Taxation and the cost of capital, Sinn (1991) kapitalkostnad

SK531 Economics of the rm, Diderik Lund, 30 August 2000
Taxation and the cost of capital, Sinn (1991)
The cost of capital (kapitalkostnad) for a limited liability
rm (a corporation) is that internal rate of return which
an investment must yield before tax in order for the rm
to give a sucient rate of return to the capital employed.
The capital can be
equity (egenkapital): The rm's shareholders must have same
rate of return after tax which they could get from an alternative
debt: The rm's creditors must have the market interest rate.
When the interest rate is given (e.g., from abroad), the cost of
capital depends on tax system. Sinn: How?
The importance of this concept:
Aects total investment in a country, since high cost of capital
implies few projects will be protable, thus more consumption,
less investment, also investment directed to other countries.
May distort composition of investments, if sectors treated differently.
May aect the debt/equity ratio of rms, thus number of bankruptcies and take-overs.
SK531 Economics of the rm, Diderik Lund, 30 August 2000
Limitations of the analysis:
Assume a given interest rate in credit market, neglect changes
in supply of credit. (Exception: Sinn, p. 33, second para.)
Neglect uncertainty, i.a. the possibility of bankruptcy.
Implies: Shareholders require same rate of return after
(personal and corporate) taxes from all projects | same
as for an investment in credit market.
A project has investment in one period, revenue in next.
Implies: Internal rate of return shows whether project
is protable or not.
Two forms of taxes: Income taxes for persons and for rms.
Neglect, e.g., wealth taxes.
Tax base for person: Income minus specic deductions, among
them net interest expenses.
Tax base for corporation: Net income (prots) after deduction
for operating costs, depreciation and net interest expenses.
Preview of problem: \Classic" tax system (e.g., in the U.S.A.) has
full double taxation of dividends: Firm's tax on prots (with no
deduction for distributed dividends), shareholder's tax on income
(including dividends). Result: High combined tax rate, high cost
of capital.
Much of economic text books and research concentrated on this,
U.S. centered. Sinn is European and more general, dierent, but
not suciently general to cover Norway.
SK531 Economics of the rm, Diderik Lund, 30 August 2000
Marginal tax rates
r = corporate tax (on retained prots)
d = corporate tax on prots distributed as dividends
dp = personal tax on distributed dividends
i = personal tax on received interest income
c = personal tax on capital gain
r and d: Usually constants (i.e., proportional taxation), but zero
in years when corporation \is out of tax position" (runs a decit).
dp; i and c: In many countries increasing with the income (i.e.,
progressive taxation). Not so in Norway after 1992 (but labor income is taxed progressively).
The return to shareholders consists of dividends and increased value
of shares (\capital gain"). Capital gains are in most countries taxed
upon realization only, not when accrued. c is present value, varies
with time until realization.
Sinn assumes dp = i (p. 28 top), valid for most OECD countries,
not Norway. Norway since 1992: dp = 0; i =0.28.
Other variables
= rate of return on marginal project
i = market rate of interest
SK531 Economics of the rm, Diderik Lund, 30 August 2000
Sinn's table of a tax system's eect on capital cost in twelve dierent
Project nanced in three alternative ways, revenue utilized in four
alternative ways:
Retained Buying back
Dividends Interest prots shares
New shares ?
irrel. ?
irrel. ?
If nancing is debt, the utilization is interest (since we consider
marginal project, with just sucient return). Thus 2 3 alternatives, plus debt.
Will consider three of these in detail, and derive the expressions:
Dividends Interest
New shares
i (1, 1)(1
, )
Retained prots i (1,1,)(1 , )
More general than Sinn, since we allow i 6= dp.
SK531 Economics of the rm, Diderik Lund, 30 August 2000
Financing: New shares. Utilization: Dividends.
Required rate of return before tax, , is determined by
(1 , d)(1 , dp) = i(1 , i)
which gives
1 , i
(1 , d)(1 , dp )
Financing: Debt. Utilization: Interest.
Project which exactly yields rate of return = i before taxes, will
not pay taxes: Interest expenses are deductible in base for corporate
income tax.
Elaboration: If > i, shareholders receive
( , i)(1 , d)(1 , dp):
Taxes reduce the surplus, but cannot change its sign from positive
to negative.
SK531 Economics of the rm, Diderik Lund, 30 August 2000
Preliminary conclusion, \old view"
Fraction (1, 1)(1
, ) clearly exceeds unity in many countries.
Debt preferred to new shares.
U.S.A.: (1,1)(1
, ) = 1, 1.85 before 1986.
For other reasons: Cannot only use debt.
Prediction from \old view": Reduction in or in will make
more investments protable.
Norge after 1992: dp = 0; d = i, taxes do not aect choice
between debt and new shares.
\New view"
Observere substantial use of internal nance, more than new
Terminology: \Internal nance" means nancing through retained earnings, one of the two sources of equity nancing. The
other is new shares.
Gross xed capital investment in the U.S.A. 1980{1985: 67.8
% internal nance, 31.0 % debt, 1.2 % new shares.
\New view" holds that corporation chooses retained earnings
instead of new shares.
SK531 Economics of the rm, Diderik Lund, 30 August 2000
Financing: Retained earnings.
Utilization: Dividends.
(Somewhat simplied compared to Sinn, p. 31:)
Corporation has prots, will pay dividends, but now or later?
(What best for shareholders?) \Later" means that prots rst
is invested in corporation, and new prots paid as dividends
one year later.
Whether now or later: Prots before taxes are multiplied with
factor (1 , d)(1 , dp ) before it reaches shareholders after taxes.
May thus neglect this when ask now or later.
With investment in corporation, dividends later: First tax on
retained earnings now, then prots , then shareholders are
taxed for capital gain. Return after tax, when (1 , d)(1 , dp )
is neglected, is (1 , c)(1 , r ).
With dividends now: Shareholder gets one year return in credit
market, and is taxed for it. Neglecting (1 , d )(1 , dp ): There
remains i(1 , i).
For marginal project these must be equal:
(1 , c)(1 , r ) = i(1 , i):
This gives:
1 , i
(1 , c)(1 , r )
SK531 Economics of the rm, Diderik Lund, 30 August 2000
Conclusions, \new view"
Cost of capital for retained prots is much closer to i than for
new shares.
Fraction (1,1,)(1 , ) may be less than unity in some countries.
Norway after 1992: c = 0 for that part of capital gain which
is already taxed, i.e., (1 , c)(1 , r ) = (1 , i), which gives
Prediction from \new view": Reduction in d or in dp will not
aect the cost of capital!
{ In spite of corporations paying dividends?
{ No, because corporations pay dividends each year.
Dierences between \old" and \new view"
\Old view": Original equity comes from outside the rm.
\New view": Most of equity comes from inside.
\Old view": Tax on dividends serious obstacle to investment.
\New view": When equity is already inside, it becomes \trapped
equity", and tax on dividends will not aect investments.
SK531 Economics of the rm, Diderik Lund, 30 August 2000
Sinn: \Another view"
Twelve eld table shows more alternatives.
Not all alternatives relevant for each company each year.
Three typical situations:
{ \Ongoing rm" has prots almost every year, pays some
dividends every year (even when no prots?).
{ \Immature rm" just started, no prots yet, cannot nance
from retained prots, will perhaps not pay dividends for
some years.
{ \Declining rm" has few new projects. Utilization of prots
is almost certainly dividends.
Financing source \retained prots" is limited in any given year.
Utilization \retained prots" is also limited in any given year,
except the rm may invest nancially. Unprotable under many
tax systems.
Conclusion: Use cheapest nancing source as long as it lasts,
then second cheapest, and so on.
Conclusion: Utilitzation (at the margin) depends on prediction
of future situation.
Separate question: Buying back of shares.
SK531 Economics of the rm, Diderik Lund, 30 August 2000
Average cost of capital?
Common to use a weighted average of several expressions from
the table.
Possible procedure: Observe that a fraction of aggregate investment is nanced from new shares, a fraction from retained
prots, and 1 , , from debt. Calculate a weigted average
from the three relevant expressions using these three weights,
+ (1 , , )75 :
i 64
(1 , d)(1 , dp) (1 , c)(1 , r )
(Could do similarly with weights for dierent utilizations.)
Objection: At the margin one particular source of nancing is
the cheapest in a particular situation. Gives the relevant cost
of capital for a new project.
(Perhaps not so clear for utilization.)
Weigted average nevertheless relevant if company has decided
to maintain a particular debt/equity ratio, implying that more
than one source of nancing is used for a new project.
SK531 Economics of the rm, Diderik Lund, 30 August 2000
More on Norwegian tax reform 1992
1969{1991: Complicated system trying to avoid double taxa-
tion of dividends.
From 1984: \Consolidation fund" (konsolideringsfond), tax exemption of retention of up to 23 percent of prots.
Main motive for reform: Same proportional tax on all types
of capital income, both corporate prots and personal capital
Domestic ows of capital should not be motivated by taxes.
r = 0.28, corporate income tax on retained prots
d = 0.28, corporate income tax on distributed prots
dp = 0, personal tax on received dividend
i = 0.28, personal tax on received interest
c = 0, personal tax on capital gains, except c = 0.28 for capital
gains not already taxed
Dividend Interest
New shares
Retained prots i
Large dierence between tax on capital income and labor income.
SK531 Economics of the rm, Diderik Lund, 30 August 2000
European system: Imputation method
Treats dividends separately from other capital income at the
hands of the shareholders. A separate deduction makes the
eective tax rate
dp = i r :
1 , r
(Sinn writes (p. 28) dp = i. Only true when he neglects the
deduction given.)
Corporation pays same tax on all prots, r = d.
Result: Cost of capital when nancing by new shares, utilization as dividend, is
1 , i
(1 , d)(1 , dp) (1 , r ) 1 , 1,,
Conclusion: Same cost of capital for new shares (with dividend
as utilization) and for debt, i.
Possible to have a higher tax on personal capital income than
on corporate prots.