Other Factors Affecting Investment Returns

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

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?

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?

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 Bs rate of return
  be 20?
• 20 1500/I 1, i.e., I 1,250

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)

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?

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

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 Bs before-tax rate of return
  at this price? RB 15/(1-40) 25
• What is investment As before-tax rate of return?
  RA 15/(1-25) 20

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.)

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)

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)

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

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

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

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?

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

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

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

19
Tax Clienteles Example

• Assume two equally-risky investments are
  available. Investment Cs before-tax return is
  10, taxable as ordinary income. Investment Ds
  before-tax return is 6, tax exempt.
• Assume a three-bracket tax rate structure
• Income lt 50,000 taxed at 25
• 50,000 lt Income lt 75,000 taxed at 40
• Income gt 75,000 taxed at 50

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?

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)

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

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

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

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

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

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

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

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

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 purchasers explicit
  rate on fully-taxed income

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