Taxation of Alternative
Investment Vehicles

Objectives:
To understand the sensitivity of
investment performance to differences in
tax treatment across alternative
investment vehicles
 To understand how algebra can represent
tax planning ideas
 Key Point: Even if we invest in assets
with identical risk and before-tax returns,
we will get different after-tax returns
depending upon the tax treatment of the
vehicle in which we invest

3-1
Taxation of Alternative
Investment Vehicles continued

We will start with a simplified
environment, in order to illustrate
how three tax-related forces impact
after-tax accumulations and after-tax
rates of return:
deductibility of investment
 deferral of taxation of earnings
 exclusion of earnings from taxation

3-2
• taxation at lower rates is equivalent to
partial exclusion
Notation
R = before-tax rate of return
 r = after-tax rate of return
 t = tax rate on ordinary income
 tcg = tax rate on capital gains
 n = number of periods
 F = future value of the investment
(after-tax accumulation at the end of
n periods)
 $I = amount of initial investment

3-3
Computing the ‘After-Tax Rate
of Return’
$I invested for n periods yields F
after-tax dollars in the future
 F =$I(1+r)n where r is the after-tax
rate of return
 Solving for r:
r = (F/$I)(1/n) - 1

3-4
Investment
Vehicle
I. MMA
II. SPDA
III.
Mutual
Fund
IV.
Foreign
Corp.
V. Tax
exempt
VI.
3-5
Pension
Is the
Frequency
Rate at
Investthat
which
ment tax earnings
earnings
deductare taxed are taxed
ible?
No
Annually
Ordinary
After-tax
accumulation
per after-tax
dollar invested
n
$I[1+R(1-t)]
n
$I(1+R) (1-t) + t$I
No
Deferred
Ordinary
No
Annually
Capital
Gains
$I[1+R(1-tcg)]
No
Deferred (no
dividends)
Capital
Gains
n
$I(1+R) (1 -
No
Never
Exempt
tcg) + tcg$I
n
$I(1+R)
Yes
Deferred
Ordinary
n
$I(1+R)
n
Investment Vehicle (IV) 5 - Tax
Exempt Earnings




3-6
$I invested in IV5 at rate R accumulates,
after 1 period, to:
F = $I(1 + R)
If F is reinvested at the same rate R, after
2 years the total accumulation is:
$I[(1+R) + (1+R)(R)]
= $I[1 + 2 R + R2]= $I(1 + R)2
What if a dollar is invested in IV5 for
n periods?
What is the after-tax rate of return for
IV5?
IV1 - Money Market Account

What is the after-tax accumulation of IV1?


3-7
Invest $1 for one year at a before-tax return of
R, say 10%. The before-tax accumulation is:
$1(1 + R) = $1(1 +.10) = $1.10
But, the earnings of 10 cents are taxed.
Let t represent the ordinary tax rate, say 30%.
So the after-tax accumulation is:
$1(1+R) - R t = 1 + R - R t = 1 + R(1 - t)
= $1.10 - .10(30%) = 1 + .10(1-30%) = $1.07
What is the after-tax accumulation of
IV1 if we invest for n years?
IV1 continued

What is the after-tax rate of return for IV1?

After-tax rate of return: r = (F/$I)(1/n) - 1 <1>
For IV1,
F = $I [1 + R(1 - t)]n
Substituting this value of F into <1> yields:
r = {[1 + R(1 - t)]n}(1/n) - 1
r = 1 + R(1 - t) - 1
r = R(1 - t)

3-8
What factors influence the after-tax rate
of return for IV1?
IV2 -SPDA

What is the after-tax accumulation if
we invest in IV2 for:
1 year: $I(1 + R) - R t = $I[1 + R(1 - t)]
Same as IV1!
 2 years:
$I(1+R)(1+R) - $I[(1 + R)(1 + R) - 1] t
= $I(1 + R)2 - $I[(1 + R)2 - 1] t
= $I(1 + R)2 - $I(1 + R)2 t - $I t
= $I(1 + R)2 (1 - t) + $I t
 n years: $I(1 + R)n (1 - t) + $I t

3-9
Compare the After-Tax
Accumulations of IV1 and IV2




3-10
Assume R = 10%, t = 30%, $I = 1, n = 40
IV1: $I[1 + R(1 - t)]n
= [1 + .10(1-.30)]40
= $14.97
IV2: $I (1 + R)n (1 - t) + t
= $1 (1 + .10)40 (1-.30) + .30
= $31.98
Result: SPDA accumulates to more
than twice as much as the MMA over
a 40 year period. Why?
Comparison of IV1 and IV2
continued
What is the key difference in the
algebraic expressions for the aftertax accumulations of IV1 and IV2?
 Compare the after-tax rate of return
of IV1 and IV2:

IV1: r = (F/$I)(1/n) - 1
= $14.97 (1/40) - 1 = 7.00%
 IV2: r = (F/$I)(1/n) - 1 = $31.98 (1/40) - 1
= 9.05%
 What happens to this difference in the
after-tax rates of return as n increases?

3-11
IV3 – Mutual Fund

The after-tax accumulation from IV3
is similar to that of IV1, except that
taxation occurs annually at the
capital gains rate rather than the
ordinary income rate

3-12
As long as t >tcg, IV3 will dominate IV1
Comparison of IV2 and IV3
Assume R = 10%, t = 30%, tcg =
20%, $I = 1, n = 40
 IV2: $I (1 + R)n (1 - t) + $I t
= $1 (1 + .10)40 (1-.30) + .30
= $31.98
 IV3: $I[1 + R(1 - tcg)]n
= [1 + .10(1-.20)]40
= $21.72
 What happens to this difference in
accumulations if n decreases?

3-13
Comparison of IV2 and IV3
continued
What if n = 10?
 IV2: $I (1 + R)n (1 - t) + $I t
= $1 (1 + .10)10 (1-.30) + .30
= $2.12
 IV3: $I[1 + r(1 - tcg)]n
= [1 + .10(1-.20)]10
= $2.16
 For shorter time horizons, IV3 can
dominate IV2

3-14
IV4 – Foreign Stock
Investment
Our analysis here assumes no
periodic dividend payments. Such
payments would be taxed to the
recipient when received as ordinary
income.
 After-tax accumulation of IV4:
$I(1 + R)n (1 - tcg) + $I tcg
 How does IV4 compare to IV2?

3-15
IV6 - Pensions

Contributions to pension vehicles are
deductible in computing current taxable
income. Thus, each dollar invested in the
pension fund costs (1 - t) dollars after tax.
Distributions from the pension fund are
taxed (in total) when distributed.



3-16
Net distribution: $I (1+R)n (1 - t)
Cost of contribution: $I (1 - t)
Return on pension investment =
Distribution/Contribution
=$I (1+R)n (1 - t)/$I (1 - t) = (1+R)n
IV6 continued

Key Point: When tax rates are constant
(i.e., the tax rate at the time of
contribution equals the tax rate at the time
of distribution), deductibility followed by
taxation at time of distribution is
equivalent to tax exemption. In this case,
IV6 is equivalent to IV5.

3-17
What if tax rates are not constant?
Let t0 = tax rate at time of contribution
tn = tax rate at time of distribution
Return becomes: $I (1+R)n (1 - tn)/$I (1 - t0)
which may be more or less than (1+R)n
IV6 continued

Key Points:
Increasing tax rates:
Pension Return < Exemption
IV6 < IV5
 Decreasing tax rates:
Pension Return > Exemption
IV6 > IV5

3-18
Summary of Tax Forces in
Basic Investment Vehicles
Deferral
Exclusion
IV2 (SPDA)
IV5 (tax exempt)
Deductibility
IV4 (Foreign IV4 (Foreign Stock Stock)
partial exclusion)
IV6
(Pension)
3-19
IV3 (mutual fund –
partial exclusion)
IV6 (Pension)
IV1 is affected by none of these tax forces, but
could be preferred when tax rates are increasing
Some General Conclusions

Compared to an environment of
constant tax rates:
Deferral is less attractive when tax rates
are increasing
 Deferral is more attractive when tax
rates are decreasing


3-20
So the dominance relations that exist
in an environment of constant tax
rates do not hold true when tax rates
are changing
Some General Conclusions
continued

3-21
If we further relax the assumptions of
no risk and constant before-tax
returns, then we see why all of these
investment vehicles are used even
though our simplified analysis
indicates that some are strictly
preferred to others
Taxation of Alternative IRAs

Recall the three tax-related forces
that impact after-tax accumulations
and after-tax rates of return:
deductibility of investment
 deferral of taxation of earnings
 exclusion of earnings from taxation

3-22
3 Types of IRAs
Frequency Rate at
InvestInvestthat
which
ment
ment tax earnings earnings
Vehicle deductible are taxed are taxed
No
Never
Exempt
Roth IRA –
IV5
Yes
Deferred
Ordinary
Traditional
IRA – IV 6
Nondeductible
IRA – IV2
3-23
No
Deferred
Ordinary
After-tax
accumulation
$I(1+R)n
$I(1+R)n (1-tn)
(1-t0)
n
$I[(1+R) (1-tn) + tn]
Computing the ‘After-Tax Rate
of Return’
$I invested for n periods yields F
after-tax dollars in the future
 F =$I(1+r)n where r is the after-tax
rate of return
 Solving for r:
r = (F/$I)(1/n) - 1

3-24
After-tax Rate of Return for
3 Types of IRAs
3-25

IV5: r = R

IV6: r = (1+R)[(1-tn)/(1-t0)](1/n) – 1

IV2: r = [(1+R)n(1-tn) + tn](1/n) – 1
Factors Influencing r

Note that:
For IV5, r does not depend on the tax
rates or the investment horizon, but
depends only on R
 For IV6, r depends on R, n, tn, and t0
 For IV2, r depends on R, n, and tn, but
does not depend on t0

3-26
Which IRA do Investors Prefer?

As noted last class
If tn > t0, IV6 < IV5 (Roth IRA preferred
to traditional IRA)
 If tn < t0, IV6 > IV5 (traditional IRA
preferred to Roth IRA)

3-27
Preferences continued

Also note that

IV5 > IV2, for all n and tn (Roth IRA
preferred to nondeductible IRA)
• Implies that IV6 > IV2 if tn < t0 (traditional
IRA preferred to nondeductible IRA)

3-28
Can IV2 be > IV6? Yes, if tn is
substantially > t0 (nondeductible IRA
preferred to traditional IRA)
Restrictions on Choice

If the Roth IRA is always preferred to
the nondeductible IRA (and the
traditional IRA is preferred to the
nondeductible IRA if tax rates fall
after retirement) why would anyone
ever choose the nondeductible IRA?

3-29
Income limits for traditional IRA and
Roth IRA