Valuation Equations
or
what’s happening inside the
computer
for the period ending
0 1 2 … T-1 T T+1 T+2 …
NOA0 NOA1 NOA2 …NOAT-1 NOAT NOAT(1+g) NOAT(1+g)2 …
-L0 -L 1 -L 2 … -L T-1 –L T -L T(1+g) -L T(1+g)2 …
CE0 CE 1 CE 2 … CE T-1 CE T CE T(1+g) CE T(1+g)2 …
NOI1 NOI2 …NOIT-1 NOIT NOIT(1+g) NOIT(1+g)2 …
-I1 -I2 … -IT-1 -IT -IT(1+g) -IT(1+g)2 …
Define net dividends Dtso that CEt= CEt-1 + NIt–Dt,
forecasted financial statements
where
Dtis the net cash distributions to equity holders,
or free cash flow to common equity,
computed as NIt–(CEt–CEt-1), and
=
−
+=
1
)1(
t
t
t
ee DrP
Equity Valued Directly as Pe Equity Valued Indirectly as Pe = Pf – Pd – Pps
Value of Common Equity Pe Value of Whole Entity Pf Value of Debt Pd Value of Preferred Stock Pps
1
1
ere wh
)1)(()1(
−
=
−=
+−
+
tett
ee
t
e
CErNIRI
rgr
r
1
1
ere wh
)1)(()1(
−
=
−=
+−
+
twtt
ww
t
w
NOArNOIRNOI
rgr
r
. ere w h
)1)(()1(
1
1
−
=
−=
+−
+
tdtt
t
dd
d
LrIRIT
rgr
r
. ere wh
)1)(()1(
1
1
−
=
−=
+−
+
tpstt
t
psps
ps
PSrPDRPD
rgr
r
Dt is cash flow to common equity; CEt = CEt-1 + NIt – Dt PDt is preferred dividend at time t
NOIt is the operating income for the period ending at time t, net of tax rps is the cost of preferred stock capital
It is the interest expense for the period ending at time t, rw is the weighted average cost of capital:
NIt is the net income for the period ending at time t; NIt = NOIt – (1-tx)It–PDt
NOAt is the net operating asset balance at time t
Figure 10.7 Summary of Valuation Equations
Valuation Attribute
Residual Income Cash Flows
psde
pspddee
wPPP
PrPrtxPr
r++
+−+
=)1(
Four Models –One Value
Define residual income RIt= NIt–reCEt-1. (NIt= RIt+ reCEt-1)
Start with Dt= NIt –(CEt–CEt-1) and substitute in RI tto get
Dt= CEt-1 –CEt+ RIt+ reCEt-1.
Substitute this for all future Dtin the dividend discount model to get
=
−++−+=
1
t
t
…..
)1()1(
11
)1( 2
2
0
1
−
+
+
+
−
+
+
+
−++=
=
ee
ee
t
t
ee r
r
r
r
CERIrP
−
++=
t
Residual Income to Common Equity Model
of expected future residual income (abnormal earnings).
=
−
++=
1
0)1(
t
t
t
ee RIrCEP
Advantages over cash flow models:
1) business, accounting and financial analysis are all in terms of
accounting numbers.
2) avoids having to “undo” the accounting to get to dividends or
Ct= NOIt–(NOAt–NOAt-1).
Ct= Dt+ It(1-txt) –Lt+ PDt–PSt.
To common
To debt holders
To preferred
Free Cash Flow to All Investors can be computed from
Statement of cash flow data as
–(CEt+Lt+PSt–CEt-1 –Lt-1–PSt-1)
= NIt –(CEt–CEt-1) + It(1–txt) –Lt + PDt –PSt
= Dt+ It(1-txt) –Lt+ PDt–PSt.
3 ways to compute FCF
1. NOI –NOA is easy
2. from the SCF, note that
◼CFO + CFI + CFF = cash (CFI and CFF usually negative)
3. OR use the “traditional” approach…
Free Cash Flow Generated (Used):
EBIT
-Taxes on EBIT
+Increase in Other Liabilities
+/-Clean Surplus Plug (Ignore)
The Traditional FCF recipe for the
DCF model is
But it works out to be exactly the