PA974‐001PA974001Monetar y Policy & Financial Rlii Gl b li d ERegulation in a Globalized Econom yLecture 7 29 September 2010pInstructor: Menzie ChinnFall 2010Discounting the Future• A dollar paid to you one year from now is less valuable than a dollar paid to Let = .10iyou todayIn one year $100 X (1+ 0.10) = $110 In two years $110 X (1 + 0.10) = $1212or 100 X (1 + 0.10)In three years $121 X (1 + 0.10) = $1333or 100 X (1 + 0.10)In yearsn4‐2y$100 X (1 + ) niSimple Present ValueSimple Present ValuePV d ' ( ) lPV = today's (present) valueCF=future cash flow (payment)CF future cash flow (payment)= the interest rateiCFPV=nPV (1 + )i4‐3Four Types f d kof Credit Market Instruments•Simple LoanSimple Loan• Fixed Payment LoanC d•Coupon Bond• Discount BondCopyright © 2007 Pearson Addison‐Wesley. All rights reserved.4‐4Yield to MaturityYield to Maturity•The interest rate that equates theThe interest rate that equates the present value of cash flow payments received from a debt instrument withfrom a debt instrument with its value todayCopyright © 2007 Pearson Addison‐Wesley. All rights reserved.4‐5Simple Loan—Yield to MaturityPV = amount borrowed = $100$CF = cash flow in one year = $110 = number of years = 1n1$110$100 = (1 + )(1 + ) $100 = $110ii(1 + ) $100 = $110$110(1 + ) = $100ii = 0.10 = 10%For simple loans, the simple interest rate equials theild iCopyright © 2007 Pearson Addison‐Wesley. All rights reserved.4‐6yield to maturityFixed Payment Loan—ldYield to MaturityThe same cash flow payment every period throughout the life of the loanLV = loan valueFP=fixed yearly paymentFP fixed yearly payment = number of years until maturityFP FP FP FPn23FP FP FP FPLV = . . . +1 + (1 + ) (1 + ) (1 + )nii i i+++Copyright © 2007 Pearson Addison‐Wesley. All rights reserved.4‐7Coupon Bond—Yield to MaturityCoupon BondYield to MaturityUsing the same strategy used for the fixed-payment loan:P = price of coupon bondppC = yearly coupon paymentF=face value of the bondF face value of the bond = years to maturity dateCC C C Fn23CC C C FP = . . . +1+ (1+ ) (1+ ) (1+ ) (1nii i i+++ ++)niCopyright © 2007 Pearson Addison‐Wesley. All rights reserved.4‐8•When the coupon bond is priced at its face value the yield•When the coupon bond is priced at its face value, the yield to maturity equals the coupon rate• The price of a coupon bond and the yield to maturity are negatively related• The yield to maturity is greater than the coupon rate when the bond price is below its face valueCopyright © 2007 Pearson Addison‐Wesley . All rights reserved. 4‐9the bond price is below its face valueConsol or PerpetuityConsol or Perpetuity•A bond with no maturity date that does not repay principal•A bond with no maturity date that does not repay principal but pays fixed coupon payments foreverP=C/iPc C/icPc = price of the consolC=yearlyinterestpaymentC = yearlyinterestpayment ic = yield to maturity of the consolCanrewriteaboveequationasiC/PCan rewriteaboveequationasic =C/PcFor coupon bonds, this equation gives current yieldŃ tlltitifildttitCopyright © 2007 Pearson Addison‐Wesley. All rights reserved.4‐10 an easy-to-calculateapproximation ofyieldtomaturityDiscount Bond—Yield to MaturityDiscount BondYield to MaturityForanyoneyeardiscountbondForanyoneyeardiscountbondi = F - PPPF = Face value of the discount bondP=currentpriceofthediscountbondPcurrentpriceofthe discountbondThe yield to maturity equals the increaseinpriceovertheyeardividedbytheinitialpricein priceovertheyeardivided bytheinitialprice.As with a coupon bond, the yield to maturity is negativelyrelatedtothecurrentbondpriceCopyright © 2007 Pearson Addison‐Wesley. All rights reserved.4‐11 negativelyrelatedtothecurrentbondprice.Yield on a Discount BasisYield on a Discount BasisLessaccuratebutlessdifficulttocalculateLessaccuratebutlessdifficulttocalculateidb= F - PF X 360days to maturityidb= yield on a discount basisF = face value of the Treasury bill (discount bond)P = purchase price of the discount bondUses the percentage gain on the face valuehildlbiiidfdPuts the yieldon an annualbasisusing 360insteadof365daysAlways understates the yield to maturityTheunderstatementbecomesmoreseverethelongerthematurityCopyright © 2007 Pearson Addison‐Wesley. All rights reserved.4‐12 The understatementbecomesmoreseverethelongerthematurityFollowing the Financial News: BdPi d I RBond Prices and Interest RatesGovernment BondsUS TreasuriesCOUPON MATURITY PRICE/YIELDPRICE/YIELD CHANGETIMEU.S. Treasuries3-Month 0.000 12/23/2010 0.14 / .14 -0.01 / -.010 09/246-Month 0.000 03/24/2011 0.18 / .19 0.003 / .003 09/2412-Month 0.000 09/22/2011 0.24 / .25 0.003 / .003 09/242-Year 0.375 08/31/2012 99-28 / .44 -0-01½ / .025 09/243-Year 0.750 09/15/2013 100-06 / .69 -0-02+ / .026 09/245-Year 1.250 08/31/2015 99-17½ / 1.35 -0-05 / .033 09/247-Year1.875 08/31/2017 99-09½ / 1.98 -0-09 / .044 09/2410-Year 2.625 08/15/2020100-05½ / 2.60-0-15 / .054 09/2430-Year 3.875 08/15/2040 101-14 / 3.79 -1-05 / .064 09/24Bloomberg.comCOUPONMATURITYPRICE/YIELDPRICE/YIELTIMEInflation Indexed TreasuryCOUPONMATURITYPRICE/YIELDD CHANGETIME5-Year 0.500 04/15/2015 102-05 / .02 -0-12 / .082 09/2410-Year1 25007/15/2020103-31 / 83-0-29 / 09609/2410Year1.25007/15/202010331 / .83029 / .096 09/2420-Year 2.500 01/15/2029 117-09 / 1.42 -1-18 / .089 09/2430-Year 2.125 02/15/2040 110-19 / 1.67 -2-11 / .095 09/24CURRENT PREV YLDCHANGE28% EQ 1WKYLD1MOYLD6MOYLDMunicipal BondsYLDPREV YLDCHANGEYLD1 WK YLD1 MO YLD6 MO YLD2-Year 0.48% 0.47% 0.01% 0.67% 0.47% 0.35% 0.60%5-Year 1.22% 1.23% -0.01% 1.69% 1.24% 1.20% 1.49%7-Year 1.80% 1.83% -0.03% 2.50% 1.85% 1.81% 2.27%10-Year 2.53% 2.55% -0.02% 3.51% 2.51% 2.55% 3.02%15Year3 50%3 49%0 01%4 86%3 39%3 61%3 81%15-Year3.50%3.49%0.01%4.86%3.39%3.61%3.81%20-Year 3.80% 3.81% -0.01% 5.28% 3.80% 4.02% 4.09%30-Year 4.11% 4.11% 0.00% 5.71% 4.10% 4.30% 4.44%Rate of ReturnRate of ReturnThe payments to the owner plus the change in