298 Final Equations
Stock Value
P
o
=
D
1
+
D
2
+
(D
3
+D
4/(rg)
)
(1+r)
(1+r)
2
(1+r)
3
P
o
price today
D
1
future dividend
D
4
+
constant growth dividend
r
period interest rate
g
growth rate
Rate of Return
r = D
1
+ [E(P
1
)  P
0
]
P
0
r
rate of return
P
o
price today
D
1
any dividends received
E(P
1
) – P
0
change in price
Realized Rate of Return(ROR)
FV = PV(1+ROR)
n
FV
future value
PV
present value
ROR
realized rate
n
number of periods
Net Present Value
NPV = initial cost + PV of future cash flows
If >0, accept. If <0 reject. If near 0, justify.
Internal Rate of Return
0 = C
0
+
C
1
+
C
2
+…
(1+IRR) (1+IRR)
2
C = future cash flow
IRR = internal rate of return
r = cost of capital
Rate that creates an NPV = 0.
If IRR>r, accept.
Easy to understand.
Beware nonconventional cash flows.
Profitability Index
PV of future revenues
PV of future costs
If >1.00, accept.
Good for capital rationing with limited cash.
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 Spring '09
 FREEDMAN
 Time Value Of Money, Net Present Value, future cash flows, possible return Pr

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