IntroductionAssets 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
Università Bocconi, A.A: 2005-2006
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
Università Bocconi, A.A: 2005-2006
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
Università Bocconi, A.A: 2005-2006
Immediately
On accrual
Other
Tax rate
Tax rate
Tax rate
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:
- 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)
Università Bocconi, A.A: 2005-2006
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 n years = [1 + R (1-t)]n
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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: $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%
0
2
4
6
8
10
12
0
10
20
30
40
Years
*
After-tax accumulations to savings vehicles I and II: R = 15%, t=30%
0
20
40
60
80
100
120
140
160
180
200
0
10
20
30
40
Years
MMA
Examples: mutual funds
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Examples: shares in corporations located in tax haven;
After n years = $K (1+R) n - $K [(1+R) n -1]tg
= $K (1+R)n (1-tg) + $K tg
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The government act as a partner in the investment
Partners Investment Accumulation
Taxpayer 1-t (1-t) (1+R)n
Government t 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)
Tax rate
I
No
Annually
Ordinary
II
No
Deferred
Ordinary
III
No
Annually
V
No
Never
Exempt
Assets with differentially taxed components
Università Bocconi, A.A: 2005-2006
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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Partners Investment Accumulation
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After tax accumulation per after tax dollar invested
If tax rates are falling, (t0 > tn) Vehicle VI is superior
If tax rates are increasing, (t0 > tn) Vehicle V is superior
Università Bocconi, A.A: 2005-2006
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
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
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
Università Bocconi, A.A: 2005-2006
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 =
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V (1+R)n tn – V t0 [(1+R)n (1-tn) + tn]
Greater than zero if t0 = tn
t0 < tn
Assets with differentially taxed components
Università Bocconi, A.A: 2005-2006
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
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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Accumulation with no taxes
(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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The Base to calculate the capital gains tax
First year: d(1-t)
Base after n years:
Università Bocconi, A.A: 2005-2006
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