1.03 = 0.773 Price = $0.773 / (0.10 – 0.03) = $11.04 Growth drops the stock price from $15 to 11.04. Growth ≠ growth opportunities! Stock prices and plowback ratio $18 6% Price (left axis) Growth (right axis) $15 5% $12 4% $9 3% $6 2% $3 1% $0 0% 0 0.1 0.2 0.3 0.4 0.5 Plowback 0.6 0.7 0.8 0.9 Growth Approach 2 Begin with a mature, no growth firm No reinvestment. Value derived from existing assets. Price = Div0 EPS0 = r r Add in growth opportunities Price = EPS0 + NPVGO r NPVGO = ‘net present value of growth opportunities’. Price equals the value of existing assets plus the value of growth opportunities. Example IBM’s stock price is $97.14. Last year, IBM earned $4.6 / share and paid dividends of $0.55. What fraction of IBM’s value comes from growth opportunities if r = 10%? How quickly must IBM grow to justify its price? Price = EPS / r + NPVGO = 4.6 / .10 + NPVGO → NPVGO = 97.14 – 46 = $51.14 FractionNPVGO = 51.14 / 97.14 = 53% Growth Price = Div / (r – g) → g = r – Div / Price Growth = 0.10 – 0.55 / 97.14 = 9.4%