Valuation Models
There are four basic
models available using free cash flow concept for valuations.
They are:
- No
growth
- Constant
growth
- Super
normal growth followed by no growth
- Super
normal growth followed by constant growth
The basic methodology
to develop a general model will be helpful in explaining the
above-mentioned four models because only some variables need
to be added in special situations. The general model is:
X0(1- T)(1- b)(1 + g)
(1+g)
(1+g)2 (1+g)n-1
V0
= ----------------------------- [1 + ----------- +
------------- + …………..+ --------------]
(1+k)
(1+k)
(1+k)2
(1+k)n-1
Where,
Xt = Cash
inflows.
kt = Cost
of capital.
Tt = Tax
rate.
g = Growth rate in cash
inflows.
b = Investment requirements
(opportunities) per unit of after-tax cash flows.
No growth model
The basic assumption
in this model is that growth (g) = 0. As a result, the firm
will not make investment, so b = 0. The formula in a no growth
model implies that there is a constant level of inflows up
to infinity. The formula is:
X0(1-T)
V0
= --------------
for k>0
k
Constant growth model
Here, the assumption
is that growth rate (g) of cash inflows is constant instead
of zero(0). Using the assumption under constant growth model
for valuation of companies, the formula is:
X0(1-T) (1-b) (1+g)
V0
= ----------------------------
for g < k.
(k - g)
This formula is applied
when cost of capital (k) is larger than growth rate (g) to
perpetuity.
Super normal growth followed by no growth
The basic assumption
for this model is that there is super normal growth in cash
inflows temporally and no growth scenario will follow. Following
the assumptions, the formula will be:
n
(1+gs)t
X0(1-T) (1+gs)n+1
V0
= X0 (1-T) (1-bs)
S
------------- + ---------------------------
t =1 (1+k)t
k (1+k)n
Super normal growth followed by constant
growth
The basic assumption
is that there is temporary super normal growth and constant
growth to perpetuity will follow. The formula for this assumption
is:
N
(1+gs)t
X0(1-T) (1- bc)
(1+ gs)n+1
V0
= X0 (1-T) (1-bs)
S
---------- + ------------------- *
------------
t=1 (1+k)t k- gc (1+k)n
All these four broad
valuation models address the general capital budgeting equation
under several growth assumptions in cash inflows.
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