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Chapter
Brealey, Myers, and Allen
Principles of Corporate Finance
11th Global Edition
THE VALUE OF COMMON STOCKS
4
4-4-22
4-1 HOW COMMON STOCKS ARE TRADED
•Primary Market• New securities
•Secondary Market• Previously-issued securities
•Common Stock• Ownership shares in publicly-held corporation
4-4-33
4-1 HOW COMMON STOCKS ARE TRADED
• Electronic Communication Networks (ECNs)• Computer networks that allow electronic trading
• Exchange-Traded Funds (ETFs)• Stock portfolios bought/sold in single trade
4-4-44
4-2 HOW COMMON STOCKS ARE VALUED
• Book Value• Net worth of firm according to balance sheet
• Dividend• Periodic cash distribution from firm to the shareholders
• P/E Ratio• Price per share divided by earnings per share
• Market Value Balance Sheet• Financial statement that uses market value of assets and liabilities
4-4-55
4-2 HOW COMMON STOCKS ARE VALUED
• Discounted Cash Flow (DCF) Formula• Value of a stock = present value of future cash flows
dividends) future dPV(expectePV(stock)
4-4-66
4-2 HOW COMMON STOCKS ARE VALUED
• Expected Return• Percentage yield forecast from specific investment over time period
• Sometimes called market capitalization rate
4-4-77
4-2 HOW COMMON STOCKS ARE VALUED
• Example• Fledgling Electronics sells for $100 per share today; they are expected to sell for $110 in one year. What is expected return if dividend in one year is forecasted to be $5.00?
15.100
1001105return Expected
4-4-88
4-2 HOW COMMON STOCKS ARE VALUED
• Price of share of stock is present value of future cash flows
• For a stock, future cash flows are dividends and ultimate sales price
r
PDivP
1
Price 110
4-4-1010
4-2 HOW COMMON STOCKS ARE VALUED
• Market Capitalization Rate• Estimated using perpetuity formula
• Also called cost of equity capital
gP
r
grP
0
1
10
Div
Divratetion Capitaliza
4-4-1111
4-2 HOW COMMON STOCKS ARE VALUED
• Dividend Discount Model• Computation of today’s stock price: share value equals present value of all expected future dividends
• H: Time horizon for investment
HHH
r
PDiv
r
Div
r
DivP
)1(...
)1()1( 22
11
0
4-4-1212
4-2 HOW COMMON STOCKS ARE VALUED
• Modified Formula
HHH
r
PDiv
r
Div
r
DivP
)1(...
)1()1( 22
11
0
HH
H
ttt
r
P
r
DivP
)1()1(10
4-4-1313
4-2 HOW COMMON STOCKS ARE VALUED
• Example• Fledgling Electronics forecasted to pay $5.00 dividend at end of year 1 and $5.50 dividend at end of year 2. End-of-second-year stock will be sold for $121. Discount rate is 15%. What is the price of stock?
00.100$PV
)15.1(
12150.5
)15.1(
00.5PV
21
4-4-1414
4-2 HOW COMMON STOCKS ARE VALUED
• Example• XYZ Company will pay dividends of $3, $3.24, and $3.50 over next three years. After three years, stock sells for $94.48. What is the price of stock given 12% expected return?
00.75$PV
)12.1(
48.9450.3
)12.1(
24.3
)12.1(
00.3PV
321
4-4-1616
4-3 ESTIMATING COST OF EQUITY CAPITAL
•Dividend Yield• Expected return on stock investment plus expected dividend growth
• Similar to capitalization rate
gP
Divr
gr
DivP
0
1
10
yield Dividend
Price
4-4-1717
4-3 ESTIMATING COST OF EQUITY CAPITAL
• Example• Northwest Natural Gas shares sold for $47.30 at start of 2012. Dividend payments for 2013 were $1.86 a share with no growth. What is dividend yield?
039.30.47
86.1
Yield Dividend
r
r
r
4-4-1818
4-3 ESTIMATING COST OF EQUITY CAPITAL
• Example• Northwest Natural Gas shares sold for $47.30 at start of 2012. Dividend payments for 2013 were $1.86 a share with 4.6% growth. What is r?
085.
046.30.47
86.1
r
r
4-4-1919
4-3 ESTIMATING COST OF EQUITY CAPITAL
• Return Measurements
0
1yield DividendP
Div
shareper equity Book
EPSROE
ROEEquityon Return
4-4-2020
4-3 ESTIMATING COST OF EQUITY CAPITAL
• Dividend Growth Rate• Derived by applying return on equity to percentage of earnings reinvested in operations
• g = return on equity × plowback ratio
4-4-2121
4-3 ESTIMATING COST OF EQUITY CAPITAL
• Valuing Non-Constant Growth
HH
HH
r
P
r
Div
r
Div
r
Div
)1()1(...
)1()1(PV
22
11
gr
DivP HH
1
4-4-2222
4-3 ESTIMATING COST OF EQUITY CAPITAL
• Example• Phoenix pays dividends in three consecutive years of 0, .31, and .65. Year-4 dividend is estimated at .67 with perpetuity growth at 4%. With 10% discount rate, what is stock price?
13.9
)04.10(.
67.
)1.1(
1
)1.1(
65.
)1.1(
31.
)1.1(
0PV
3321
4-4-2323
4-4 STOCK PRICE AND EARNINGS PER SHARE
• If firm pays lower dividend and reinvests funds, stock price may increase due to higher future dividends
• Payout Ratio• Fraction of earnings paid out as dividends
• Plowback Ratio • Fraction of earnings retained by firm
4-4-2424
4-4 STOCK PRICE AND EARNINGS PER SHARE
• Example• Company plans $8.33 dividend next year (100% of earnings). Investors will get 15% expected return. Instead, company plows back 40% of earnings at firm’s current return on equity of 25%. What is the stock value before and after plowback decision?
4-4-2525
4-4 STOCK PRICE AND EARNINGS PER SHARE
• Example, continued• No Growth
• With Growth
56.55$15.
33.80 P
00.100$10.15.
00.5
10.40.25.
0
P
g
4-4-2626
4-4 STOCK PRICE AND EARNINGS PER SHARE
• Example, continued• Stock price remains at $55.56 with no earnings plowed back
• With plowback, price is $100.00
• Difference is called present value of growth opportunities (PVGO)
44.44$56.5500.100PVGO
4-4-2727
4-4 STOCK PRICE AND EARNINGS PER SHARE
• Present Value of Growth Opportunities (PVGO)• Net present value of firm’s future investments
• Sustainable Growth Rate• Steady rate at which firm can grow: plowback ratio x return on equity
4-4-2828
4-5 VALUING A BUSINESS
• Valuing a Business or Project• Usually computed as discounted value of FCF to valuation horizon (H)
• Valuation horizon sometimes called terminal value and calculated like PVGO
HH
HH
rrrr )1(
PV
)1(
FCF...
)1(
FCF
)1(
FCFPV
22
11
4-4-2929
4-5 VALUING A BUSINESS
• Valuing a Business or Project
HH
HH
rrrr )1(
PV
)1(
FCF...
)1(
FCF
)1(
FCFPV
22
11
PV (free cash flows) PV (horizon value)
4-4-3030
4-5 VALUING A BUSINESS
• Example• Given cash flows for Concatenator Manufacturing Division, calculate PV of near-term cash flows, PV (horizon value), and total value of firm; r = 10% and g = 6%
4-4-3131
4-5 VALUING A BUSINESS
• Example, Continued
4.22
06.10.
59.1
1.1
1 value)PV(horizon 6
6.3
1.1
23.
1.1
20.
1.1
39.1
1.1
15.1
1.1
96.
1.1
.80PV(FCF) 65432