SCEG OATT Formula Transmission Rate Filing.pdf - SCANA ...

20091231-0037 FERC PDF (Unofficia1) 12/29/2009
Direct Testimony of Michael J. Viibert EXHIBIT NO. SeE-IS
AppendixB
Docket No. ERIO- -000 Page B-4
D D D D
p; __ I_+ 2 + 3 + ... + T
(l+k) (l+k)' (l+k)3 (l+k)' (B-1)
where "P" is the market price of the stock; "D/" is the dividend cash flow expected at the
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end of period t (i.e., subscript period 1, 2, 3 or T in the equation); "k" is the cost of
capital; and "T' is the last period in which a dividend cash flow is to be received. The
formula just says that the stock price is equal to the sum of the expected future dividends,
each discounted for the time and risk between now and the time the dividend is expected
to be received.
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Very often, when the DCF is applied in regulatory proceedings, very strong (i.e.,
unrealistic) assumptions are used that yield a simplification of the standard formula,
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which then can be rearranged to estimate the cost of capital.
that investors expect a dividend stream that will grow forever
Specifically, it is assumed
at a steady rate, and if so,
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the market price of the stock will be given by a very simple formula,
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P= DI
(k- g)
where "D/' is the dividend expected at the end of the first period, "gOO
(B-2)
is the perpetual
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growth rate, and "P" and "k" are the market price and the cost of capital, as before.
Equation (B-2) is a simplified version of Equation (B-1) that can be solved to yield the
well known "DCF formula" for the cost of capital:
D
k; _I +g
P
Dox(l+g)
; +g
P
(B-3)
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where" Do" is the current dividend, which investors expect to increase at rate g by the end
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ofthe next period, and the other symbols are defined as before.
Equation (B-3) says that
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if Equation (B-2) is satisfied, the cost of equity equals the expected dividend yield plus
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the (perpetual) expected future (forever constant) growth rate of dividends.
I refer to this
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as the simple DCF model because this simplification of the model relies on the use of
very strong assumptions that are unlikely to reflect actual circumstances.