Valuation Equations

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Valuation Equations

• or
• whats happening inside the computer

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forecasted financial statements
Define net dividends Dt so that CEt CEt-1 NIt
Dt, or Dt NIt (CEt CEt-1). Value is
determined by your forecasts!
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DCF to Common Equity Model where Dt is the
net cash distributions to equity holders, or
free cash flow to common equity, computed as NIt
(CEt CEt-1), and re is the cost of equity
capital.
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Four Models One Value
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Residual Income to Common Equity Model
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Price equals the current book value plus the
discounted sum of expected future residual income
(abnormal earnings).

• Advantages over cash flow models
• business, accounting and financial analysis are
  all in terms of accounting numbers.
• 2) avoids having to "undo" the accounting to get
  to dividends or free cash flow - estimate value
  using the accounting numbers directly.

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DCF to All Investors
Free Cash Flow to All Investors can be computed
from Income statement and Balance sheet data
as Ct NOIt (NOAt NOAt-1).
Free Cash Flow to All Investors can be computed
from Statement of cash flow data as
Ct Dt It(1-txt) - DLt PDt - DPSt.
To common equity holders
To debt holders (net of tax shield)
To preferred stockholders
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and the two equations are equivalent!
Ct NOIt (NOAt NOAt-1). NIt It(1-txt)
PDt (CEt LtPSt CEt-1
Lt-1-PSt-1) NIt (CEt CEt-1) It(1-txt) -
DLt PDt DPSt Dt It(1-txt) - DLt PDt -
DPSt.
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3 ways to compute FCF

• NOI DNOA is easy
• from the SCF, note that
• CFO CFI CFF Dcash (CFI and CFF usually
  negative)
• compute FCF CFO CFI Dcash I(1-t).
• compute FCF CFF I(1-t).
• See Cash Flow Analysis sheet in eVal.
• OR use the traditional approach

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The Traditional FCF recipe for the DCF model is
NOI
DNOA
But it works out to be exactly the same as my
accounting-based formula.
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DCF to All Investors
Value to Common Equity Pe Pf Pd Pps
Value to all investors
Value to debtholders
Value to preferred stockholders
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Where did all the money go?
Ct Dt It(1-txt) - DL PDt - DPSt.
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RI to All InvestorsRNOIt NOIt rwNOAt-1.
Value to Common Equity Pe Pf Pd Pps
Value to all investors
Value to debtholders
Value to preferred stockholders
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Discount Rates and Present Value Computations

• What is the cost of equity capital, debt capital
  and preferred capital?
• What is the after-tax weighted average cost of
  capital?
• How do we compute the present value of a
  perpetuity?

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The Cost of Equity Capital

• Must capture time value of money and risk
• CAPM
• re rf B(rm-rf)
• rf between 4 and 6
• rm-rf between 5 and 8
• B from http//finance.yahoo.com/ under key
  statistics
• SIZE model
• re rf rsize

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Size Model
re rf rsize
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One standard deviation variation in risk premium
and beta, assuming rf 5.2

• risk premium 2.5, beta.88
• re 7.4
• risk premium 7.9, beta 1.12
• re 14.0

maybe we should just use 10!
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WACC
tx is the firms estimated effective tax rate, re
is the firms estimated cost of equity
capital, rd is the firm's estimated cost of debt
capital, rps is the firm's estimated cost of
preferred stock capital, Pe is the resulting
value of the firms common equity, Pd is the
resulting value of the firms debt, and Pps is
the resulting value of the firms preferred stock.
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So you think you understand the perpetuity
formula???
But which sequence does this apply to? t0
t1 t2 t3
t4 pmt pmt(1g) pmt(1g)2 .. pmt
pmt(1g) pmt(1g)2 ..
pmt(1g) pmt(1g)2 pmt(1g)3 ..
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DCF to equity using perpetuity formula
finite horizon value terminal value
PV at of time 0 of perpetuity of payments,
growing at rate g, starting with DT1 .