SØK531 Economics of the firm, Diderik Lund, 6 March 2002
Taxation and the cost of capital, Sinn (1991)
Definition:
The cost of capital (kapitalkostnad) for a limited liability
firm (a corporation) is that internal rate of return which
an investment must yield before tax in order for the firm
to give a sufficient rate of return to the capital employed.
The capital can be
• equity (egenkapital): The firm’s shareholders must have same
rate of return after tax which they could get from an alternative
investment.
• debt: The firm’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:
• Affects total investment in a country, since high cost of capital
implies few projects will be profitable, thus more consumption,
less investment, also investment directed to other countries.
• May distort composition of investments, if sectors treated differently.
• May affect the debt/equity ratio of firms, thus number of bankruptcies and take-overs.
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SØK531 Economics of the firm, Diderik Lund, 6 March 2002
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 profitable or not.
• Two forms of taxes: Income taxes for persons and for firms.
Neglect, e.g., wealth taxes.
• Tax base for person: Income minus specific deductions, among
them net interest expenses.
• Tax base for corporation: Net income (profits) 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 profits (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, different, but
not sufficiently general to cover Norway.
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SØK531 Economics of the firm, Diderik Lund, 6 March 2002
Marginal tax rates
τr = corporate tax (on retained profits)
τd = corporate tax on profits distributed as dividends
τdp = personal tax on distributed dividends
τi = personal tax on received interest income
τc = personal tax on capital gain
τr and τd: Usually constants (i.e., proportional taxation), but zero
in years when corporation “is out of tax position” (runs a deficit).
τdp, τi and τc: 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. τc is present value, varies
with time until realization.
Sinn assumes τdp = τi (p. 28 top), valid for most OECD countries,
not Norway. Norway since 1992 (except 2001): τdp = 0, τi =0.28.
Other variables
π = rate of return on marginal project
i = market rate of interest
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SØK531 Economics of the firm, Diderik Lund, 6 March 2002
Sinn’s table of a tax system’s effect on capital cost in twelve different
cases:
Project financed in three alternative ways, revenue utilized in four
alternative ways:
Revenue
utilized
Financed
New shares
Retained
profits
Debt
Retained Buying back
Dividends Interest profits
shares
?
irrel.
?
?
?
irrel.
irrel.
?
?
irrel.
?
irrel.
If financing is debt, the utilization is interest (since we consider
marginal project, with just sufficient return). Thus 2 × 3 alternatives, plus debt.
Will consider three of these in detail, and derive the expressions:
New shares
Dividends
i
i (1−τ 1−τ
)(1−τ
d
Interest
dp )
i
Retained profits i (1−τ1−τ
c )(1−τr )
Debt
i
More general than Sinn, since we allow τi = τdp.
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SØK531 Economics of the firm, Diderik Lund, 6 March 2002
Financing: New shares. Utilization: Dividends.
Required rate of return before tax, π, is determined by
π(1 − τd)(1 − τdp) = i(1 − τi)
which gives
π=i
1 − τi
(1 − τd)(1 − τdp)
Financing: Debt. Utilization: Interest.
Project which exactly yields rate of return π = i before taxes, will
not pay taxes: Interest expenses are deductible in base for corporate
income tax. Cost of capital is i.
Elaboration: If π > i, shareholders receive
(π − i)(1 − τd)(1 − τdp).
Taxes reduce the surplus, but cannot change its sign from positive
to negative.
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SØK531 Economics of the firm, Diderik Lund, 6 March 2002
Preliminary conclusion, “old view”
i
clearly exceeds unity in many countries.
• Fraction (1−τ 1−τ
d )(1−τdp )
Debt preferred to new shares.
• U.S.A.:
1−τi
(1−τd )(1−τdp )
=
1
1−τd
≈ 1.85 before 1986.
• For other reasons: Cannot only use debt.
• Prediction from “old view”: Reduction in τd or in τdp will make
more investments profitable.
• Norway after 1992 (except 2001): τdp = 0, τd = τi, taxes do not
affect choice between debt and new shares.
“New view”
• Observere substantial use of internal finance, more than new
shares.
• Terminology: “Internal finance” means financing through retained earnings, one of the two sources of equity financing. The
other is new shares.
• Gross fixed capital investment in the U.S.A. 1980–1985: 67.8
% internal finance, 31.0 % debt, 1.2 % new shares.
• “New view” holds that corporation chooses retained earnings
instead of new shares.
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SØK531 Economics of the firm, Diderik Lund, 6 March 2002
Financing: Retained earnings.
Utilization: Dividends.
(Somewhat simplified compared to Sinn, p. 31:)
• Corporation has profits, will pay dividends, but now or later?
(What best for shareholders?) “Later” means that profits first
is invested in corporation, and new profits paid as dividends
one year later.
• Whether now or later: Profits before taxes are multiplied with
factor (1−τd)(1−τdp ) 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 profits π, then shareholders are
taxed for capital gain. Return after tax, when (1 − τd)(1 − τdp )
is neglected, is π(1 − τc)(1 − τr ).
• With dividends now: Shareholder gets one year return in credit
market, and is taxed for it. Neglecting (1 − τd)(1 − τdp): There
remains i(1 − τi).
• For marginal project these must be equal:
π(1 − τc)(1 − τr ) = i(1 − τi).
• This gives:
π=i
1 − τi
.
(1 − τc)(1 − τr )
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SØK531 Economics of the firm, Diderik Lund, 6 March 2002
Conclusions, “new view”
• Cost of capital for retained profits is much closer to i than for
new shares.
• Fraction
1−τi
(1−τc )(1−τr )
may be less than unity in some countries.
• Norway after 1992 (except 2001): τc = 0 for that part of capital
gain which is already taxed, i.e., (1 − τc)(1 − τr ) = (1 − τi),
which gives neutrality.
• Prediction from “new view”: Reduction in τd or in τdp will not
affect the cost of capital! (Paradox?)
– In spite of corporations paying dividends?
– No, because corporations pay dividends each year.
Differences between “old” and “new view”
• “Old view”: Original equity comes from outside the firm.
• “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 affect investments.
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SØK531 Economics of the firm, Diderik Lund, 6 March 2002
Sinn: “Another view”
• Twelve field table shows more alternatives.
• Not all alternatives relevant for each company each year.
• Three typical situations:
– “Ongoing firm” has profits almost every year, pays some
dividends every year (even when no profits?).
– “Immature firm” just started, no profits yet, cannot finance
from retained profits, will perhaps not pay dividends for
some years.
– “Declining firm” has few new projects. Utilization of profits
is almost certainly dividends.
• Financing source “retained profits” is limited in any given year.
• Utilization “retained profits” is also limited in any given year,
except the firm may invest financially. Unprofitable under many
tax systems.
• Conclusion: Use cheapest financing 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.
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SØK531 Economics of the firm, Diderik Lund, 6 March 2002
Average cost of capital?
• Common to use a weighted average of several expressions from
the table.
• Possible procedure: Observe that a fraction α of aggregate investment is financed from new shares, a fraction β from retained
profits, and 1 − α − β from debt. Calculate a weigted average
from the three relevant expressions using these three weights,


1 − τi
1 − τi
i α
+β
+ (1 − α − β) .
(1 − τd)(1 − τdp)
(1 − τc)(1 − τr )
• (Could do similarly with weights for different utilizations.)
• Objection: At the margin one particular source of financing 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 financing is used for a new project.
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SØK531 Economics of the firm, Diderik Lund, 6 March 2002
More on Norwegian tax reform 1992
• 1969–1991: Complicated system trying to avoid double taxation of dividends.
• From 1984: “Consolidation fund” (konsolideringsfond), tax exemption of retention of up to 23 percent of profits.
• Main motive for reform: Same proportional tax on all types
of capital income, both corporate profits and personal capital
income.
• Domestic flows of capital should not be motivated by taxes.
Rates:
τr = 0.28, corporate income tax on retained profits
τd = 0.28, corporate income tax on distributed profits
τdp = 0, personal tax on received dividend
τi = 0.28, personal tax on received interest
τc = 0, personal tax on capital gains, except τc = 0.28 for capital
gains not already taxed
Result:
Dividend Interest
New shares
i
Retained profits i
Debt
i
Large difference between tax on capital income and labor income.
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SØK531 Economics of the firm, Diderik Lund, 6 March 2002
European system: Imputation method
(Godtgjrelsesmetoden)
• Treats dividends separately from other capital income at the
hands of the shareholders. A separate deduction makes the
effective tax rate
τi − τ r
.
τdp =
1 − τr
• (Sinn writes (p. 28) τdp = τi. Only true when he neglects the
deduction given.)
• Corporation pays same tax on all profits, τr = τd.
• Result: Cost of capital when financing by new shares, utilization as dividend, is
i
1 − τi
1 − τi
= i
=i
τi −τr
(1 − τd)(1 − τdp)
(1 − τr ) 1 − 1−τr
• 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 profits.
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SØK531 Economics of the firm, Diderik Lund, 6 March 2002
Current Norwegian debate
• Should there be double taxation of dividends? (I.e., a classical
system, such as in the U.S.A.)
• 1969–1992: Imperfect attempt to avoid this.
• 1992–2000: Avoided double taxation.
• 2001: Double taxation introduced.
• 2002: Double taxation abolished.
• Argument for double taxation: Too low tax rates on capital
income as compared with marginal tax rates on labor income.
• Argument against: “But this is double taxation.” Not quite
clear why this is so bad. Can, e.g., argue that all income spent
domestically is taxed twice, because of value added tax on consumption.
• Better argument (in my opinion): Uniform tax on capital income would minimize distortions.
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SØK531 Economics of the firm, Diderik Lund, 6 March 2002
• Taxing dividends more than capital gains (as in 2001) leads to
less dividends paid.
• More profits retained in firms.
• Obstacle to creation of new firms, preserving instead structure
of firms, giving existing firms advantage in creation of new activity.
• Shareholders will prefer to sell some shares when/if they need
cash, instead of receiving dividends.
• Easy for shares traded on stock exchange. Disadvantage for
small and new firms.
• Inefficient to tax different forms of capital income differently.
• Alternative: Increase tax rate for all types of capital income.
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