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Chapter 5: Learning Objectives

Chapter 5: Learning Objectives

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Chapter 5: Learning Objectives

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  1. Chapter 5:Learning Objectives • What is the Interest Rate? • Different Interest Rate Measures: • from YTM to STRIPS • Nominal vs. Real Interest Rates • Interest Rates and Taxes

  2. Payment Schemes • Simple loan: one payment at maturity • Fixed payment loan: payments at fixed intervals • Coupon bond: fixed payouts & principal repayment • Discounted bonds: Treasury bill • STRIPS: Separate Trading of Registered Principal & Interest of Securities

  3. The Basic Present Value Principle $X $100 t t+1 Present Value Future Value

  4. 2006 Present Value of $100

  5. The Coupon Bond PV = [$C/(1+R)] + …+ [$C/(1+R)n] + [$FV/(1+R)n] $C $FV $C $C R R R t+n t+n-1 t t+1

  6. Bond Prices and Interest Rates

  7. Discounted Bills: The Treasury Bill R = [($FV - $PD)/$PD]X (360/90) Maturity period $PD $FV

  8. Current Yield R = $C/Pt + Pt/Pt Current Yield = one-period return + Capital gain/loss $C Pt Pt+1

  9. STRIPS Investors wanting a lump-sum payment will prefer option I I $FV Pt Pt (1 + R)n = FV $C $C $C $C II $C=% FV Investors wanting regular payments will want Option II

  10. Internal Rate of Return $NF0={$NF1/(1+R)}+ {$NF1/(1+R)2}+…+{$NFn/(1+R)n} NF1 Initial Outlay of $NF0 t=0 NFn Cash flows over n periods

  11. Nominal vs. Real Interest Rates e e e Ex ante    t+1 t+3 t+2 Ex post R R=+e R=+ Nominal Interest rate fixed

  12. Nominal Interest Rate and Inflation

  13. Real Interest Rates in Canada

  14. Inflation and Nominal Interest RatesAcross Countries: 1980-2003

  15. Financial Focus 5.2: Real Return Bonds

  16. How the Real return bond works: An Example • Reference vs Actual Date • Need to interpolate because CPI is available monthly with a lag • Purchase date: 20 JAN 2003; Selling date: 20 July 2003 (= 6 month holding period) • Reference date is: 20 April 2003 • CPI 20 July 2003= (130.1 [CPI 30/4/03] * (20/31=interpolation period) + 129.9 [CPI 31/3/03])= 130.03 • Inflation during holding period is: (130.03-126.64)/126.64=2.68%

  17. How the Real return bond works: An Example • Amounts received for a $100,000 real return bond held for 6 months: • compensation for inflation: $100,000*1.0268= $102,677.94 • Compensation for real return: $102,677.94*.02125 (1/2 of 4.25% real return) = $2181.91 • TOTAL: $102,677.94+ $2181.91 = $104,859.83

  18. Summary • Debt is like a futures contract • The “price” of debt is the “interest rate” • The PV of a stream of payments is discounted by the interest rate until the term to maturity • The key mathematical relations are: • Xt = X0 / (1+R)n • PVt = [$C/(1+R)] + … + [$C/(1+R)n)] + [$FV/(1+R)n] • R = ($FV - $PD)/ $PD X (360/90) • Rct = C/ Pt • Fisher equation: R =  + 