1. 5-1 Other Factors Affecting Investment Returns l Analysis in Chapter 3 assumed: Equal before-tax returns Homogeneous investors Equal risk Perfectly competitive markets No restrictions on trade No costs of trade

2. 5-2 Relaxing the Assumption of Equal R – An Example l For now, ignore taxation (assume its zero). Then R = r l Two investment alternatives: Investment A will have a value of $1,200 in one year Investment B will have a value of $1,500 in one year If both investments are of equal risk and require an initial cash outlay of $1,000, which investment is preferred?

3. 5-3 Example continued l Calculate the rate of return on each investment Recall: r = (F/$I) 1/n –1 Investment A: r = 20% Investment B: r = 50% l If the supply of investment B is limited, would you be willing to pay more than $1,000 for this investment? How much more?

4. 5-4 Example continued l Suppose you were willing to pay $1,200 for investment B. Now what is its rate of return? r = $1500/$1200 – 1 = 25% At this return, will you still be willing to pay more for investment B? How much more? At what investment price will B’s rate of return be 20%? 20% = $1500/I –1, i.e., I = $1,250

5. 5-5 Conclusions regarding R l Our example shows that with no taxation, equal risk, competitive markets, no trade restrictions and no non-tax costs, unequal R cannot exist in equilibrium! Investors will bid up the price of investments with higher R until it drops (or sellers will lower the price of investments with lower R until it rises)

6. 5-6 Impact of Taxation on R – Example continued l Now suppose that the return on each of these investments is taxed If both are taxed at same rate, prices will still adjust so that R A = R B (and thus r A = r B ) What if the return on investment A is taxed at 25% and the return on investment B is taxed at 40%?

7. 5-7 Example continued l What is the after-tax rate of return from each investment if price = $1,000? Investment A: Future value = $1,200 – 25%($1,200 - $1,000) = $1,150 r = 15% Investment B: Future value = $1,500 – 40%($1,500 - $1,000) = $1,300 r = 30%

8. 5-8 Example continued l What will happen to the price of investment B? At what price will the after-tax return from investment B equal the after-tax return from investment A? 15% = F/I – 1 where F = $1,500 – 40%($1,500 – I) Solving above for I yields I = $1,200, thus F = $1,380 What is investment B’s before-tax rate of return at this price? R B = 15%/(1-40%) = 25% What is investment A’s before-tax rate of return? R A = 15%/(1-25%) = 20%

9. 5-9 Conclusions Regarding the Impact of Taxation on R l If taxation impacts all investments equally, before-tax returns are unaffected l If taxation does not impact all investments equally, before-tax returns of tax-favored investments are lower than before-tax returns of tax-disfavored investments How much lower? Enough that after-tax returns are equal (given equal risk, homogeneous investors, competitive markets, etc.)

10. 5-10 Examples of Tax-Favored Treatment l Full tax exemption (municipal bonds) l Partial tax exemption (capital gains) l Tax credits (research credit, low- income housing credit) l Accelerated deductions (MACRS depreciation, research cost deduction) l Deferred taxation of income (installment sale method, gains on long-term investments)

11. 5-11 Examples of Tax- Disfavored Treatment l Special tax assessments (excise and import taxes) l Accelerated taxation of income (pre-paid income) l Deferral of tax deductions (arbitrary 15-year amortization period for purchased intangibles even when economic life is shorter)

12. 5-12 Implicit Taxes l Definition: reduction in before- tax rate of return to a tax- favored investment l Calculation: Requires a benchmark asset for comparing before-tax returns Risk-free bond whose returns are fully taxable each year at ordinary tax rates

13. 5-13 Calculating Implicit Taxes l Notation: t Ia = the implicit tax rate on tax- favored investment a R b = before-tax rate of return on benchmark asset R a = before-tax rate of return on tax-favored investment a r* = competitive after-tax return to all investments in equilibrium

14. 5-14 Calculating Implicit Taxes continued l Note that R b (1 – t Ia ) = R a thus, t Ia = (R b – R a )/R b l Total implicit tax on investment a = $I a (R b – R a ) l Total explicit tax on investment a = $I a (R a – r*) l Total tax on investment a = implicit tax + explicit tax l Total tax rate on investment a = (R b – R a )/R b + (R a – r*)/R b = (R b – r*)/R b l Total explicit tax on investment b = $I b (R b – r*) l Total tax rate on investment b = (R b – r*)/R b

15. 5-15 Calculating Implicit Taxes - Example l Recall that investment B bears tax at 40% while investment A bears tax at 25%. Also recall that R A = 20%, R B = 25%, r A = r B = r* = 15% Which investment is the benchmark asset and which is the tax-favored asset?

16. 5-16 Example continued l Calculate: t IA Total implicit tax on investment A Total explicit tax on investment A Total tax on investment A Total tax rate on investment A Total tax on investment B Total tax rate on investment B

17. 5-17 Tax Clienteles l Investor preferences for investments depend on total tax burden (implicit + explicit taxes) If investment a is tax favored, but bears implicit taxes such that the total tax burden is the same as investment b, investors are indifferent

18. 5-18 Tax Clienteles continued l If we allow tax rates to vary across investors, then the explicit taxes borne by different investors will differ, resulting in different total tax burdens Define marginal investors as those who are indifferent between two differentially taxed assets Define inframarginal investors as those who are not indifferent between two differentially taxed assets

19. 5-19 Tax Clienteles Example l Assume two equally-risky investments are available. Investment C’s before-tax return is 10%, taxable as ordinary income. Investment D’s before-tax return is 6%, tax exempt. l Assume a three-bracket tax rate structure: Income < $50,000 taxed at 25% $50,000 < Income < $75,000 taxed at 40% Income > $75,000 taxed at 50%

20. 5-20 Tax Clienteles Example continued l Calculate the after-tax rate of return from each investment for an investor in the 25% bracket, the 40% bracket, and the 50% bracket Which investor is the marginal investor? Which investors are inframarginal? Which investments do they prefer?

21. 5-21 Risk l Riskier assets will provide higher before-tax rates of return, to compensate the investor for the increased risk of default l Adjusting for risk requires some means to calculate the risk premium (such as CAPM)

22. 5-22 Adjusting for Risk continued l Implicit taxes should be calculated on risk-adjusted rates of return; otherwise cannot disentangle tax effects from risk effects Why? Because the higher before- tax return results in higher taxes, altering the tax relationships in ways unrelated to tax-favored or disfavored asset treatment

23. 5-23 Tax Arbitrage l Definition: activity that generates positive after-tax returns by buying one asset while simultaneously selling another such that the taxpayer has a zero net investment position and bears zero risk Organizational form arbitrage Clientele-based arbitrage

24. 5-24 Organizational Form Arbitrage l Involves taking a long position (purchase) in an asset through a favorably-taxed organizational form and a short position (sale) in an asset through an unfavorably-taxed organizational form

25. 5-25 Organizational Form Arbitrage – A Theoretical Example l Suppose a taxpayer wishes to shelter $100,000 of salary income from tax Borrow $1 million at 10% interest Invest $1 million in tax-exempt insurance product earning 10% IF interest expense is deductible, taxable income is reduced to zero

26. 5-26 Organizational Form Arbitrage – A Real Example l Prior to 1997, shareholders used a technique called ‘shorting against the box’ to defer taxation of stock gains while obtaining cash ‘borrow’ shares equal to the number owned, then sell the borrowed shares At later date, repay loan by delivering shares originally owned

27. 5-27 Frictions and Restrictions on Organizational Form Arbitrage l Sec. 163(d) provides a tax deduction for investment interest only to extent of investment income l Portion of life insurance policy is term insurance rather than savings vehicle l With market frictions, rate of earnings may be less than rate of interest on borrowing l Other limits on use of pension funds restrict their use for arbitrage

28. 5-28 Clientele-Based Arbitrage l Involves a high-tax-rate taxpayer taking a long position in a tax- favored asset and a short position in a tax-disfavored asset, or a low-tax-rate taxpayer taking a short position in a tax-favored asset and a long position in a tax- disfavored asset

29. 5-29 Clientele-Based Arbitrage – A Theoretical Example l Suppose a taxpayer with a 40% marginal tax rate wishes to shelter $100,000 of salary income from tax Borrow $1 million at 10% interest Invest $1 million in municipal bonds yielding 7% IF interest is deductible, taxable income is zero Taxpayer ends up with $70,000 cash flow versus $60,000 if paid tax on salary

30. 5-30 Clientele-Based Arbitrage – A Real Example l Leveraged financing of business assets Borrow money to purchase new business assets, with term of borrowing longer than MACRS recovery life of the asset Arbitrage profits require that total tax rate (implicit and explicit) inherent in purchase price of assets be less than purchaser’s explicit rate on fully-taxed income

31. 5-31 Frictions and Restrictions on Clientele-Based Arbitrage l Sec. 265 provides that expenses to generate tax- exempt income are not deductible l Investment in tax-favored asset generates lower before-tax returns due to implicit taxes