Taxation of Alternative Investment Vehicles

1
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

2
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
• taxation at lower rates is equivalent to partial
  exclusion

3
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

4
Computing the After-Tax Rate of Return

• I invested for n periods yields F after-tax
  dollars in the future
• F I(1r)n where r is the after-tax rate
  of return
• Solving for r r (F/I)(1/n) - 1

5
(No Transcript)
6
Investment Vehicle (IV) 5 - Tax Exempt Earnings

• 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 isI(1R)
  (1R)(R) I1 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?

7
IV1 - Money Market Account

• What is the after-tax accumulation of IV1?
• 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) 1.10But, the earnings
  of 10 cents are taxed.Let t represent the
  ordinary tax rate, say 30.So the after-tax
  accumulation is1(1R) - 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?

8
IV1 continued

• What is the after-tax rate of return for IV1?
• After-tax rate of return r (F/I)(1/n) - 1
  lt1gtFor IV1, F I 1 R(1 -
  t)nSubstituting this value of F into lt1gt
  yieldsr 1 R(1 - t)n(1/n) - 1r 1
  R(1 - t) - 1r R(1 - t)
• What factors influence the after-tax rate of
  return for IV1?

9
IV2 -SPDA

• What is the after-tax accumulation if we invest
  in IV2 for
• 1 year I(1 R) - R t I1 R(1 - t)Same
  as IV1!
• 2 yearsI(1R)(1R) - 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

10
Compare the After-Tax Accumulations of IV1 and IV2

• Assume R 10, t 30, I 1, n 40
• IV1 I1 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?

11
Comparison of IV1 and IV2 continued

• What is the key difference in the algebraic
  expressions for the after-tax 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?

12
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
• As long as t gttcg, IV3 will dominate IV1

13
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 I1 R(1 - tcg)n 1
  .10(1-.20)40 21.72
• What happens to this difference in accumulations
  if n decreases?

14
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 I1 r(1 - tcg)n 1
  .10(1-.20)10 2.16
• For shorter time horizons, IV3 can dominate IV2

15
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?

16
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.
• Net distribution I (1R)n (1 - t)
• Cost of contribution I (1 - t)
• Return on pension investment Distribution/Con
  tribution I (1R)n (1 - t)/I (1 - t)
  (1R)n

17
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.
• What if tax rates are not constant?Let t0 tax
  rate at time of contribution tn tax rate
  at time of distributionReturn becomes I (1R)n
  (1 - tn)/I (1 - t0) which may be more or less
  than (1R)n

18
IV6 continued

• Key Points
• Increasing tax rates Pension Return lt
  Exemption IV6 lt IV5
• Decreasing tax rates Pension Return gt
  Exemption IV6 gt IV5

19
Summary of Tax Forces in Basic Investment Vehicles
IV1 is affected by none of these tax forces, but
could be preferred when tax rates are increasing
20
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
• So the dominance relations that exist in an
  environment of constant tax rates do not hold
  true when tax rates are changing

21
Some General Conclusions continued

• 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

22
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

23
3 Types of IRAs
24
Computing the After-Tax Rate of Return

• I invested for n periods yields F after-tax
  dollars in the future
• F I(1r)n where r is the after-tax rate
  of return
• Solving for r r (F/I)(1/n) - 1

25
After-tax Rate of Return for 3 Types of IRAs

• IV5 r R
• IV6 r (1R)(1-tn)/(1-t0)(1/n) 1
• IV2 r (1R)n(1-tn) tn(1/n) 1

26
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

27
Which IRA do Investors Prefer?

• As noted last class
• If tn gt t0, IV6 lt IV5 (Roth IRA preferred to
  traditional IRA)
• If tn lt t0, IV6 gt IV5 (traditional IRA preferred
  to Roth IRA)

28
Preferences continued

• Also note that
• IV5 gt IV2, for all n and tn (Roth IRA preferred
  to nondeductible IRA)
• Implies that IV6 gt IV2 if tn lt t0 (traditional
  IRA preferred to nondeductible IRA)
• Can IV2 be gt IV6? Yes, if tn is substantially gt
  t0 (nondeductible IRA preferred to traditional
  IRA)

29
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?
• Income limits for traditional IRA and Roth IRA