Modeling Tax-Specific Yield Curve

# Modeling Tax-Specific Yield Curve - Yield Curve Modeling...

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Yield Curve Modeling Modeling The Tax-Specific Yield Curve Copyright © 1996-2006 Investment Analytics

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Copyright © 1996-2006 Investment Analytics Modeling Tax-Specific Yield Curves Slide: 2 Modeling the Tax-Specific Yield Curve ¾ The impact of taxes ¾ Implication for bond valuation ¾ Bond Efficiency ¾ Tax Arbitrage ¾ Building an After-Tax Yield Curve
Copyright © 1996-2006 Investment Analytics Modeling Tax-Specific Yield Curves Slide: 3 Tax Effects ¾ Tax effects in most bond markets ¾ Tax effects are important even for tax-exempt investors ¾ Tax effects typically create arbitrage opportunities, depending on: 9 frictions (spreads) 9 short-selling constraints 9 asymmetric tax treatment of long and short positions

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Copyright © 1996-2006 Investment Analytics Modeling Tax-Specific Yield Curves Slide: 4 Summary of Analysis Without Taxes ¾ Price = Present value for each bond 9 All bonds, all investors) ¾ Each investor prepared to hold any bond ¾ PRICE = COUPON X ANNUITY FACTOR + 100 X DISCOUNT FACTOR PC D D D D PCA F D n in i n n n + × + × + × 1 1 100
Copyright © 1996-2006 Investment Analytics Modeling Tax-Specific Yield Curves Slide: 5 The Price-Coupon Relationship with No Taxes Price Coupon (%)

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Copyright © 1996-2006 Investment Analytics Modeling Tax-Specific Yield Curves Slide: 6 The Problem of Tax Effects ¾ Investors in different tax brackets will not agree on relative value of bonds After Tax Cash Flows Coupon T = 0% T = 30% T = 60% 3% 103 102.1 101.2 9% 109 106.3 103.6 15% 115 110.5 106 V15/V3 115.0/103.0 110.5/102.1106.0/101.2 = 1.117 = 1.082 = 1.047
Copyright © 1996-2006 Investment Analytics Modeling Tax-Specific Yield Curves Slide: 7 Tax Analysis of Bonds ¾ Suppose we live a world with 3 coupon bonds All three are 1 year bonds Coupons are 3%, 9% and 15% The 1 yr. spot rate is 10% ¾ Suppose we have 3 groups of tax-payers 0%, 30% and 60% ¾ What are the bond prices? What are the post-tax cash flows? What are the post-tax yields? ¾ Use worksheet: Bonds & Taxes

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Copyright © 1996-2006 Investment Analytics Modeling Tax-Specific Yield Curves Slide: 8 Solution: Tax Analysis of Bonds ¾ BOND 123 Coupon 3% 9% 15% Price 93.64 99.09 104.55 After-tax cash flows Tax rate 0% 103.0 109.0 115.0 Tax rate 30% 102.1 106.3 110.5 Tax rate 60% 101.2 103.6 106.0 After-tax yield Tax rate 0% 10% 10% 10% Tax rate 30% 9.0% 7.3% 5.7% Tax rate 60% 8.1% 4.6% 1.4%
Copyright © 1996-2006 Investment Analytics Modeling Tax-Specific Yield Curves Slide: 9 Implications of Tax Analysis ¾ A Zero Tax Payer All the bonds offer the same yield Hence, s/he will hold any of the bonds ¾ A Tax Payer Will receive higher yield on low coupon bond Hence, will prefer a low coupon bond to high coupon bond

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Copyright © 1996-2006 Investment Analytics Modeling Tax-Specific Yield Curves Slide: 10 Efficient Bonds ¾ Bond Price > NPV of cash flows for some investors ¾ An Efficient Bond: Price = NPV ¾ Example: The 3% coupon bond is efficient For both 30% and 60% taxpayers ¾ Next Issue: What is the spot rate?
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## This document was uploaded on 11/04/2011 for the course ECON 421 at CUNY York.

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Modeling Tax-Specific Yield Curve - Yield Curve Modeling...

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