Beatrice Presentation February 22, 2005 Robert M. Hull, Beatrice Professor Summer 2005 School of...
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Beatrice Presentation February 22, 2005 Robert M. Hull, Beatrice Professor Summer 2005 School of Business, Washburn University, 1700 SW College Avenue, Topeka, KS 66621 Phone : + 1-785‑231‑1010; FAX: + 785‑231‑1063. E‑mail address: [email protected] (R. Hull) Earlier Version Published in Proceedings of: Southwestern Finance Association, Dallas, TX, March 2005 Final Version Accepted for Publication February 4, 2005: Regional Business Review (Forthcoming 2005)
Beatrice Presentation February 22, 2005 Robert M. Hull, Beatrice Professor Summer 2005 School of Business, Washburn University, 1700 SW College Avenue,
Beatrice Presentation February 22, 2005 Robert M. Hull,
Beatrice Professor Summer 2005 School of Business, Washburn
University, 1700 SW College Avenue, Topeka, KS 66621 Phone: + 1-785
231 1010; FAX: + 785 231 1063. E mail address:
[email protected] (R. Hull) Earlier Version Published in
Proceedings of: Southwestern Finance Association, Dallas, TX, March
2005 Final Version Accepted for Publication February 4, 2005:
Regional Business Review (Forthcoming 2005)
Slide 3
Building on the no growth perpetuity framework first developed
by Modigliani and Miller (1963), this paper attempts to offer gain
to leverage (G L ) formulations useable by managers in making debt-
equity choices. These formulations focus on how changes in equity
and debt discount rates influence firm value. A real world
application (using data suggested by independent analysts) seeks to
determine the gain to leverage for nine different debt-equity
choices. Using our formulation with constant growth, we offer
results that can support the suggested target debt-equity choice as
the choice that maximizes firm value. Abstract JEL
Classification:G32 Key Words:Gain to Leverage; Debt-to-Equity
Choice; Costs of Capital
Slide 4
Definitions Gain to Leverage (GL) formulations are formulations
that measure the change in value caused by changing the amount of
debt. Equity discount rate is the firms cost of borrowing for
equity or the return required by investors in equity (for most
firms equity is just common equity). Debt discount rate is the
firms cost of borrowing for debt or the return required by
investors in debt (for most firms debt is long-term debt such as
bonds). Target debt-equity choice is the amount of debt relative to
the amount equity at which the firm and its manager strive to
obtain (the target can be viewed as involving the amount of debt
that maximizes firm value). Perpetuity with growth involves a
perpetual cash, a discount rate, and a growth rate. Any series of
uneven cash flows can be approximated by a perpetuity with
growth.
Slide 5
According to Compustat, since the beginning of the century
there have been about 1,650 firms per year that on average have
reported no long-term debt (which includes capitalized lease
obligations). Theoretical research begins with Modigliani and
Miller, MM, (1963) who derive a gain to leverage (G L ) formulation
in the context of an unleveraged firm issuing risk-free debt to
replace risky equity. For MM, G L is the corporate tax rate
multiplied by debt value. The applicability of MMs G L formulation
is limited as it implies that financial executives issue
unrestricted amounts of debt. Empirical research (Altman, 1984;
Cutler and Summers, 1988; Hull, 1999; Graham and Harvey, 2001)
contend that debt affects firm value. Hull (1999) offers event
study evidence supporting an optimal debt-equity choice. Given the
presence of debt in the capital structure of most firms as well as
the evidence concerning leverage-related wealth effects, there is a
need to offer usable equations that can quantify these effects.
This paper aims to fill this void by offering G L formulations
quantifying these effects.
Slide 6
MM (1958): Gain to Leverage (G L ) = 0. Value determined solely
by operating assets. MM (1958): Gain to Leverage (G L ) = 0. Value
determined solely by operating assets. MM (1963): Gain to Leverage
(G L ) = T C D where T C is the applicable corporate tax rate and D
= I/R D where I is the perpetual interest payment and R D is the
cost of debt. MM (1963): Gain to Leverage (G L ) = T C D where T C
is the applicable corporate tax rate and D = I/R D where I is the
perpetual interest payment and R D is the cost of debt. Miller
(1977): Gain to Leverage (G L ) = (1 )D where = (1 T PE )(1 T C
)/(1 T PD ) with T PE and T PD the personal tax rates applicable to
income from equity and debt and D now equals (1 T PD )I/R D. Miller
(1977): Gain to Leverage (G L ) = (1 )D where = (1 T PE )(1 T C
)/(1 T PD ) with T PE and T PD the personal tax rates applicable to
income from equity and debt and D now equals (1 T PD )I/R D. PRIOR
RESEARCH
Slide 7
Motivation for Research Ensuing G L extensions of MM (DeAngelo
and Masulis, 1980; Kim, 1982; Modigliani, 1982; Ross, 1985)
consider a variety of leverage- related costs and show that an
optimal debt level exists even when personal taxes are recognized.
Leland and Toft (1996) extend the closed-form results of Leland
(1994) to a much richer class of possible debt structures
permitting the study of the optimal amount of maturity of debt.
Leland (1998) attempts to provide quantitative guidance on the
amount and maturity of debt, the financial restructuring, and the
optimal risk strategy. The G L extensions are characterized by the
inability to make explicit how changes in equity and debt discount
rates impact firm value within a model that financial managers
might find useable. This paper is motivated to fill in the gap
missing in G L research by incorporating discount rates.
Slide 8
Purpose We seek to offer GL formulations for an unleveraged
firm situation and show the applicability of the GL formulations
using empirical data.
Slide 9
G L Formulation without Personal Taxes Starting Point: G L = V
L V U where V L is leveraged firm value and V U is unleveraged firm
value. V U = (1T C )C / R U where C is the unleveraged equity
before-tax cash flow with R U > R D. V L = E L + D where E L =
(1T C )( C-I) / R L and D = I/R D.
Slide 10
Result of G L Derivation Without Personal Taxes (from Appendix
A) In Appendix A we show that: G L = [1-(aR D /R L )]D + [(R U /R L
)-1]E U (8) Note that [1-(aR D /R L )]D is always positive because
aR D /R L < 1 is expected to always hold not only because R D /R
L < 1 but a < 1. With no personal taxes, we have: = (1 T C ).
If R D = R L, then [1-(aR D /R L )]D = [1-(a)]D = [1-(1-T C )]D = T
C D which is MM (1963). We see how incorporating discount rates
changes the G L formulation. Note that [1-(aR D /R L )]D is always
positive because aR D /R L < 1 is expected to always hold not
only because R D /R L < 1 but a < 1. With no personal taxes,
we have: = (1 T C ). If R D = R L, then [1-(aR D /R L )]D =
[1-(a)]D = [1-(1-T C )]D = T C D which is MM (1963). We see how
incorporating discount rates changes the G L formulation. Note that
[(R U /R L )-1]E U is always negative because R U /R L < 1 is
always true. Note that if R U = R L, then [(R U /R L )-1]E U = 0.
Thus, we have G L = Positive Components + Negative Component. Which
ever component dominates will determine whether G L is positive or
negative.
Slide 11
Illustration: No Personal Taxes Versus Personal Taxes TC = 0.3
(30%); RU = 0.1 (10%); C = $10 VU = (1-TC)C / RU = (1-0.3)$10 / 0.1
= $70 TPE = 0.05 (5%);TC = 0.3 (30%); RU = 0.1 (10%) VU =
(1-TPE)(1-TC)C / RU = (1-0.05)(1-0.3)$10 / 0.1 = $66.50 Difference
is $70.00 - $66.50 = $3.50 For D, where TPD = 0.20 differences
would be four times greater per $100. For example, if D = (I / RD)
= $100, we have: (1-TPD)D = (10.2)($100) = $80. Here the difference
is $100 - $80 = $20 $20 / 100 = 0.2 on the dollar compared to $3.50
/ $70 = 0.05 because TPD / TPE = 0.2 / 0.05 = 4 (four times
greater).
Slide 12
Result of G L Derivation With Personal Taxes and Constant
Growth (Appendix B) IIn Appendix B, we derive G L with personal
taxes and constant growth and show that G L can still be expressed
as two components. FFor the first component we now have: {1 [ R D /
(R L L ) ] }D FFor the second component we now have: {1 [ (R U L )
/ (R L L ) ] } E U PPutting these together, we have: G L = {1 [ R D
/ (R L L ) ] }D + {1 [ (R U L ) / (R L L ) ] } E U (12) NNote that
the first component is no longer always positive and the second
component is no longer always negative.
Slide 13
Growth Makes A Difference Consider the following perpetuity:
Cash Flow = $150 Discount Rate = 0.15 Value of Perpetuity = $150 /
0.15 = $1,000 If Cash Flow growing by 0.05 (5%), we have: $150 /
(0.15 0.05) = $150 / 0.10 = $1,500 Difference is $500 of $500 /
$1,000 = 0.5 or 50%.
Slide 14
Application Using Company Data In our application, we consider
Australian Gas Light Company (AGL Co.) which is a major retailer of
gas and electricity with about three million customers. In our
application, we consider Australian Gas Light Company (AGL Co.)
which is a major retailer of gas and electricity with about three
million customers. We attempt to determine G L if the suggested
target debt- equity choice is reached and simultaneously try to
show that this can be the optimal. We attempt to determine G L if
the suggested target debt- equity choice is reached and
simultaneously try to show that this can be the optimal. To achieve
this aim we gather market data and company data from sources
including independent analysis from a firm offering audit, tax, and
advisory services (KPMG International) and a brokerage firm (State
One Stockbroking Ltd.). To achieve this aim we gather market data
and company data from sources including independent analysis from a
firm offering audit, tax, and advisory services (KPMG
International) and a brokerage firm (State One Stockbroking Ltd.).
To compute G L, we will use equation (12) which incorporates
personal taxes and constant growth To compute G L, we will use
equation (12) which incorporates personal taxes and constant growth
All monetary values will be given in Australian dollars (A$). All
monetary values will be given in Australian dollars (A$).
Slide 15
Table 1. Market and Tax Rate Data R R = Real Rate = 3.42% and R
INF = Inflation Rate = 2.17% R F = Risk-Free Rate = R R + R INF +
(R R )( R INF ) = 5.664% M PREM = Market Premium = (R M R F ) =
6.00% T C = Corporate Tax Rate = 30.00% = Imputation Tax Credit =
40.00% T E = Effective Tax Rate = T C (1) = 18.00% T E = Effective
Tax Rate = {1 T C )} / {[1 [T C (1)]} = 14.634% Average T E =
(18.00% + 14.634%) = 16.317% 16.32% Average (1 T E ) = 1 0.16317 =
0.83683 83.68% T PE = 4.77% and T PD = 20.34% = (1 T PE )(1 T C
)/(1 T PD ) 83.68% Average (1 T E ) (1 ) = 0.163181 16.32% Average
T E
Slide 16
Table 2. Cost of Capital Data Current Book D/E 1.0 D/V 0.5
& E/V 0.5 D PREM = Debt Premium = D (R M R F ) = D (M PREM ) =
1.75% D = Debt Beta = D PREM / M PREM = 1.75% / 6% 0.292 R D = Cost
of Debt = R F + D M PREM = 5.664% + 0.292(6%) 7.414% L = Leveraged
Equity Beta = 1.05 R L = Cost of Equity = R F + L M PREM = 5.664% +
1.05(6%) = 11.964% U = Unleveraged Equity Beta Using Hamada (1972)
0.74 R U = Cost of Unleveraged Equity = R F + U M PREM 10.09%
Slide 17
Debt Betas & Costs of Debt for D/V Book Choices from 0.1 to
0.9 D/V 0.100.200.300.400.500.600.700.800.90 0.29* D
0.060.120.180.230.29*0.380.470.560.65 R D
6.0%6.4%6.7%7.1%7.4%7.9%8.5%9.0%9.6% 1.05 L
0.800.860.930.991.051.111.171.422.00 R L
10.5%10.8%11.2%11.6%12.0%12.3%12.7%14.2%17.7% * * If D/V = 0 then D
= 0. If D/V = 0.5 then D 0.29; As D/V 1.0 then D U 0.74. Thus, can
interpolate from above for D s.
Slide 18
N L = Number of Shares when Leveraged with Current Book D/E is
1.0 = 456,000,000 N U = Number of Shares when Unleveraged = N L /
Current Book E/V = 456,000,000 / 0.5 = 912,000,000 C = Estimated by
Average EBITDA (2003 2006) = $905,200,000 Target D/E = Analysts
Suggested Market Target Debt-Equity Choice = 1.5 L = Estimated
Growth Rate in After-Tax Cash Flows for Target Debt-Equity Choice =
5.4% I = Interest Paid for Targeted Leveraged Situation
$493,000,000 = (1 T PE )(1 T)(C I) = (1 0.0477)(1 0.3)($905,200,000
$493,093,903)0.054 = $14,834,558 g = (1 T PE )(1 T C )(C I) L = (1
0.0477)(1 0.3)($905,200,000 $493,093,903)0.054 = $14,834,558 U = g
/ (1 T PE )(1 T C )C = $14,834,558.46 / (1 0.0477)(1
0.3)$905,200,000 2.46% E U = V U = (1 T PE )(1 T C )C/(R U u ) = (1
0.0477)(1 0.3)$905,200,000/(0.1010.0246) = $7.9 billion E U (before
personal taxes) = $7,906,124,561/(1 T PE ) = $7,906,124,561/(1
0.0477) $8.3 billion P U (per share unleveraged market price) = E U
/ N U = $8,302,136,471 / 912,000,000 $9.10 Table 3. Data Related to
Unleveraged Situation And Target Market Debt-Equity Choice
Slide 19
Table 4. Company Data Related to Market Debt-Equity Target
(Values for Market Debt-Equity Choice 1.5, which is Book Debt-Firm
Value Choice = 0.7) R = Unleveraged Shares Exchanged = (D/V)N U =
0.7(912 million) = 638.4 million shares Book D/V = Book Value
Leverage Choice Given by Shares Retired = R / N U = 638.4 / 912 =
0.7 A = Dollar Amount of E U Retired = P U (R) =
$9.10322(638,400,000) = $5,811,495,529 I (Interest Paid) = R D A =
0.084848($5,811,495,529) = $493,093,903 E L = (1 T PE )(1 T C )(C
I) /(R L L ) = (1 0.0477)(1 0.3)($905,200,000
$493,093,903)/(0.12713626-0.054) = $3,756,195,004 (1 0.0477)(1
0.3)($905,200,000 $493,093,903)/(0.12713626-0.054) = $3,756,195,004
D = (1-T PD )I / R D = (1 0.2034)$493,093,903 / 0.08484802 =
$4,629,437,339 V L = E L + D = $3,756,195,004 + $4,629,437,339 =
$8,385,632,343 Target Market D/E (On Before Personal Tax Basis) =
$4,629,437,339 (10.2034)/$3,756,195,004(10.0477) 1.5 G L = {1 [ R D
/ (R L L ) ] }D + {1 [ (R U L ) / (R L L ) ] } E U =
{1[0.837(0.085)/(0.1270.054)]}$4.63M +
{1[(0.1010.0246)/(0.1270.054)]}$7.91M = $135,068,376 + $344,439,406
= $479,507,782
Slide 20
Results for All Nine Debt Level Choices for the Application
Table 5 gives gain to leverage (G L ) results for the unleveraged
application for AGL Co. for all nine debt level choice. The
application assumes the previously mentioned data including the
betas needed to compute the costs of capital. The below conditions
are formally stated so as to include values for key variables. From
these values, we can determine values for other variables all of
which are needed to compute G L using (12). (a) debt is risky with
R D > R F = 5.6642% and R D positively related to debt (b) tax
rates are relevant with T PE = 4.77%, T PD = 20.34%, and T C = 30%
(c) perpetual before-tax cash flows: C = $905,200,000 (d) constant
growth rate when target market approximated: L = 5.4% with dollar
growth = g = $14,834,558 (e) an unleveraged firm with risky equity
faces a finite set of perpetual debt-for-equity choices with R L
> R U = 10.0907%.
Slide 21
Table 5 Application of Gain to Leverage Formulation for a Real
World Firm Assuming Risky Debt, Personal Taxes, and Constant Growth
Rate Panel A. On After Personal Tax Basis with Currency in Billions
of Australian Dollars Book 1 st 2 nd Market Book 1 st 2 nd Market
D/V R D R L ComponentComponent G L D E L V L D/E D/V R D R L
ComponentComponent G L D E L V L D/E 0.1000.0600.105 0.238-0.232
0.0060.6617.2507.9120.091 0.2000.0640.108 0.448-0.417
0.0321.3236.6157.9380.200 0.3000.0670.112 0.625-0.547
0.0781.9846.0007.9840.331 0.4000.0710.115 0.755-0.611
0.1442.6455.4058.0500.489 0.5000.0740.120 0.817-0.583
0.2343.3074.8348.1400.684 0.6000.0800.123 0.656-0.334
0.3223.9684.2608.2280.932 0.7000.0850.127 0.135 0.344
0.4804.6293.7568.3861.232 0.8000.0900.142-0.485 0.821
0.3365.2912.9518.2461.793 0.9000.0960.177-1.945 2.106
0.1615.9522.1158.0672.814
Slide 22
Table 5. Application of Gain to Leverage Formulation for a Real
World Firm Assuming Risky Debt, Personal Taxes, and Constant Dollar
Grow Panel B. On Before Personal Tax Basis with Currency in
Billions of Australian Dollars Book 1 st 2 nd Market Book 1 st 2 nd
Market D/V R D R L Component Component G L D E L V L D/E D/V R D R
L Component Component G L D E L V L D/E 0.1000.0600.105 0.386-0.244
0.1420.8307.6148.444 0.109 0.2000.0640.108 0.742-0.437
0.3051.6606.9478.6070.239 0.3000.0670.112 1.063-0.574
0.4892.4916.3008.7910.395 0.4000.0710.116 1.335-0.641
0.6943.3215.6768.9960.585 0.5000.0740.120 1.536-0.612
0.9254.1515.0769.2270.818 0.6000.0800.123 1.503-0.351
1.1524.9814.4739.4541.114 0.7000.0850.127 1.092 0.362
1.4545.8813.9449.7561.473 0.8000.0900.142 0.577 0.862
1.4396.6423.0999.7412.143 0.9000.0960.177-0.821 2.211
1.3917.4722.2219.6933.364
Slide 23
Each panel has two bold-faced rows. The 1st bold-faced row is
for the current situation where book D/V = 0.5, while the 2nd
bold-faced row is for book D/V = 0.7, which is where G L is
maximized for both panels. As seen in the last column of Panel B,
it is also the row which is nearest the market target D/E of 1.5.
For this row, we get G L = $1.4537 billion on a before personal tax
basis (which is what the market sees). For this row, dividing E L
by the number of outstanding shares (N L ), we get a share price
$14.42. For example, with D/V = 0.7 (or E/V = 0.3), we have N L =
(E/V)(NU) = 0.3(912,000,000) = 273,600,000 shares giving the share
price as: P Before Personal Tax = E L / N L = $3,944,340,023 /
273,600,000 shares = $14.4164 per share $14.42. This is less than
the average market price at the time of this writing, which has
averaged $13.83 for January 2005. Thus, $14.42 can be considered a
prediction of the future price (absent effects beyond those
stemming from the increased debt) if the market target is achieved.
The prediction for the stock price at the time we begin estimating
values for our variables (February 2004) can be computed for the
1st bold-faced row where NL = 456,000,000 shares. We have: P Before
Personal Tax = E L / N L = $5,075,687,792 / 456,000,000 shares =
$11.1309 per share $11.13. This price is consistent with both the
average price of $11.06 for AGL Co. for February 2004 and also for
the average price of $11.29 for the year of the 2003 annual report
(7/1/03 to 6/30/04).
Slide 24
We can point out four shortcomings of our application, which in
general are found in all models that rely on accurate estimates of
values for given variables. First, personal tax rates were not
directly known. This problem was ameliorated through use of an
effective tax rate and analysis of before personal tax values.
Second, we had to unleverage our firm in an attempt to estimate the
number of shares outstanding if it had no debt. The estimate
appears to be workable given that our share estimates gave
predictions for stock prices that were quite consistent with given
market prices. Third, we encountered problems when approximating
betas. For example, we had to interpolate from endpoints and a
midpoint to get reasonable D s for each debt level choice. From
there we could proceed to get U and then obtain L s for the nine
debt level choices by using a standard formula. However, unless
adjusted upward, those L computations for higher debt levels would
suggest that firms aim for extremely high leverage targets that we
do not find in the real world. This caused us to make intuitive
assignments for several leveraged equity betas. Future research
needs to explore other ways of estimating betas and costs of
capital such as suggested by Fama and French (1997) and Lally
(2004). Fourth, the application had to estimate a constant dollar
level of growth (g) based upon a chosen growth rate at the target
debt-equity choice (which was L = 5.4%). Using a software program,
like Excel, we were able to solve for g by first computing the
interest paid. Shortcomings of Application
Slide 25
Summary & Conclusion This research derives G L formulations
based on definitions for unleveraged and leveraged firm values.
Such formulations include discount rates for unleveraged equity,
leveraged equity, and debt. The inclusion of these rates makes it
possible for G L values to eventually decrease with increasing debt
levels. Three G L formulations for an unleveraged situation are
offered to aid managers (when making the debt- equity choice) and
educators (when explaining the ramifications of this choice). The
application using analysts data for AGL Co. showed how managers can
use the G L formulation with growth to estimate how issuing debt
changes firm value. While this papers model (like any model) relies
on accurate estimates of values for variables, its optimal G L did
conform to the suggested market target D/E of 1.5. Prior research
offers G L formulations difficult for practitioners. They tend to
include variables virtually immeasurable in themselves (e.g.,
bankruptcy and agency costs). As such, financial managers are hard
pressed to find utility in their application. To the extent changes
in discount rates are easier to estimate, this paper's G L
formulations offer more practical potential. This papers practical
application suggests a wealth maximizing D/E choice. The choice
depends not only on changes in discount rates but also tax and
growth rates. The applications results are consistent with prior
empirical and theoretical research in regard to the belief that
taxes, bankruptcy costs, and agency effects can determine a firms
optimal debt-equity choice. The G L formulations found in this
paper reaffirm, synthesize, and extend prior G L formulations,
while opening up a fresh vista from which to view the D/E choice
faced by managers. This vista offers a practical vantage point in
that capital structure decision-making can be based on variables
heretofore not fully utilized.