Tax Exempt Bonds
Fisher Assumptions
1. 2. 3. 4. 5. No inflation No taxes No uncertainty Two-period world No transaction costs
What’s New
• Investors have a choice of instruments • In equilibrium we determine
– A spread (a second interest rate) – Incremental gains from trade – A division of investors into clienteles
The Investor’s Choice Taxable or Tax-exempt?
Example
T = individual tax rate 34%
rT = yield on taxable securities rE = yield on tax exempt securities
8.5% 6.2%
Rule: chose the investment with the largest after tax yield
After tax returns
• Tax exempt investment rE = .062 • Taxable investment rT*(1-T) = .085(1-.34) = .056
• This investor prefers tax exempts
Buy tax exempts if
rE > rT*(1-T)
Or T > 1 – (rE / rT)
“High” tax bracket investors prefer tax exempts, “low” bracket investors prefer taxables
The “implied” tax rate
An investor is indifferent between taxable and tax exempts if his tax bracket satisfies T = 1 – (rE / rT) Given market data one can always calculate the tax bracket that satisfies this equation. This is the “implied” or “marginal” tax bracket
• This is the dividing line between “high” bracket people – who buy tax exempts – and “low” bracket people who buy taxable • In the example TI = 1 – (.062/.085) = .27
A Note on Terminology
• “Supply” and “Demand” can be confusing terms in this context
– The households who “supply” loans “demand” bonds. – The businesses that “supply” or issue bonds “demand” loans.
• To avoid confusion I talk in terms of Lenders’ Curve and Borrowers’ Curves
Constructing the Lenders’ Curve Investors in Aggregate
Constructing Lenders’ Curve
• We take rT as given • Line up potential lenders, starting with the most eager investor • We ask what is lowest return at which each investor would be willing to buy tax exempts
Example
• Tax brackets Required tax exempt return
34% .085(1-.34) = .056
28% 15%
.085(1-.28) = .0612 .085(1-.15) = .07225
• These are the “steps” of the lenders’ curve
Market Equilibrium
Borrowers’ Curve
• Because tax-exempt borrowing is cheaper, anyone allowed to issue tax-exempt debt will do so. • Thus borrowers’ curve reflects total demand for loans by state and local governments • The curve slopes down for reasons similar to those discussed for other borrowers
Equilibrium
• As before equilibrium determines
– Tax exempt yield rE* – Quantity of tax exempt bonds, QE*
• Also determines
– The marginal tax bracket TM – Who is in which clientele
Application Question
• What is the effect of an increase in the taxable interest rate, rT, on
1. the tax exempt rate, rE 2. the quantity of tax exempts issued, QE , and 3. the marginal tax bracket, TM?
Application Question
• What is the effect of a general tax cut, for example a 10% reduction in all Ti , on
1. the tax exempt rate, rE 2. the quantity of tax exempts issued, QE , and 3. the marginal tax bracket, TM?
Application Question
• Suppose the alarming state America’s infrastructure leads to massive state and local road building programs. What is the effect on:
1. the tax exempt rate, rE 2. the quantity of tax exempts issued, QE , and 3. the marginal tax bracket, TM?