1. 3-1 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. 3-2 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. 3-3 Notation R = before-tax rate of return r = after-tax rate of return t = tax rate on ordinary income t cg = 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. 3-4 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

5. 3-5

6. 3-6 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 is: $I[(1+R) + (1+R)(R)] = $I[1 + 2 R + R 2 ]= $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. 3-7 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) = $1.10 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?

8. 3-8 IV1 continued What is the after-tax rate of return for IV1? After-tax rate of return: r = (F/$I) (1/n) - 1 For IV1, F = $I [1 + R(1 - t)] n Substituting this value of F into yields: r = {[1 + R(1 - t)] n } (1/n) - 1 r = 1 + R(1 - t) - 1 r = R(1 - t) What factors influence the after-tax rate of return for IV1?

9. 3-9 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

10. 3-10 Compare the After-Tax Accumulations of IV1 and IV2 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?

11. 3-11 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. 3-12 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 >t cg, IV3 will dominate IV1

13. 3-13 Comparison of IV2 and IV3 Assume R = 10%, t = 30%, t cg = 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 - t cg )] n = [1 +.10(1-.20)] 40 = $21.72 What happens to this difference in accumulations if n decreases?

14. 3-14 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: $I[1 + r(1 - t cg )] n = [1 +.10(1-.20)] 10 = $2.16 For shorter time horizons, IV3 can dominate IV2

15. 3-15 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 - t cg ) + $I t cg How does IV4 compare to IV2?

16. 3-16 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 (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

17. 3-17 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 t 0 = tax rate at time of contribution t n = tax rate at time of distribution Return becomes: $I (1+R) n (1 - t n )/$I (1 - t 0 ) which may be more or less than (1+R) n

18. 3-18 IV6 continued Key Points: Increasing tax rates: Pension Return < Exemption IV6 < IV5 Decreasing tax rates: Pension Return > Exemption IV6 > IV5

19. 3-19 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. 3-20 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. 3-21 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. 3-22 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. 3-23 3 Types of IRAs

24. 3-24 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

25. 3-25 After-tax Rate of Return for 3 Types of IRAs IV5: r = R IV6: r = (1+R)[(1-t n )/(1-t 0 )] (1/n) – 1 IV2: r = [(1+R) n (1-t n ) + t n ] (1/n) – 1

26. 3-26 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, t n, and t 0 For IV2, r depends on R, n, and t n, but does not depend on t 0

27. 3-27 Which IRA do Investors Prefer? As noted last class If t n > t 0, IV6 < IV5 (Roth IRA preferred to traditional IRA) If t n IV5 (traditional IRA preferred to Roth IRA)

28. 3-28 Preferences continued Also note that IV5 > IV2, for all n and t n (Roth IRA preferred to nondeductible IRA) Implies that IV6 > IV2 if t n < t 0 (traditional IRA preferred to nondeductible IRA) Can IV2 be > IV6? Yes, if t n is substantially > t 0 (nondeductible IRA preferred to traditional IRA)

29. 3-29 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