Smeal College of Business Taxation and Management Decisions: ACCTG 550Pennsylvania State University Professor HuddartBefore- and After-tax Returns1. Effect of Organizational Form on ReturnsTerminal AnnualizedInstrument Payoff ReturnI. Money Market Fund [1 + R(1 − t)]nR(1 − t)II. SPDA [(1 + R)n(1 − t)+t] [(1 + R)n(1 − t)+t]1/n− 1III. Mutual Fund [1 + R(1 − g)]nR(1 − g)IV. Foreign Corporation (1 + R)n(1 − g)+g [(1 + R)n(1 − g)+g]1/n− 1V. Insurance Policy (1 + R)nRVI. Pension11−t(1 + R)n(1 − t) RTable 1.R annual pre-tax returnn investment horizon in yearst tax rate on ordinary incomeg capital gains tax rateQuestions• What instrument(s) dominate?• Why would anyone own any but an undominated instrument?cSteven Huddart, 1995–2005. All rights reserved. www.smeal.psu.edu/faculty/huddartACCTG 550 Before- and After-tax Returns2. Comparing After-tax Returns2.1 Example: Pensions versus SPDA versus munisSuppose munis yield 7%. The tax rate today is t0= 30% and the taxrate in the future is 40% (i.e., t1,t2,...,tn= 40%). How does investing inmunis compare with investing in a pension and investing in a single premiumdeferred annuity when the before tax return on each of these investments is10%?n SPDA Pension((1.1)n(1 − 40%) + 40%)1n− 1(11−30%1.1n(1 − 40%))1n− 11 6.00% -5.71%2 6.11% 1.84%3 6.22% 4.49%4 6.33% 5.84%5 6.44% 6.66%10 6.94% 8.32%20 7.73% 9.16%1,000 9.94% 9.98%• At what investment horizon does the pension first dominate the taxexempt bond?• When n is very large, what do the annualized returns on the SPDA andpension tend to?• Why does the pension dominate the muni at long horizons?• Why does the pension dominate the SPDA when the investment horizonis 10 or more years?• Why does the pension not always dominate the SPDA?• Suppose that tax rates are constant over time. Then the after tax returnon pensions always dominates the return on SPDAs. Why do SPDAssurvive at all in the marketplace?Page 2Before- and After-tax Returns ACCTG 5502.2 Example: Changes in tax ratesSuppose an asset offers a pre-tax return of R = 10%. From now (year1) until year n − 1, the tax rate is 30%. In year n and after, the tax rateis 40% (i.e., t1,t2,...,tn−1= 30%, and tn= 40%). How does investing in amoney market account compare with investing in a pension when all fundsare withdrawn in year n?n Money Market PensionAfter-tax After-taxTerminal Value Annualized Terminal Value Annualized(per $ invested) Return (per $ invested) Return(1+10%(1−30%))n−1(1+10%(1−40%))1−40%1−30%(1 + 10%)n1 1.06 6.00% 0.94 -5.71%2 1.13 6.50% 1.04 1.84%3 1.21 6.67% 1.14 4.49%4 1.30 6.75% 1.25 5.84%5 1.39 6.80% 1.38 6.66%10 1.95 6.90% 2.22 8.32%20 3.83 6.95% 5.77 9.16%1,000 2.40E +29 7.00% 2.12E +41 9.98%• Why does the return on pensions in this example not differ from thereturn in the previous example?• Does the return on the money market in this example differ from thereturn that would be computed assuming the tax rates in the previoussection? Why?• Does the annualized return offered on pension investments at longhorizons depend on tax rates? If so, how?Page 3ACCTG 550 Before- and After-tax Returns2.3 Questions about TRA86TRA86 significantly lowered individual tax rates.• Were the retirement savings of your parents favorably or unfavorablyaffected by this event?• What about your own retirement contributions made in the 1987 to 1992period?2.4 Roth IRAAn interesting application of this logic to a new savings vehicle ispresented by the creation of the Roth IRA under the 1997 Taxpayer ReliefAct. Several limitations apply.1Since the vehicle is intended to encourage saving only for certainpurposes (namely first time home purchase, retirement, disability, andproviding for family members or other beneficiaries following the death ofthe Roth IRA holder) a ten percent penalty tax applies to withdrawals ofearnings from the plan that do not meet prescribed conditions. In contrastto other provisions in the tax code, Roth IRA distributions are deemed tobe contributions first.Suppose your are saving for a purpose that is not approved, i.e.,distributions of earnings from the plan will be subject to the ten percentpenalty tax. Can it still be worthwhile to save through a Roth IRA? Supposeyour marginal tax rate is t = 30% and you may invest in bonds that offer apretax return of R = 8%.1Contributions are not tax deductible. Individual and spousal contributions arecapped at $2,000 annually. Eligibility is phased out for high income individuals.Page