Transcript Document
Equity Valuation
15.1 VALUATION BY COMPARABLES
◦ ◦ ◦ Basic Types of Models Balance Sheet Models Dividend Discount Models Price/Earnings Ratios
Valuation models use comparables ◦ Look at the relationship between price and various determinants of value for similar firms
◦ ◦ Book value Based on historical values Not the floor Can book value represent a floor value?
Better approaches ◦ Liquidation value If below, attractive ◦ Replacement cost Tobin ’ s q (ratio of market price to replacement cost)
14.2 INTRINSIC VALUE VERSUS MARKET PRICE
• Example (1-year horizon), whether the price today is attractively priced given your forecast of next year’s price and dividend
P
0 48, 1 52, 1 4 • Rf=6%, beta=1.2 Rm=11%
compare expected HPR and required return expected HPR ◦ The return on a stock investment comprises cash dividends and capital gains or losses Assuming a one-year holding period
E D
1 )
E P
1
P
0
P
0 16.7%
required return CAPM gave us required return:
k
f
M
)
r f k
If the stock is priced correctly ◦ Required return should equal expected return
Intrinsic value ◦ The Example:
V
0 present value of all cash payments to the investor, including dividends and proceeds from the ultimate sale of the stock, discounted at the appropriate risk-adjusted interest rate, k
V
0 1
k
50 50>48, undervalued
Market Price ◦ Consensus value of all potential traders ◦ Current market price will reflect intrinsic value estimates ◦ Trading Signal ◦ IV > MP Buy ◦ IV < MP Sell or Short Sell ◦ This consensus value of the required rate of return, k , is the market capitalization rate IV = MP Hold or Fairly Priced
14.3 DIVIDEND DISCOUNT MODELS
V
0
D
1 1
k P
1
P
1
D
2 1
k P
2
V
0 1
D
1
k
D
2 1
k
P
2 2
V
0 1
D
1
k
D
2 1
k
P
2 2
D H
1
k
P H H
◦ DDM Stock price should equal the present value of all expected future dividends into perpetuity
V o
t
1 ( 1
D t
k
)
t
V o
t
1 ( 1
D t
k
)
t
V
0
= Value of Stock D
t
= Dividend k = required return
Constant Growth Model ◦
Assuming dividends are trending upward at a stable growth rate g
V o
D o
( 1
k
g g
)
g = constant perpetual growth rate
Constant growth DDM
P
0
D
0
k
1
g g
k D
1
g
A Stock ’ s price will be greater ◦
Larger its expected dividend per share
◦
Lower k
◦
Higher g
Stock price is expected to grow at the same rate as dividends
P
1
k D
2
g
D
1
k
1
g g
P
0 1
g
If market price equals its intrinsic value, expected HPR will be equal to required return
D
1
P
1
P
0
D
1
k P
0
P
0
P
0
Vo
D o
( 1
k
g g
)
E
1
(1-b) = 60% V
0
= $5.00 b = 40% D
1
k = 15% = $3.00 g = 8% = 3.00 / (.15 - .08) = $42.86
Vo
D o
( 1
k
g g
) g=0
V o
D k
◦ Stocks that have earnings and dividends that are expected to remain constant Preferred Stock
V o
D k
E V
1 0
= D
1
= $5.00
k = 12.5% = $5.00 / .125 = $40
Consider two companies ◦ Cash Cow, Inc ◦ Growth Prospects k=12.5% IF pay out all as dividends ( payout ratio =100%), perpetual dividend=5 Both valued at 5/12.5%=40, neither firm will grow in value GP, project ’ s ROE=15%, what should be GP’s dividend policy ?
investment=$100 million, 3 million shares outstanding, expected earnings in coming year (EPS)=$100*15%/3= $5
Suppose, Growth Prospects lower payout ratio (40%) Earnings retention ratio b=1-40%=60% Total earning=$100*15%=$15 million Reinvestment=$15*60%=$9 million (capital increase 9/100=9%) 9% more capital, 9% more income, 9% higher dividend Low-reinvestment-rate plan, pay higher initial dividends, but result in a lower dividend growth rate High-reinvestment-rate, lower initial dividends, but result in higher dividend growth
g
ROE
*
b
g = growth rate in dividends ROE = Return on Equity for the firm b = plowback or retention percentage rate = (1- dividend payout percentage rate)
g=15%*60%=9%
P
0
k D
1
g
5* 40% 57.14
The project ’ s ROE >required rate (the project has positive NPV), reduce dividend payout ratio and reinvest in the positive NPV project. The firm ’ s value rises by the NPV of the project PVGO: net present value of growth opportunities
Value of the firm rises by the NPV of the investment opportunities Price = No-growth value per share ( NGV ) +present value of growth opportunities ( PVGO )
P
0
E
1
k
PVGO
PVGO=57.14-40=17.14
Where: and E 1 = Earnings Per Share for period 1
PVGO
D
(
0
k
(1
g g
) )
E k
1
Growth enhance company value only if it is achieved by investment in projects with attractive profit opportunities (ROE>k) If the project ’ s ROE=12.5%=k, lower the dividend payout ratio (40%) Then stock price=?
g= ROE*b=12.5%*60%=7.5%
P
0
k D
1
g
5* 40% 40 No different from no-growth strategy To justify reinvestment, the firm must engage in projects with better prospective returns than those shareholders can find elsewhere If ROE=k, no advantage to reinvestment
ROE = 20% d = 60% b = 40% E 1 = $5.00 D 1 = $3.00 k = 15% g = .20 x .40 = .08 or 8%
Partitioning Value: Example
P o
3 (.
.
)
$42.
86
NGV o PVGO
.
5 15
$42.
$33.
86
33 $33.
33
$9.
52
P o = price with growth NGV o = no growth component value PVGO = Present Value of Growth Opportunities
◦ Constant-growth DDM Assume dividend growth rate be constant In fact, different dividend profiles in different phases ◦ ◦ In early years, high return, high reinvestment, high growth In later years, low return, low reinvestment, low growth, as mature companies Multistage version of DDM
P o
D o t T
(
1 1 ( 1
g
1
k
)
t
)
t
(
D T
( 1
2 )( 1
g
2 )
k
)
T
g 1 g 2 = first growth rate = second growth rate T = number of periods of growth at g 1
D 0 = $2.00 g 1 = 20% g 2 = 5% k = 15% T = 3 D 1 =2*1.2= 2.40 D 2 = 2.4*1.2=2.88 D 3 =2.88*1.2= 3.46
D 4 =3.46*1.05= 3.63
V 0 V 0 = D 1 /(1.15) + D 2 /(1.15) 2 D 4 / (.15 - .05) ( (1.15) 3 + D 3 /(1.15) 3 + = 2.09 + 2.18 + 2.27 + 23.86 = $30.40
14.4 PRICE-EARNINGS RATIOS
Used to assess the valuation of one firm versus another based on a fundamental indicator such as earnings. Price-to-earnings multiple Price-to-book ratio Price-to-cash-flow ratio Price-to-sales ratio
P/E Ratios are a function of two factors ◦ Required Rates of Return (k) ◦ Expected growth in Dividends Uses ◦ Relative valuation ◦ Extensive use in industry
Useful indicator of expectations of growth opportunities
P E
0 1 1
k
1
PVGO E
k
Ratio of PVGO/(E/k), component of firm value due to growth opportunities to the component of value due to assets already in place High P/E ratio indicates ample growth opportunities ◦ GROWTH PROSPECT, 57.14/5=11.4
◦ CASH COW, 40/5=8
Investor may well pay a higher price per dollar of current earnings if he or she expects that earnings stream to grow more rapidly P/E ratio a reflection of the market’s optimism concerning a firm’s growth prospects, but whether they are more of less optimistic than the market ?
P
0
E
1
P E
1 0
k
1
k
E 1 ◦ E 1 - expected earnings for next year is equal to D 1 under no growth k - required rate of return
P P
0
E
1 0
k D
1
g
1
k b k
(
E
( 1
ROE
) ( 1
b
)
ROE
)
b = retention ration ROE = Return on Equity Higher ROE, higher P/E Higher b, higher P/E, only if ROE>k
E 0 = $2.50 k = 12.5%, ROE=15%, No growth: g=0 P/E=?
With growth: payout ratio=40%, P/E=?
E 0 = $2.50 g = 0 k = 12.5% P 0 = D/k = $2.50/.125 = $20.00
P/E = 1/k = 1/.125 = 8
b = 60% ROE = 15% (1-b) = 40% g = (.6)(.15)= 9% E 1 = $2.50 (1 +9%) = $2.73
D 1 k = 12.5% g = 9% P 0 = $2.73 (1-.6) = $1.09
= 1.09/(.125-.09) = $31.14
P/E = 31.14/2.73 = 11.4
P/E = (1 - .60) / (.125 - .09) = 11.4
Holding all else equal ◦ Riskier stocks will have lower P/E multiples ◦ Higher values of k ; therefore, the P/E multiple will be lower
P E
k
1
b
g
Use of accounting earnings ◦ Influenced by somewhat arbitrary accounting rules , use of historical cost in depreciation and inventory valuation (earnings management) Inflation ◦ P/E ratio have tended to be lower when inflation has been higher ◦ Market ’ s assessment that earnings in these periods are of lower quality Reported earnings fluctuate around the business cycle No way to say P/E is overly high or low without referring to the company’s long-run growth and current EPS relative to the long-run trend line
Price-to-book ratio Price-to-cash-flow ratio Price-to-sales ratio Creative: price-to-hits ratio for retail internet firms
14.5 FREE CASH FLOW VALUATION APPROACHES
Discount the free cash flow for the firm Discount rate is the firm ’ s cost of capital Components of free cash flow ◦ After tax EBIT ◦ Depreciation ◦ Capital expenditures ◦ Increase in net working capital
discount FCFF at the weighted-average cost of capital , Subtract existing value of debt FCFF = EBIT (1 t c ) + Depreciation
–
Capital expenditures
–
Increase in NWC where: EBIT = earnings before interest and taxes t c = the corporate tax rate NWC = net working capital
Another approach focuses on the free cash flow to the equity discounts the cash flows directly at the of equity holders (FCFE) and cost FCFE = FCFF – Interest expense (1 Increases in net debt t c ) +
◦ Free cash flow approach should provide same estimate of IV as the dividend growth model In practice the two approaches may differ substantially Simplifying assumptions are used