INT Exhibit 101 Campbell.pdf

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intermountain Gas Company
Case No. U-l034-88
Exhibit 101
Schedule 1, Page 1 of 4
Wi tness: Campbell
THE RELATIONSHIP BETWEEN MARKET MlD BOOK PRICES
IN REGULATORY PROCEEDINGS
This schedule develops the fact that if the firm's stockholders'
minimally acceptable rate of return is applied to the equity corn-
.ponent of its rate base (book value), then the current market
price of the firm's common equity will approach its current book
value (on a per share basis). Two different approaches are used
to ill ustrate this fact.
APPROACH 1
Let the allowed rate of return on common equity applied to the
equity component of rate base (book value) be designated byII R. IIallowed .If the firm were expected to earn this amount, then
the dollars expected to be available for stockholder distribution
equal:
(1) Dollars Expected to be
Available for Stock-holder Distribution
=(Rallowed) (BVcommon equity)
For simplicity assume that the firm pays out all earnings
available to equity-holders in the form of dividends (this assump-
tion is not necessary for the results but it simplifies the analy-
sis) . Further assume that the firm earns this amount forever.
The maximum current price, "PO", a stockholder will pay (on
a per share basis) to acquire this future stream of expected
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Intermountain Gas Company
Case No. U-l034-88
Exhibit 101
Schedule 1, Page 2 of 4
Wi tness: Campbell
earnings is:
P =o
Dollars Expected to be Available
for Stockholder Distribution (on
a per share basis)
.T R~~i9âJèHö~d!?¥s
( 2)
I f the return allowed is a good estimate of the firm's cost
of common equity (its stockholders' demanded rate of return),
then substituting "Rdemanded by stockholders" for "Rallowed" in
equation (1), dividing both sides by numbers of shares of common
BVt~~O~hãe~H ty
Dollars Available
= for StockholderDistribution
(per share)
~RilemandedOy st:õcRholders
( 3)
Comparing equations (2) and (3) it can be concluded that,
current market prices on a per share basis should have a tendency
to equal current book value per share of common stock, i.e.,
"PO" = "BVcornmon equity (per share)".
APPROACH II
One can also illustrate the fact that current market prices
should roughly equal current book value (on a per share basis) if
the allowed rate of return is applied to the equity component of
rate base (book value) using the Gordon perpetual growth model.
This model, used extensively in finance and by financial
analysts, is presented in Schedule 8 of Exhibit 101. Equation
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Intermountain Gas Company
Case No. U-l034-88
Exhibi t 101
Schedule 1, Page 3 of 4
Wi tness: Campbell
( 5) of Schedule 8, page 3 of 3" contains the Gordon perpetual
growth model (commonly called the DCF method in regulatory
proceedings). It states that:
(1) Po =Di
ke-g
where "P IIo represents the investor's current maximum per share
price he is willing to pay to acquire the firm's common stock,
II Di II represents the future period per share dividend, like ii repre-
sents the stockholder's minimally acceptable rate of return, and
"g" represents the growth rate in per share dividends.
Letting "d" represent the firm's dividend payout ratio and
letting liRa II represent the allowed and expected to be earned rate
of return on the equity component of rate base (current book
value, II BVo" ) on a per share basis, then the expected future per
share dividend, ii Di", equals:
( 2) Di = d Ra BVo
Additionally, to the extent that the firm is retaining and
reinvesting some of its current funds (d ( 1), future dividends
will be able to be higher in the future than the present (g ) 0).
In fact, if the firm was expected to continue to earn liRa ii and
payout "d" percent of its expected earnings available to common,
then:
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Intermountain Gas Company
Case No. U-l034-88
Exhibi t 101
Schedule 1, Page 4 of 4
Wi tness : Campbell
( 3 ) g = (1 - d) Ra
Substituting equation (2) and (3) into equation (1) implies
that current market prices, set by investors, equal:
( 4)Po =dRa BVo
ke-( l-d )Ra
If the allowed rate of return is a good approximation of
investor's demanded rate of return (ke), and the firm can be
reasonably expected to earn this rate, then Ra = ke, and equation
( 4) may be rewritten as equation (5).
( 5)Po =d ke BVo
ke-( l-d )ke
=d ke BVo
d ke
=BVO
Again we are led to conclude that the regulatory process of
applying an estimate of the firm's stockholders' minimally accep-
table rate of return to the equity component of rate base will
result in a tendency for the company's current market price of
common to approximate its current book value (on a per share
basis), if the estimate of the firm's cost of common equity is an
accurate estimate, and if the company is given a fair opportunity
to earn this rate, and if no flotation costs are incurred by the
firm when new common equity is issued or when old common equity
was issued.
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Intermountain Gas Company
Case No. U-l034-88
Exhibit 101
Schedule 2, Page 1 of 2
Wi tness: Campbell
FLOTATION COST ADJUSTMENT
Equation (4) of Schedule 1, page 4 of 4, shows that the maxi-
mum per share price that an investor is willing to pay to acquire
a firm's stock is given by:
( 1)Po =dRa BVo
ke- (l-d )Ra
A fair rate of return occurs when the firm can issue new com-
mon stock and net new proceeds at pre-issue book values (on a per
share basis). Thus, a fair market price, if flotation costs are
10%, is stated as:
( 2) Pfair market = 1.11 BVo.
Substi tuting for lip IIo in equation (1) for "Pfair market" in
equation (2) implies that the firm's allowed and fair rate of
return on common equity must solve:
( 3)
dR fairBVa 0
ke (l-d )Ra
= 1. 11 BVo
By equation (3), if the firm retains no earnings (d = 1),
then the fair allowed rate of return equals:
( 4 ) Ra fa i r = (1 . 11) ( ke ) ;
That is, if a firm pays out all of its earnings as dividends, the
fair rate of return that the firm should be given an opportunity
to earn equals, roughly, 1.1 times its stockholders' minimally
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Intermountain Gas Company
Case No. U-l034-88
Exhibi t 101
Sched ule 2, Page 2 of 2
Wi tness: Campbell
acceptable rate of return, "ke",
More generally, for any dividend payout ratio, the flotation
cost adj ustment that is necessary to generate a fair rate of
return on common equity may be specif ied as:
(5 )R fair - k ( 1.11a - e ( I-d) ( 1.11) + d
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Intermountain Gas Company
Case No. U-l034-88
Exhibit 101
Schedule 3, Page 1 of 1
Wi tness: Campbell
AAA CORPORATE BOND YI ELDS
(1950-1979 )
( Source: Moody's Bond Record)
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
Average AverageYieldYearYield
2.6 1965 4.5
2.9 1966 5.1
3.0 1967 5.5
3.2 1968 6.22.9 1969 7.03.1 1970 8.03.4 1971 7.43.9 1972 7.2
3.8 1973 7.4
4.4 1974 8.64.4 1975 8.84.4 1976 8.44.3 1977 8.04.3 1978 8.74.4 1979 9.6
Year
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Intermountain Gas Company
Case No. U-l034-88
Exhibi t 101
Schedule 4, Page 1 of 1
Wi tness : Campbell
New York Stock Exchange Market Composite
Annual Compounded Rates of Return, 1926-1979
Ending Period Compounded Annual
Rate of Return Ending Period Compounded Annual
Rate of Return
1926
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
9.57
32.8039.20-14.60-28.42-44.57-8.89
58.56
3.44
44.77
32.80-34.3827.70
1. 87-7.81-9.77
16.66
27.93
21. 17
35.58-6.423.30
2.1320.23
30.46
21.15
13.35
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
.37
51. 2925.70
8.69-10.77
44.21
13.18
7.56
27.06-9.33
21. 33
16.5013.91-9.06
26.99
12.78-9.80
1.41
15.85
17.87-16.99-26.87
37.8126.36-4.89
7.41
18.50
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Intermountain Gas Company
Case No. U-I034-88
Exhibi t 101
Schedule 5, Page 1 of 1
Wi tness: Campbell
9l-Day U. S. Treasury Bills, 1926-l979,
Stated on an Ann'ual Coupon Basis*
Compounded Annual Compounded AnnualEnding Period Rate of Return Ending Period Rate of Return
1926 3.34 1953 1. 9819273.21 1954 .9719284.13 1955 1.7919294.61 1956 2.7419302.29 1957 3.4019311. 43 1958 1. 891932.90 1959 3.521933.53 1960 3.031934.26 1961 2.451935.14 1962 2.871936.14 1963 3.271937.45 1964 3.671938.05 1965 4.111939.02 1966 5.071940.01 1967 4.481941.10 1968 5.591942.34 1969 7.031943.38 1970 6.781944.38 1971 4.511945.38 1972 4.241946.38 1973 7.461947.60 1974 8.3619481. 06 1975 6.1019491. 12 1976 5.2019501. 25 1977 5.5319511. 59 1978 7.6319521. 82 1979 10.47
* Source:A History of Interest Rates and Federal Reserve Data.-
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Intermountain Gas Company
Case No. U-l034-88
Exhibit 101
Schedule 6, Page 1 of 1
Wi tness: Campbell
30-Day U. S. Treasury Bills, 1926-1979,
Stated on an Annual Coupon Basis*
Ending Period Compounded Annual
Rate of Return Ending Period
Compounded Annual
Rate of Return
1926
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
3.3
3. 13.24.82.31.1
1. 0
.2
.2.2.2
.30.0
0.0
0.0
.1.2
.3
.3
.3
.4
.5
.81.1
1. 2
1. 5
1. 7
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1. 8.9
1. 5
2.53.1
1. 6
3.02.62.22.73.23.5
3.9
4.84.2
5.26.66.54.43.86.98.0
5.8
5: 15.27.1
10.0
*Source: Computer Directions Advisors update of Ibbotson-S inquef ield 's Stocks, Bonds, Bills and Inflation: ThePast and the Future.
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I Intermountain Gas Company
Case No.U-l034-88
Exhibit 10l
I Schedule 7,Page 1 of 3
Wi tness:Campbell
I INTERMOUNTAIN GAS INDUSTRIES
I NYSE CompositeStockCashRate of Rate of Return,
I Datel Price2 Dividend Return3 (1979)4
I 1/31/73 15 2/8 $.26 -7.403 -2.5342/28/73 14 1/8 -7.377 -3.9823/30/73 14 4/8 2.655 -.547
:1
4/30/73 14 3/8 $.26 0.931 -4.6465/31/73 14 -2.609 -1. 8376/29/73 14 2/8 1.786 -.882
I 7/31/73 14 2/8 $.26 1. 825 5.2498/31/73 13 4/8 -5.263 -3.0109/28/73 15 11. ILL 5.243
I 10/31/73 15 5/8 $.30 6.167 -.18511/30/73 14 4/8 -7.200 -11.66712/31/73 15 3.448 1.514
I 1/31/74 14 2/8 $.30 -3.000 -.ll02/28/74 14 3/8 0.877 .336I3/29/74 14 2/8 -0.870 -2.3954/30/74 13 3/8 $.30 -4.035 -4.3225/3l/74 13 -2.804 -3.527I6/28/74 l2 5/8 -2.885 -1. 9397/31/74 11 6/8 $.38 -3.92l -7.2938/30/74 10 6/8 -8.5ll -8.540I9/30/74 10 7/8 1. 163 -ll.01710/31/74 II $.32 4.092 16.76811/29/74 10 2/8 -6.818 -3.995I12/31/74 10 6/8 4.878 -2.32l
1/31/75 12 1/8 $.32 15.767 13.479I2/28/75 11 2/8 -7.216 6.0823/31/75 11 4/8 2.222 2.9454/30/75 10 4/8 $.32 -5.913 4.698I5/30/75 10 3/8 -1. 190 5.4706/30/75 12 7/8 24.096 5.1847/31/75 11 6/8 $.32 -6.252 -6.374I8/29/75 11 4/8 -2.128 -2.0409/30/75 11 6/8 2.174 -3.66210/31/75 12 1/8 $.32 5.915 6.096I11/28/75 12 3/8 2.062 3. lSi12/31/75 12 -3.303 -1.048
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Intermountain Gas Company
Case No.U-l034-88
Exhibit 101
Schedule 7,Page 2 of 3IWi tness:Campbell
I 1/30/76 13 4/8 $.32 15.167 12.5202/27/76 13 2/8 -1. 852 .1273/31/76 13 4/8 1. 887 3.000I4/30/76 12 7/8 $.32 -2.259 -10.8065/28/76 12 6/8 -0.971 -.8826/30/76 12 7/8 0.980 4.725I7/30/76 13 $.32 3.456 -.7508/31/76 13 1/8 0.962 .020
I
9/30/76 14 6/8 12.381 2.57210/29/76 14 5/8 $.325 1. 356 -2.143ll/30/76 15 4/8 5.983 .471
I
12/31/76 15 4/8 0.000 5.855
1/31/77 17 3/8 $.34 14.290 -3.981
I 2/28/77 17 2/8 -0.719 -1.6223/31/77 18 4.348 -1. 0754/29/77 19 $.34 7.444 .388
I
5/31/77 18 2/8 -3.947 -1.2556/30/77 21 6/8 19.178 5.0887/29/77 20 $.35 -6.437 -1. 573
I 8/31/77 17 7/8 -10.625 -1. 4049/30/77 18 3/8 2.797 .06810/31/77 18 3/8 $.35 1. 905 -3.943
I 11/30/77 18 3/8 0.000 4.19812/30/77 18 5/8 $.35 3.265 .526
I 1/31/78 17 6/8 -4.698 -5.6872/28/78 16 3/8 -7.746 -1.2l03/31/78 15 1/8 -7.633 3.186
I 4/28/78 15 $.35 1. 488 8.3375/31/78 14 4/8 -3.333 1.8686/30/78 14 2/8 $.35 0.690 -1. 282
I 7/31/78 15 6/8 10.526 5.6428/31/78 16 1. 587 3.7219/29/78 16 3/8 2.344 -.633
I 10/31/78 12 7/8 $.35 -19.237 -10.176ll/30/78 13 1/8 1. 942 3.13112/29/78 13 1/8 0.000 1.672
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1/31/792/28/793/30/794/30/79
5/31/796/29/797/31/798/31/799/28/79
Intermountain Gas Company
Case No. U-I034-88
Exhibit 101
Schedule 7, Page 3 of 3Wi tness : Campbell
14 2/8
13 5/8
14 1/8
13 6/8
13 3/814 6/8
14 2/814 3/8
14
$.35 l1. 238-4.386
3.670-0.177-2.727
10.280
-1. 017
0.877-2.609
4.701
-2.8676.045
.630
-1. 430
4.432
1. 482
6.293
.048
$.35
$.35
lLast trading day of the month.
2Bid Price (Source: Standard and Poor's ISL: Daily Stock Price
Index (O-T-C)),3p~Divt - Pt-l' where t = month.
Pt-l
4source: CRSP Data Files.
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Intermountain Gas Company
Case No. U-l034-88
Exhibit 10l
Schedule 8, Page 1 of 3Wi tness : Campbell
CAPM and DCF
FORMULAE
Sharpe's market model may be stated as follows:
(1) Rit = Ai + Bi Rmt + Eit,
where "Rit" represents the possible returns of firm "i" 's common
stock during period "t". "Rmt" represents the poss ible return on
the market portfolio during period "t", and "Èit" represents the
possible error terms in this relationship.
Simply stated, the Sharpe market model states that the
returns on security "i" for any time period lit" can be explained
by the returns on the market during that period, plus an error
term "Eit".
The capital asset pricing model is stated as:
(2) E(Ri) = Rf + Bi (E(Rm) - Rfl,-
where liE (Ri)" represents the expected return on the common stock
of firm II i", "Rf" represents the riskfree rate of return, "Bi"
measures the risk (volatility) of firm "i" 's common stock rela--
tive to the average risk of the market, and" (E(Rm) - Rfl "--the
expected return on the stock market in excess of the riskfree
rate--is called the expected market risk premium. It measures
the returns that one should expect, in excess of the riskfree
rate, if the firm's common stock is of average market risk.
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Intermountain Gas Company
Case No. U-l034-88
Exhibit 10l
Sched ule 8, Page 2 of 3
Wi tness: Campbell
Using the capital asset pricing model for intermountain,
(3) E(Rintmnt) = Rf + Bintmnt (E(Rm) - Rfl,-
where "E(Rintmnt)" represents the minimal rate of return that
Intermountain's stockholders must expect before they will divert
their funds away from riskfree investing into common stock
investing in Intermountain. And "BIntmnt" represents
Intermountain's beta, or market response coeff icient.
The maximum price an investor is willing to pay for one share
of common stock if mathematically determined by
( 4)Po
00
Z=t-l
Dt
(l+ke)t
f
Because common stock has no maturity, the investor must project
all future cash flows (Dt represents future dividends) that the
stock can be expected to produce over its lifetime. To trans-
form these future expected cash flows to their present value,
these flows are discounted by the investor's minimal1y acceptable
rate of return,"k IIe .Their present value represents the maximum
current price an investor would be willing to pay to acquire the
share of common stock.
If it was assumed that future dividends, on average, can be
expected to increase at a reasonably constant rate of growth,
"g", then "Dt = Do(l+g)tii for any period lit' and equation (4) can
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Intermountain Gas Company
Case No. U-l034-88
Exhibit 101
Schedule 8, Page 3 of 3
wi tness: Campbell
be vastly simplified to the form contained in equation (5).
( 5)Po =Di
ke-g
where "Di" represents the investor's expectation of future annual
dividends, "ke" represents his minimally acceptable rate of
return on the firm's common equity, and "g" represents the
investor's expectation of future dividend growth associated with
this particular share of common stock.
Solving for "k IIe ,the investor's implied minimally acceptable
rate of return from the previous equation, we find that it can be
estimated by using equation (6).
( 6)ke =Di-p +g.