SK531 Economics of the rm, Diderik Lund, 8 September 2000
Taxation under uncertainty, Varian
How do various tax regimes aect investment decisions when
there is uncertainty?
Two-period models only: Invest today, uncertain result next
period
Will show: Tax may lead to more investment. Paradox?
First shown by Domar and Musgrave in 1944 article
Warning: Economics literature has many dierent descriptions
of
{ investment possibilities
{ tax system
{ preferences
{ equlibrium eects
Thus many dierent results
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SK531 Economics of the rm, Diderik Lund, 8 September 2000
Portfolio choice without tax: Riskless vs. risky investment
(Varian p. 227{228, originally Arrow (1965))
One risk averse individual maximizes expected utility
A given wealth w divided between risky (x 0) and riskless
(w , x 0) investment
Risky rate of return r~ for x, only two possible outcomes, rg > rb
Pr(rg ) = No rate of return for w , x.
For consumption in second period:
V~ = w , x + x(1 + r~) = w + xr~
Let Vg w + xrg ; Vb w + xrb, and maximize
u(Vg ) + (1 , )u(Vb)
Results (independent of closer specication of u function, but assume risk aversion):
Choose corner solution x = 0 if and only if E (~r) < 0
When solution is interior (x), it is characterized by
u0(w + xrg )rg + (1 , )u0(w + xrb)rb = 0
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SK531 Economics of the rm, Diderik Lund, 8 September 2000
Portfolio choice with tax: Riskless vs. risky investment
(Varian p. 227{229, originally Domar and Musgrave (1944) and
(with expected utility) Mossin (1968))
Same model as before, but tax on rate of return, tr~.
Consumption in second period
(w , x) + x(1 + r~) , txr~ = w + x(1 , t)~r:
All of w remains untaxed. Choice consists in scaling the additional x(1 , t)~r.
First order condition for interior solution, x^:
u0(w+^x(1,t)rg )(1,t)rg +(1, )u0(w+^x(1,t)rb )(1,t)rb = 0
Simplied:
u0(w + x^(1 , t)rg )rg + (1 , )u0(w + x^(1 , t)rb )rb = 0
Result: Can show that
x
x^ =
1,t
When introduced into rst order condition,
x
x
0
0
u (w +
(1 , t)rg )rg + (1 , )u (w +
(1 , t)rb )rb = 0
1,t
1,t
this becomes identical to the rst order condition without tax
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SK531 Economics of the rm, Diderik Lund, 8 September 2000
Portfolio choice with tax: Riskless vs. risky (contd.)
x is solution without tax, independent of tax rate
x^ = x=(1 , t) is solution with tax
We then nd
x
x^
dx^
=
=
> 0:
dt (1 , t)2 1 , t
Paradox(?): Higher tax rate on risky rate of return leads to choice
of higher x, i.e., more invested in risky alternative.
Interpretation: By scaling up x by the factor 1,1 t , the same rate of
return after tax is achieved as in the model without tax:
xr~ = x^(1 , t)~r
This is exactly optimal, since it is the optimal addition to w, chosen
in both models. The choice is how to scale the risky addition to w,
and the solution is the same in both models.
More complicated if w , x has some riskless rate of return > 0,
subject to the same tax rate. Still possible that dx^=dt > 0 holds.
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SK531 Economics of the rm, Diderik Lund, 8 September 2000
Underutilization of depreciation deductions
Aarbu and MacKie-Mason
Observe an unexpected phenomenon
Review a number of (own and others') potential explanations
Translate explanations into testable hypotheses
Use very detailed data for testing
What are depreciation deductions?
Capital equipment with substantial value and durability (ex-
ceeding NOK 10 000 and three years, respectively) may not be
deducted as expenses at time of acquisition, but as depreciation
In accounting regulations: \Book" depreciation, dB
General rule: Let dB reect loss of economic value over time
Dierent rules employed: dB exponentially decreasing, or constant
General rule: Sum of dB over time equals acquisition value
In tax regulations: Tax depreciation, dT
Usually dB dT in the rst years, tax favorization of investment, but converse may occur
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SK531 Economics of the rm, Diderik Lund, 8 September 2000
Maximum present value of deductions?
Firm wants to pay minimum tax, calculated as present value
Delaying a deduction: Loss of present value
Thus: Want tax depreciation as soon as possible
But observe exceptions | why?
(Precondition: The rm has a choice)
Tax law prescribes maximum yearly percentage depreciation
(xed percentage of remaining value, saldoavskrivning)
When fully utilized: Remaining value falls exponentially
When fully utilized: Deduction falls exponentially
If less than full utilization one year: Maximum percentage next
year is the same
Thus: Underutilitation gives more than one year's delay of deduction
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SK531 Economics of the rm, Diderik Lund, 8 September 2000
Underutilization of depreciation deduction in Norway:
Data
Year
1988 1991 1992 1993
Sample size
1700 4400 4300 2400
Average percentage underutilization
10 21
8
9
Percentage of corporations underutilizing 39 44 25 20
Data from tax returns of corporations
Relative underutilization:
allowed , actual depr. deductions
actual
Similar phenomenon in Sweden and Finland
(Why not elsewhere? Depreciation deductions compulsory?)
Dierence: In Sweden and Finland mostly in large corporations,
in Norway mostly in small
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SK531 Economics of the rm, Diderik Lund, 8 September 2000
Possible explanations for underutilization
1. Higher book prots allow higher dividend distribution
2. Bank debt is preferred to tax debt because banks monitor the
corporation
3. Deducting losses carried forward is preferred to faster depreciation deductions
4. Window-dressing
5. Administrative costs of complicated accounting
Regression analysis to test these ve hypotheses
Observational unit: Norwegian corporation, sample
Left-hand side (independent) variable: Underutilization
16 regressions: Separately for each of the four years, and for
each of four size categories
Linear regression, one or more explanatory variables for each
hypothesis
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SK531 Economics of the rm, Diderik Lund, 8 September 2000
Notation:
= operating surplus (= revenues , operating cost)
rB = net interest expenses
T = corporate income tax
I = investment (expenses on capital equipment)
F = increase in consolidation fund
R = increase in reserve fund
= increase in free equity
D = dividend
Three types of surplus after tax:
Cash surplus:
Book prots:
, rB , T , I
, rB , T , dB
Taxable prots, minus taxes:
, rB , T , dT = D + R + F + (Equation (5) in Aarbu and MacKie-Mason)
Book prots can be increased by lowering dB , may imply lower
dT
(If = 0:) Lower dT allows higher D
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SK531 Economics of the rm, Diderik Lund, 8 September 2000
Increased book and/or taxable prots allows increased
dividends
Presumes the rm is willing to pay something (higher present
value of taxes) to increase dividends, cf. Bernheim and Wantz
Firm may have cash available for dividends without corresponding book prots
Dividends limited by book or taxable prots
Hypothesis: When equation (5) is a binding limitation: Higher
tendency to underutilize depreciation
Limitation disappears with 1992 tax reform
Explanatory variable: Dummy = 1 when = 0
Expect positive coecient for 1988 and 1991
Result: No clear support for the hypothesis
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SK531 Economics of the rm, Diderik Lund, 8 September 2000
Bank debt preferred to interest free tax debt because
banks monitor the rm
Higher depreciation now implies deferred tax, a kind of interest
free debt
This may explain underutilization: The alternative, interest
carrying debt, gives some advantages
Advantage (for shareholders): Banks monitor the rm
Observable variables: (i) Increase in long term bank debt (ii)
Accumulated interest free debt (deferred taxes)
Hypothesis: Lower tendency to underutilize if rm simultaneously increases its long term debt (| printing error in table 2,
see instead section 5.3)
Hypothesis: Higher tendency to underutilize if rm has previously accumulated much interest free debt
Result: No clear support for any of the hypotheses
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SK531 Economics of the rm, Diderik Lund, 8 September 2000
Carry-forward of losses preferred to depreciation
Equation (5): Neglects carry-forward of losses
If rm had negative taxable prots previous year: Carry-forward
of loss to this year, deductible in taxable prots
May be accumulated: If also loss this year (after deduction for
previous year's loss): Carry forward one more year
Limitation: No more than ten years carry-forward
When negative taxable prots this year, and carry-forward from
previous years: Trade-o between using full depreciation and
deduction of loss carried forward
If only present value of tax payments counts:
{ Use maximum depreciation if no danger for hitting ten-year
limitation
{ Use less than maximum depreciation if high probability for
hitting ten-year limitation
Observe dummy variable: Is rm in tax position (i.e., is taxable
prots strictly positive after all claimed deductions)?
Hypothesis: Higher tendency for underutilization when rm is
in tax position
Result: Clearly signicant in all 16 regressions
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SK531 Economics of the rm, Diderik Lund, 8 September 2000
Window-dressing
Outsiders, both creditors and the stock market, have limited
capacity to monitor rm
May therefore emphasize accounting numbers, even when these
do not reect economic result
May emphasize positive prots, even if rm loses in the long
run from underutilization of depreciation deductions
Observable variables: (i) After-tax prots as if full depreciation
were claimed, (ii) Financial strength (indebtedness, etc.)
Hypothesis: Lower tendency for underutilization when high values for each of these variables
Result: Conrmed, in particular for (i)
After 1992 reform much of eect disappears for large rms
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SK531 Economics of the rm, Diderik Lund, 8 September 2000
Administrative costs of complicated book-keeping
Simpler to have dT = dB , but rules allow dT > dB the rst
years
Observable variable: Accumulated dierence previous year, dummy
= 1 when accumulated dierence is zero
Hypothesis: Higher tendency for underutilization (i.e., setting
dT = dB ) if dierence is zero
Result: Conrmed, in particular for small rms
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SK531 Economics of the rm, Diderik Lund, 8 September 2000
Summing up the results
These hypotheses are conrmed:
Deduction of losses carried forward is preferred to depreciation
Window-dressing
Administrative costs of complicated book-keeping
These hypotheses are not conrmed:
Increased book and/or taxable prots allow increased dividends
Bank debt is preferred to taxable debt because banks monitor
the rm
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SK531 Economics of the rm, Diderik Lund, 8 September 2000
Econometric method
Estimating linear equations
Hypothesis: Linear function of explanatory variables, plus nor-
mally distributed error term, gives the desired underutilization
Problem: Underutilitzation limited above by the maximum allowed depreciation, and below by zero, but right-hand side of
regression will have values outside this range
Solution: Assume right-hand side (linear function pluss error
term) gives the rm's desired underutilization
But: When desired underutilization is outside allowed range,
the actual will be just inside, i.e., maximum or zero, respectively
Need separate estimation method
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