Comparative public economics

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Università Bocconi A.A. 2005-2006
Comparative public economics Giampaolo Arachi
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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
Insurance policy
Pension Yes Annually 11
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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 rR(1-t)

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Vehicle INot tax deductible Taxed annually
Ordinary income

• Examples Corporate bonds, money market accounts
  offered by banks
• Returns
• After 1 year K (1R) - K(1R-1) t K K R
  KRt
• K 1R(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 (1R) - (1R-1) t 1 R
  (1-t)
• After 2 years K (1R) (1R) - K (1R) (1R)
  -1 t
• K (1R)2 - K (1R)2 t K t
• K (1R)2 (1-t) K t
• After n years K (1R) n - K (1R) n -1 t
• K (1R)n (1-t) K t

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After-tax accumulations to savings vehicles I and
II R 7, t30
12
10
8
6
After tax accumulation
4
2
0
0
10
20
30
40
Years
SV I
SV II
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After-tax accumulations to savings vehicles I and
II R 15, t30
200
180
160
140
120
100
After tax accumulation
80
60
40
20
0
0
10
20
30
40
Years
MMA
SV I
SV II
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Savings Vehicle III Not tax deductible Taxed
annually Capital gains

• Examples mutual funds
• After n years 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 K (1R) n - K (1R) n
  -1tg
• K (1R)n (1-tg) K tg

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Savings Vehicle VITax deductible Deferred
taxation Ordinary income

• The government act as a partner in the investment
• Partners Investment Accumulation
• Taxpayer 1-t (1-t)
  (1R)n
• Government t
  t (1R)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 (1R)n (1-t) K t
III No Annually Capital Gains K 1 R(1-tg) n
IV No Deferred Capital Gains K (1R)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 Investment
  Accumulation
• Taxpayer 1-t0 (1-tn) (1R)n
• Government t0 tn
  (1R)n

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Vehicle VI (Pension plans) vs Vehicle V
(Insurance policy)

• After tax accumulation per after tax dollar
  invested
• If tax rates are falling, (t0 gt tn) Vehicle VI is
  superior
• If tax rates are increasing, (t0 gt 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 (1R)n (1-tn)
• Rollover Roth accumulation V (1R)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 (1R)n (1-tn) tn
• Rollover Roth accumulation
• V (1R)n V t0 (1R)n (1-tn) tn

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Rollover into a different vehicle

• Rollover Roth accumulation Deductible IRA
• V (1R)n tn V t0 (1R)n (1-tn) tn
• Greater than zero if t0 tn
• t0 lt 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
• (1dRC)n
• Accumulation after dividend tax
• (1d(1-t)RC)n
• Accumulation after dividend and capital gains tax
• (1d(1-t)RC)n tg(1d(1-t)RC)n Base) or
• (1d(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 d(1-t)
• Second year d(1-t) (1d(1-t)RC)
• Third year d(1-t) (1d(1-t)RC)2
• Base after n years

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Dividends and capital gains
d Rc tg/tdiv After tax accumulated wealth K1000, n10
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