5-1

Other Factors Affecting Investment Returns

Analysis in Chapter 3 assumed:• Equal before-tax returns• Homogeneous investors• Equal risk• Perfectly competitive markets• No restrictions on trade• No costs of trade

5-2

Relaxing the Assumption of Equal R – An Example

For now, ignore taxation (assume its zero). Then R = r

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?

5-3

Example continued

Calculate the rate of return on each investment• Recall: r = (F/$I)1/n –1• Investment A: r = 20%• Investment B: r = 50%

If the supply of investment B is limited, would you be willing to pay more than $1,000 for this investment? How much more?

5-4

Example continued

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

Conclusions regarding R

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)

5-6

Impact of Taxation on R – Example continued

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 RA = RB (and thus rA = rB)

• What if the return on investment A is taxed at 25% and the return on investment B is taxed at 40%?

5-7

Example continued

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%

5-8

Example continued

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? RB = 15%/(1-40%) = 25%• What is investment A’s before-tax rate of return? RA

= 15%/(1-25%) = 20%

5-9

Conclusions Regarding the Impact of Taxation on

R If taxation impacts all investments equally,

before-tax returns are unaffected 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.)

5-10

Examples of Tax-Favored Treatment

Full tax exemption (municipal bonds) Partial tax exemption (capital gains) Tax credits (research credit, low-income

housing credit) Accelerated deductions (MACRS

depreciation, research cost deduction) Deferred taxation of income

(installment sale method, gains on long-term investments)

5-11

Examples of Tax-Disfavored Treatment

Special tax assessments (excise and import taxes)

Accelerated taxation of income (pre-paid income)

Deferral of tax deductions (arbitrary 15-year amortization period for purchased intangibles even when economic life is shorter)

5-12

Implicit Taxes

Definition: reduction in before-tax rate of return to a tax-favored investment

Calculation:• Requires a benchmark asset for

comparing before-tax returns• Risk-free bond whose returns are fully

taxable each year at ordinary tax rates

5-13

Calculating Implicit Taxes

Notation:• tIa = the implicit tax rate on tax-

favored investment a• Rb = before-tax rate of return on

benchmark asset• Ra = before-tax rate of return on tax-

favored investment a• r* = competitive after-tax return to all

investments in equilibrium

5-14

Calculating Implicit Taxes continued

Note that Rb (1 – tIa) = Ra thus, tIa = (Rb – Ra)/Rb Total implicit tax on investment a = $Ia(Rb – Ra) Total explicit tax on investment a = $Ia(Ra – r*) Total tax on investment a = implicit tax + explicit

tax Total tax rate on investment a =

(Rb – Ra)/Rb + (Ra – r*)/Rb = (Rb – r*)/Rb Total explicit tax on investment b = $Ib(Rb – r*) Total tax rate on investment b = (Rb – r*)/Rb

5-15

Calculating Implicit Taxes - Example

Recall that investment B bears tax at 40% while investment A bears tax at 25%. Also recall that RA = 20%, RB = 25%, rA = rB = r* = 15%• Which investment is the benchmark

asset and which is the tax-favored asset?

5-16

Example continued

Calculate:• tIA

• 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

5-17

Tax Clienteles

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

5-18

Tax Clienteles continued

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

5-19

Tax Clienteles Example

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.

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%

5-20

Tax Clienteles Example continued

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?

5-21

Risk

Riskier assets will provide higher before-tax rates of return, to compensate the investor for the increased risk of default

Adjusting for risk requires some means to calculate the risk premium (such as CAPM)

5-22

Adjusting for Risk continued

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

5-23

Tax Arbitrage

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

5-24

Organizational Form Arbitrage

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

5-25

Organizational Form Arbitrage – A Theoretical

Example 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

5-26

Organizational Form Arbitrage – A Real

Example 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

5-27

Frictions and Restrictions on Organizational Form

Arbitrage Sec. 163(d) provides a tax deduction for

investment interest only to extent of investment income

Portion of life insurance policy is term insurance rather than savings vehicle

With market frictions, rate of earnings may be less than rate of interest on borrowing

Other limits on use of pension funds restrict their use for arbitrage

5-28

Clientele-Based Arbitrage

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

5-29

Clientele-Based Arbitrage – A Theoretical Example

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

5-30

Clientele-Based Arbitrage – A Real Example

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

5-31

Frictions and Restrictions on Clientele-Based Arbitrage

Sec. 265 provides that expenses to generate tax-exempt income are not deductible

Investment in tax-favored asset generates lower before-tax returns due to implicit taxes