Lec 5

1
Lec 5

• Equities (chapter 18)

2
Valuation

• How would you value the share of a company?
• (Value of company)/(of shares outstanding)
• Value of companyNet Worth (accounting book
  value, i.e. assets-liabilities)
• Valueliquidation value
• Valuereplacement cost of assets-liabilities
• Cant be priced much higher than this otherwise
  outsiders have incentive to replicate business
  model and enter
• Forecast Dividends and Capital Gains (addressed
  later)

3
Equities

• What is an equity security (stock)?
• A financial asset secured by the equity of a
  company.
• What is Equity?
• A theoretical concept, the present value of what
  creditors dont have claims on.
• How do you measure it?
• Accountants have book valueAssets-Liabilities

4
Equity

• Stockholders own a prorated share of equity.
• Let EQ be the equity per share and N the of
  shares, then EquityEQN

Assets
Liabilities
Equity
5
Equity Growth

• Let Et be the earnings per share in the period
  between time t-1 and time t
• Net of capital depreciation
• i.e. the maximum flow of income from the company
  without depleting productive capacity.
• Let ROEt be the return on equity in the period
  between time t-1 and time t
• E1 ROE1 EQ0
• Et1 ROEt1 EQt
• Let EQt be the equity in place per share at time
  t and b be the fraction of earning retained
• EQt1 EQt bEt1

6
Earnings

• What can a company do with earnings (Et)?
• Pay dividends Dt (1-b)Et
• Reinvest in the company bEt
• Buy back shares
• Enrich employees

7
Questions

• What if the company decides to retain no earnings
  (b0)?
• No growth EQt1 EQt bEt1
• If EQtlt0 and the company liquidates, what do the
  owners owe the creditors?
• Nothing
• If the company issues new shares for a price less
  than the book value of equity per share, what
  happens to existing shareholders?
• The book value of equity per share goes down for
  all shareholders
• Ownership is diluted (voting is prorated)
• Future Equity per share may or may not be lowered
  (why?)

8
Intrinsic Value

• Ignore the problem of forecasting Dividends and
  Capital Gains.
• Example P0 100, E(P1)110, and E(D1)5
• What is Expected holding period return (HPR)?
• Is this a good value? Is the price correct?
• Depends on the risk. Depends on the alternative
  investments.

9
Intrinsic Value

• Example Continued P0 100, E(P1)110, and
  E(D1)5
• Solution discount all cash payments at the
  market capitalization rate k.
• Def The market capitalization rate k is the rate
  of return in the market for assets of identical
  risk (aka required rate of return)
• Accounting for opportunity cost,
• V0

10
Dividend Discount Model (DDM)

• H period model using intrinsic value in each
  period.
• V0
• The model in the limit assuming bounded expected
  prices.
• V0
• Assume btb and ROEtROE for all t
• Recall
• EQt1 EQt bEt1 and Et1 ROEt1 EQt
• EQt1...
• Et
• Dt
• V0 (depends on k w.r.t. bROE)

11
Intuition arising from DDM

• How does V0 depend on
• D1
• K
• b
• ROE

12
Accounting for growth

• Present Value of Growth Opportunities (PVGO)
  consists of the difference between
• Price
• Present Value of the assets in place assuming
  productive capital is maintained in perpetuity
  with no added investment.
• PVGO
• PVGO depends on k relative to ROE (show)

13
Accounting for Growth

• P/E ratio price (per share) over earning (per)
  share.
• Reflects growth prospects
• There are historical regularities that indicate
  this can only get so large. (link)
• This represents the same notion as House price to
  rental rate (link)
• This is a retrospective measure, we can relate it
  theoretically as a prospective measure
• P/E1

14
http//www.frbsf.org/news/speeches/2008/charts.pdf
15
http//www.econ.yale.edu/shiller/data/ie_data.xls