Transcript Introduction

Università Bocconi A.A. 2005-2006
Comparative public economics
Giampaolo Arachi
Università Bocconi, A.A: 2005-2006
Mec – Comparative public economics
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Alternative savings vehicles
Intertemporally constant rates
Changes in tax rates over time
Assets with differentially taxed components
References:
M. Scholes, M. A. Wolfson, M. Erickson, E. L. Maydew, T.
Shevlin (SWEMS), Taxes and business strategy: a
planning approach, Pearson Prentice Hall, third
edition, 2005, ch. 3
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Alternative savings vehicles
Intertemporally constant rates
Changes in tax rates over time
Assets with differentially taxed components
References:
M. Scholes, M. A. Wolfson, M. Erickson, E. L. Maydew, T.
Shevlin (SWEMS), Taxes and business strategy: a
planning approach, Pearson Prentice Hall, third
edition, 2005, ch. 3
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Different Legal Organizational Forms
There are different legal organizational forms (Alternative
Savings Vehicles) through which individuals save for
the future
– Different needs: insurance policies v. bank deposits
– Different regulations or policy aims: short and long period
Differences may be leveled out through new contractual
arrangements or financial innovation
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Four main tax attributes
Is the deposit into a savings account tax deductible?
–Immediately
–Through time (depreciation allowances)
Frequency that earnings are taxed
–On accrual
–Annually
–On realization
–Never
Tax base
–Selling or purchasing price
–Difference between selling and purchasing price
–Other
Tax rate
–Ordinary income PIT rate
–Capital Gains tax
–Schedular or exempt
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Alternative savings vehicles U.S.
Savings vehicle
(example)
Is the investment
tax deductible?
Frequency that
earnings are tax
Tax rate
Money market fund
No
Annually
Ordinary
Single premium
deferred annuity
No
Deferred
Ordinary
Mutual fund
No
Annually
Capital Gains
Foreing corporation
No
Deferred
Capital Gains
Insurance policy
No
Never
Exempt
Pension
Yes
Deferred
Ordinary
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Alternative savings vehicles U.K.
Savings vehicle
(example)
Is the investment
tax deductible?
Frequency that
earnings are tax
Tax rate
Money market fund
No
Annually
Ordinary
Single premium
deferred annuity
No
Deferred
Ordinary
Mutual fund
No
Annually
Capital Gains
Foreing corporation
No
Deferred/
Annually
Capital Gains/
Ordinary
Insurance policy
No
Never
Exempt
Pension
Yes
Deferred
Ordinary
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Alternative savings vehicles Italy
Savings vehicle
(example)
Is the investment
tax deductible?
Frequency that
earnings are tax
Tax rate
Money market fund
No
Annually
27%
Single premium
deferred annuity
No
Deferred
12.5% /
Ordinary
Mutual fund
No
On accrual
12.5%
Foreing corporation
No
Deferred
Capital Gains
Yes
Annually
11%
Insurance policy
Pension
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Comparisons
 The same underlying investment will be held in each of the
savings vehicles. As a result the before tax rates of return will
be identical in each case
 The after-tax rates of return will differ widely as the investment
returns will be taxed differently across the alternatives
Simplifying assumptions:
- Intertemporally constant tax rates
- No non-tax costs
Notation:
- R denotes the pretax rate of return
- r denotes the after-tax rate of return
- for a one-year investment in a simple interest-bearing
savings account, the after-tax rate of return is r=R(1-t)
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Vehicle I
Not tax deductible; Taxed annually; Ordinary income
Examples: Corporate bonds, money market accounts
offered by banks
Returns
After 1 year: $K (1+R) - $K(1+R-1) t = $K + $K R – $KRt
= $K [1+R(1-t)]
After 2 years = [1 + R (1-t)] [1 + R (1-t)]
After n years = [1 + R (1-t)]n
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Vehicle II
Not tax deductible; Deferred taxation; Ordinary income
Examples: Single premium deferred annuity (US)
After one year: $K (1+R) - (1+R-1) t = 1 + R (1-t)
After 2 years: $K (1+R) (1+R) - $K [(1+R) (1+R) -1] t
= $K (1+R)2 - $K (1+R)2 t + $K t
= $K (1+R)2 (1-t) + $K t
After n years:
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$K (1+R) n - $K [(1+R) n -1] t
= $K (1+R)n (1-t) + $K t
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After-tax accumulations to savings vehicles I and II: R = 7%, t=30%
12
After tax accumulation
10
8
6
4
2
0
0
10
20
30
40
Years
SV I
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SV II
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After-tax accumulations to savings vehicles I and II: R = 15%, t=30%
200
180
After tax accumulation
160
140
120
100
80
60
40
20
0
0
10
20
30
40
Years
SV
I
MMA
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SV II
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Savings Vehicle III
Not tax deductible; Taxed annually; Capital gains
Examples: mutual funds
After n years =
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$K [1+ R(1-tg)] n
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Savings Vehicle IV
Not tax deductible; Deferred taxation; Capital gains
Examples: shares in corporations located in tax haven;
After n years =
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$K (1+R) n - $K [(1+R) n -1]tg
= $K (1+R)n (1-tg) + $K tg
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Savings Vehicle VI
Tax deductible; Deferred taxation; Ordinary income
The government act as a partner in the investment
Partners
Taxpayer
Government
Investment
1-t
t
Accumulation
(1-t) (1+R)n
t (1+R)n
Each dollar invested in the pension fund costs only (1-t)
dollars after tax
After tax accumulation per after tax dollar invested =
$ K (l + R) n (l - t) = (l + R) n
(l - t)
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Summing up
Savings
vehicle
Is the
investment tax
deductible?
Frequency
that
earnings
are tax
Tax rate
After tax accumulation
per after tax dollar $ I
Invested
I
No
Annually
Ordinary
$K [1 + R (1-t)]n
II
No
Deferred
Ordinary
$K (1+R)n (1-t) + $K t
III
No
Annually
Capital
Gains
$K [1+ R(1-tg)] n
IV
No
Deferred
Capital
Gains
$K (1+R)n (1-tg) + $K tg
V
No
Never
Exempt
$K (1 + R)
n
VI
Yes
Deferred
Ordinary
$K (1 + R)
n
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Outline
Intertemporally constant rates
Changes in tax rates over time
Assets with differentially taxed components
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Changes in tax rates over time
Simplifying assumption: future tax rates are known
• Returns depends on realization strategy: realize profit when taxes
are low and losses when taxes are high
• Simple dominance relations no longer hold
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Vehicle VI (Pension plans)
t0 relevant tax rate when contributions are made
tn relevant tax rate when withdrawals are made
Partners
Taxpayer
Government
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Investment
1-t0
t0
Accumulation
(1-tn) (1+R)n
tn (1+R)n
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Vehicle VI (Pension plans) vs Vehicle V (Insurance
policy)
After tax accumulation per after tax dollar invested

1
n
(1 R) 1 - t n  (1 R) n



1- t o


 Insurance
Pension
If tax rates are falling, (t0 > tn) Vehicle VI is superior
If tax rates are increasing, (t0 > tn) Vehicle V is superior
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Rollover into a different vehicle
Traditional deductible IRA
An eligible taxpayer may contribute up to $2000 per
year. Contributions are tax deductible and earnings
in the pension account are tax deferred until the
taxpayer makes withdrawals in retirement.
Savings Vehicle VI
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Rollover into a different vehicle
Roth IRA
An eligible taxpayer may contribute up to $2000 per
year. Contributions are NOT tax deductible and
withdrawals are tax free.
Savings Vehicle V
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Rollover into a different vehicle
Since 1998 taxpayers with balances in deductible IRAs
can rollover the balance into a Roth IRA.
The amount rolled over is included in the taxapayer
taxable income in the year of the rollover
Is it the rollover profitable?
Deductible IRA accumulation = V (1+R)n (1-tn)
Rollover Roth accumulation = V (1+R)n - taxes paid at
rollover - returns lost on taxes paid
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Rollover into a different vehicle
Taxes due on rollover paid out of funds invested in
Vehicle II
taxes paid at rollover + returns lost on taxes paid
V t0 [(1+R)n (1-tn) + tn]
Rollover Roth accumulation =
V (1+R)n – V t0 [(1+R)n (1-tn) + tn]
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Rollover into a different vehicle
Rollover Roth accumulation – Deductible IRA =
V (1+R)n tn – V t0 [(1+R)n (1-tn) + tn]
Greater than zero if
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t0 = tn
t0 < tn
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Outline
Intertemporally constant rates
Changes in tax rates over time
Assets with differentially taxed components
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Assets with differentially taxed components
Shares pay dividend and deferred capital gains
Two additional issues
Two different tax rates
By reinvesting there is a change in the value of the stock
Simplifying assumptions
Dividend rate is constant and equal to d
tdiv tax rate on dividends
Return thruogh capital gains constant and equal to RC
Capital Gains are tax when share are sold at rate tg
After-tax dividends are invested in shares
Dividend are paid at the end of the year
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Assets with differentially taxed components
Accumulation with no taxes
(1+d+RC)n
Accumulation after dividend tax:
(1+d(1-t)+RC)n
Accumulation after dividend and capital gains tax
(1+d(1-t)+RC)n – tg[(1+d(1-t)+RC)n – Base) or
(1+d(1-t)+RC)n (1-tg) + tg Base
Which is the Base?
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Assets with differentially taxed components
The Base to calculate the capital gains tax
First year:
Second year:
Third year:
Base after n years:
d(1-t)
d(1-t) (1+d(1-t)+RC)
d(1-t) (1+d(1-t)+RC)2
1  d(1 t)
year 1
n
 1 d(1 t)  R 
c
year 1
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Dividends and capital gains
d
Rc
tg/tdiv
After tax accumulated
wealth
$K=1000, n=10
10%
0%
1
1967
5%
5%
1
2038
0%
10%
1
2116
10%
0%
0.5%
1967
5%
5%
0.5%
2150
0%
10%
0.5%
2355
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