Description
Hall (2007) challenges a fundamental point in
the analysis of Lally (2007) and earlier papers:
if the risk free rate within the allowed rate of
return matches the regulatory term, then the
present value of future cash flows PV0 equals
equityholders initial investment C(1-L).
Accounting Research Journal
Rejoinder: Regulation and the Term of the Risk Free Rate: Implications of Corporate Debt
Martin Lally
Article information:
To cite this document:
Martin Lally, (2007),"Rejoinder: Regulation and the Term of the Risk Free Rate: Implications of Corporate Debt", Accounting
Research J ournal, Vol. 20 Iss 2 pp. 87 - 88
Permanent link to this document:http://dx.doi.org/10.1108/10309610780000693
Downloaded on: 24 January 2016, At: 21:02 (PT)
References: this document contains references to 0 other documents.
To copy this document: [email protected]
The fulltext of this document has been downloaded 257 times since 2007*
Users who downloaded this article also downloaded:
Martin Lally, (2007),"Regulation and the Term of the Risk Free Rate: Implications of Corporate Debt", Accounting Research
J ournal, Vol. 20 Iss 2 pp. 73-80http://dx.doi.org/10.1108/10309610780000691
J ason Hall, (2007),"Comment on Regulation and the Term of the Risk Free Rate: Implications of Corporate Debt",
Accounting Research J ournal, Vol. 20 Iss 2 pp. 81-86http://dx.doi.org/10.1108/10309610780000692
Sungsoo Yoon, Seung Won Yoo, (2007),"Diffusion of Tax Innovation and Post-Audit Settlement", Accounting Research
J ournal, Vol. 20 Iss 2 pp. 89-95http://dx.doi.org/10.1108/10309610780000694
Access to this document was granted through an Emerald subscription provided by emerald-srm:115632 []
For Authors
If you would like to write for this, or any other Emerald publication, then please use our Emerald for Authors service
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Emerald is a global publisher linking research and practice to the benefit of society. The company manages a portfolio of
more than 290 journals and over 2,350 books and book series volumes, as well as providing an extensive range of online
products and additional customer resources and services.
Emerald is both COUNTER 4 and TRANSFER compliant. The organization is a partner of the Committee on Publication
Ethics (COPE) and also works with Portico and the LOCKSS initiative for digital archive preservation.
*Related content and download information correct at time of download.
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Rejoinder: Regulation and the Term of the Risk Free Rate: Implications of Corporate Debt
87
Rejoinder:
Regulation and the Term of the Risk Free
Rate: Implications of Corporate Debt
Martin Lally
School of Economics and Finance
Victoria University of Wellington
Hall (2007) challenges a fundamental point in
the analysis of Lally (2007) and earlier papers:
if the risk free rate within the allowed rate of
return matches the regulatory term, then the
present value of future cash flows PV
0
equals
equityholders initial investment C(1-L). Hall
argues that this result implicitly assumes that
forward rates equal expected spot rates. If this
were true, it would undercut Lally’s analysis
because the empirical evidence does not support
the alleged assumption. Hall proceeds as
follows.
Point 1: Hall (2007, pp. 2–3) argues that,
following Lally’s approach to setting the
allowed rate of return, changing the length of
the review period would change the allowed
rate of return (and therefore the expected cash
flows) whilst leaving discount rates unaffected;
consequently, PV
0
would change and therefore
diverge from C(1-L), contrary to Lally’s
conclusion. However, whilst the set of discount
rates would be unaffected, the appropriate
discount rate fromthat set will change if the
review period changes. For example, if the
review period changes from a three to a five
year term, the appropriate risk free rate within
the discount rate changes from the three year to
the five year yield to maturity. Accordingly,
PV
0
=C(1-L) is still true. Furthermore, if Hall’s
argument here was correct, it would contradict
his own assertion that Lally’s analysis is correct
so long as forward rates equal expected spot
rates.
Point 2: Hall (2007, pp. 3-4) presents the
derivation underlying equation (5) in Lally
(2007), and does this in the equations
surrounding (1) in his paper. Since Hall is
presenting the analysis in Lally (2007), he
needs to invoke the same definitions. However,
he has not done so. In particular, Hall defines
R
12
as “the expected interest rate on a one-year
Government bond in one year’s time” and he
defines F
2
as the “expected cash flow” to equity
holders at time 2. However, in Lally (2007,
section 2), R
12
is defined as “the one year rate
that will arise in one year” and F
2
as the “cash
flow” to equity holders at time 2, i.e., these are
outcomes rather than expectations. If Hall had
defined R
12
and F
2
in exactly the same way as in
Lally (2007), then the equation immediately
preceding his equation (1) would have been as
follows.
)] ( 1 )[ 1 (
) (
1
12 01
2
01
1
0
R E R
F E
R
F
PV
+ +
+
+
=
(I)
Point 3: Hall (2007, p. 4) asserts that
equation (I) is wrong. I agree. However,
equation (I) does not correspond to anything in
Lally (2007); the analysis in Lally is devoid of
the expectation operators and is recursive, i.e.,
F
2
is valued at time 1 using R
12
, and then valued
at time 0 using R
01
. Thus, Hall has set up a straw
man and then proceeded to blow it over.
Point 4: Hall (2007, p. 4) next claims that the
correct discount rate on E(F
2
) in equation (I)
above is the “yield-to-maturity on a zero-
coupon bond maturing in two years”, i.e., the
two year spot rate, which can be expressed in
terms of the one year spot rate (R
01
) and the
forward rate for the second year (
F
R
12
). The
result corresponds to that immediately
preceding Hall’s equation (3):
] 1 )[ 1 (
) (
1
12 01
2
01
1
0
F
R R
F E
R
F
PV
+ +
+
+
=
(II)
However, the two year spot rate is only
appropriate for valuing a cash flow arising in
two years if the cash flow is certain. Clearly F
2
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ACCOUNTING RESEARCH JOURNAL VOLUME 20 NO 2 (2007)
88
is not certain and therefore equation (II) is
invalid. The correct way to discount F
2
, whose
uncertainty parallels the payoff on a floating
rate bond, is recursive using R
12
to generate PV
1
followed by R
01
to generate PV
0
as in Lally
(2007).
Point 5: Hall (2007, p. 5) then shows, given
equation (II) above, that PV
0
= C(1–L) if
F
R R E
12 12
) ( = . The derivation is correct.
In summary, Hall’s points (3) and (5) are
correct. However, his points (1), (2) and (4) are
not correct, i.e., he has not demonstrated any
anomaly in Lally (2007), he has not correctly
represented Lally’s analysis (because he has
changed the definitions of some symbols), and
his proposed valuation equation (II) above is
incorrect. The last point is crucial. If equation
(II) were valid, Hall’s case would be proven.
However, equation (II) is wrong: the current
two year risk free rate cannot be used to
discount the risky cash flow F
2
. The correct
valuation approach is the recursive process
shown in Lally (2007), and it involves no
assumptions whatsoever about interest rates.
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This article has been cited by:
1. Kevin Davis. 2014. The Debt Maturity Issue in Access Pricing. Economic Record 90:10.1111/ecor.2014.90.issue-290, 271-281.
[CrossRef]
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doc_356150148.pdf
Hall (2007) challenges a fundamental point in
the analysis of Lally (2007) and earlier papers:
if the risk free rate within the allowed rate of
return matches the regulatory term, then the
present value of future cash flows PV0 equals
equityholders initial investment C(1-L).
Accounting Research Journal
Rejoinder: Regulation and the Term of the Risk Free Rate: Implications of Corporate Debt
Martin Lally
Article information:
To cite this document:
Martin Lally, (2007),"Rejoinder: Regulation and the Term of the Risk Free Rate: Implications of Corporate Debt", Accounting
Research J ournal, Vol. 20 Iss 2 pp. 87 - 88
Permanent link to this document:http://dx.doi.org/10.1108/10309610780000693
Downloaded on: 24 January 2016, At: 21:02 (PT)
References: this document contains references to 0 other documents.
To copy this document: [email protected]
The fulltext of this document has been downloaded 257 times since 2007*
Users who downloaded this article also downloaded:
Martin Lally, (2007),"Regulation and the Term of the Risk Free Rate: Implications of Corporate Debt", Accounting Research
J ournal, Vol. 20 Iss 2 pp. 73-80http://dx.doi.org/10.1108/10309610780000691
J ason Hall, (2007),"Comment on Regulation and the Term of the Risk Free Rate: Implications of Corporate Debt",
Accounting Research J ournal, Vol. 20 Iss 2 pp. 81-86http://dx.doi.org/10.1108/10309610780000692
Sungsoo Yoon, Seung Won Yoo, (2007),"Diffusion of Tax Innovation and Post-Audit Settlement", Accounting Research
J ournal, Vol. 20 Iss 2 pp. 89-95http://dx.doi.org/10.1108/10309610780000694
Access to this document was granted through an Emerald subscription provided by emerald-srm:115632 []
For Authors
If you would like to write for this, or any other Emerald publication, then please use our Emerald for Authors service
information about how to choose which publication to write for and submission guidelines are available for all. Please visit
www.emeraldinsight.com/authors for more information.
About Emerald www.emeraldinsight.com
Emerald is a global publisher linking research and practice to the benefit of society. The company manages a portfolio of
more than 290 journals and over 2,350 books and book series volumes, as well as providing an extensive range of online
products and additional customer resources and services.
Emerald is both COUNTER 4 and TRANSFER compliant. The organization is a partner of the Committee on Publication
Ethics (COPE) and also works with Portico and the LOCKSS initiative for digital archive preservation.
*Related content and download information correct at time of download.
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o
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Rejoinder: Regulation and the Term of the Risk Free Rate: Implications of Corporate Debt
87
Rejoinder:
Regulation and the Term of the Risk Free
Rate: Implications of Corporate Debt
Martin Lally
School of Economics and Finance
Victoria University of Wellington
Hall (2007) challenges a fundamental point in
the analysis of Lally (2007) and earlier papers:
if the risk free rate within the allowed rate of
return matches the regulatory term, then the
present value of future cash flows PV
0
equals
equityholders initial investment C(1-L). Hall
argues that this result implicitly assumes that
forward rates equal expected spot rates. If this
were true, it would undercut Lally’s analysis
because the empirical evidence does not support
the alleged assumption. Hall proceeds as
follows.
Point 1: Hall (2007, pp. 2–3) argues that,
following Lally’s approach to setting the
allowed rate of return, changing the length of
the review period would change the allowed
rate of return (and therefore the expected cash
flows) whilst leaving discount rates unaffected;
consequently, PV
0
would change and therefore
diverge from C(1-L), contrary to Lally’s
conclusion. However, whilst the set of discount
rates would be unaffected, the appropriate
discount rate fromthat set will change if the
review period changes. For example, if the
review period changes from a three to a five
year term, the appropriate risk free rate within
the discount rate changes from the three year to
the five year yield to maturity. Accordingly,
PV
0
=C(1-L) is still true. Furthermore, if Hall’s
argument here was correct, it would contradict
his own assertion that Lally’s analysis is correct
so long as forward rates equal expected spot
rates.
Point 2: Hall (2007, pp. 3-4) presents the
derivation underlying equation (5) in Lally
(2007), and does this in the equations
surrounding (1) in his paper. Since Hall is
presenting the analysis in Lally (2007), he
needs to invoke the same definitions. However,
he has not done so. In particular, Hall defines
R
12
as “the expected interest rate on a one-year
Government bond in one year’s time” and he
defines F
2
as the “expected cash flow” to equity
holders at time 2. However, in Lally (2007,
section 2), R
12
is defined as “the one year rate
that will arise in one year” and F
2
as the “cash
flow” to equity holders at time 2, i.e., these are
outcomes rather than expectations. If Hall had
defined R
12
and F
2
in exactly the same way as in
Lally (2007), then the equation immediately
preceding his equation (1) would have been as
follows.
)] ( 1 )[ 1 (
) (
1
12 01
2
01
1
0
R E R
F E
R
F
PV
+ +
+
+
=
(I)
Point 3: Hall (2007, p. 4) asserts that
equation (I) is wrong. I agree. However,
equation (I) does not correspond to anything in
Lally (2007); the analysis in Lally is devoid of
the expectation operators and is recursive, i.e.,
F
2
is valued at time 1 using R
12
, and then valued
at time 0 using R
01
. Thus, Hall has set up a straw
man and then proceeded to blow it over.
Point 4: Hall (2007, p. 4) next claims that the
correct discount rate on E(F
2
) in equation (I)
above is the “yield-to-maturity on a zero-
coupon bond maturing in two years”, i.e., the
two year spot rate, which can be expressed in
terms of the one year spot rate (R
01
) and the
forward rate for the second year (
F
R
12
). The
result corresponds to that immediately
preceding Hall’s equation (3):
] 1 )[ 1 (
) (
1
12 01
2
01
1
0
F
R R
F E
R
F
PV
+ +
+
+
=
(II)
However, the two year spot rate is only
appropriate for valuing a cash flow arising in
two years if the cash flow is certain. Clearly F
2
D
o
w
n
l
o
a
d
e
d
b
y
P
O
N
D
I
C
H
E
R
R
Y
U
N
I
V
E
R
S
I
T
Y
A
t
2
1
:
0
2
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
ACCOUNTING RESEARCH JOURNAL VOLUME 20 NO 2 (2007)
88
is not certain and therefore equation (II) is
invalid. The correct way to discount F
2
, whose
uncertainty parallels the payoff on a floating
rate bond, is recursive using R
12
to generate PV
1
followed by R
01
to generate PV
0
as in Lally
(2007).
Point 5: Hall (2007, p. 5) then shows, given
equation (II) above, that PV
0
= C(1–L) if
F
R R E
12 12
) ( = . The derivation is correct.
In summary, Hall’s points (3) and (5) are
correct. However, his points (1), (2) and (4) are
not correct, i.e., he has not demonstrated any
anomaly in Lally (2007), he has not correctly
represented Lally’s analysis (because he has
changed the definitions of some symbols), and
his proposed valuation equation (II) above is
incorrect. The last point is crucial. If equation
(II) were valid, Hall’s case would be proven.
However, equation (II) is wrong: the current
two year risk free rate cannot be used to
discount the risky cash flow F
2
. The correct
valuation approach is the recursive process
shown in Lally (2007), and it involves no
assumptions whatsoever about interest rates.
D
o
w
n
l
o
a
d
e
d
b
y
P
O
N
D
I
C
H
E
R
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1
:
0
2
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
This article has been cited by:
1. Kevin Davis. 2014. The Debt Maturity Issue in Access Pricing. Economic Record 90:10.1111/ecor.2014.90.issue-290, 271-281.
[CrossRef]
D
o
w
n
l
o
a
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b
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P
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doc_356150148.pdf