NYU ECON-UA 231 - Chapter 4
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Present Discounted Valuea.Bondsb.Yield to Maturityc.Mortgagesd.Yield vs Returne.Outline1.Depreciates purchasing power over time1)Rate: percentage rate in prices2)Inflation i.Interest from investing now1)Compensation for delaying gratification 2)Investmentii.Today vs future - \$1000a.Comparing income streams2.n = number of periods in the futurea.PV = today's present value in today's dollarsb.CF = future cash flow in future dollarsc.Always assume nominal interest ratei.i= interest rate (nominal) = r+∏ed.Future Value = Present Value (1+i)^ni.1000 today, if i=5%, what will you have in 7 years1)X = 1000(1.05)^72)Example ii.CF = PV (1+i)^ne.Present value of a future valuei.Expect \$1000 two years from now, if i=3%, then what is it worth today1)X2 = 1000/(1.03)^22)Exampleii.PV = CF/(1+i)^nf.Present Discounted Value3.THE interest rate that equates the present value of cash glow payments associated with a debt instrument with its value todayi.Discountingii.Just the interest rate that you associate with the present value of cash flowsiii.YTMa.Equate the value of an asset today with the present value of the future income (benefit) stream generated by the asseti.Classical Theory of asset pricingb.Interest rate or yield to maturity4.i.Mortgage is a loan for buying a housea.Dollar amount per period is the same1)the principal a)interest rateb)Includes effectively2)fp = fixed paymenti.i=interest rate on mortgageii.n= maturity date on the loaniii.Components b.Application of PDV: Fixed Payment Loans (Mortgages)5.Costs \$1mma.Down payment: 10% \$100,000b.Pay \$50,000 a yearc.Examples: Mortgage Rates and House Prices6.Interest rate is fixedi.Traditional - fixed rate 30 yearsa.Rate is fixed for some time, and then flexiblei."7/1 ARM" for 7 years its fixed, then resets every 1 yearii.Adjustable Rate Mortgage (ARM) b.Mortgage Types7.Maturity Date (n)a.Face Value (F)b.Coupon Payment (C) c.c= 100 x C/Fi.Coupon rate (c )d.Price (P)e.Bonds8.Most commoni.Coupon Bonda.Bond Types9.Recitation - most questions will be covered•1 question required, 2 pick•1 question you make up •Problem setsToday: \$1000Ch 4Wednesday, January 29, 201411:01 AM M&B lecture notes[Conflict] Page 1c= 100 x C/Fi.Price (P)e.Most commoni.Coupon payment >0ii.Maturity date known iii.Price can be greater or less than face valueiv.Coupon Bonda.No coupon paymentsi.Price < face valueii.Less given now, for more lateriii.Discount bond (zero coupon bond)b.No maturity datei.P = C/iii.Consol (annuity)c.All info on bond is in real termsi.Nominal coupon payments (C) indexed to inflationii.Face value indexed to inflationiii.Inflation Indexed Bonds (TIPS in US)d.Bond Types9.THE interest rate that equates the PV of cash flow payments associated with a debt instrument with its value todaya.Always derived from the face value1)A percentage of the face value2)Coupon paymenti.Coupon Bondb.Interest Rate or Yield to Maturity10.As P↑ => i↓a.YTM as bond price changes11.Negative relationshipi.Relationship between P and Ia.When P = F, i=cb.When P<F, i>ci.When P>F, i<cc.Bond Price and YTM12.Bond is a debt instrument, so a way of borrowinga.Coupon payment C (or coupon rate c = C/F)i.Face Value (always 1000)ii.Maturity dateiii.Unchanging infob.Price of the bond (P)i.Yield (i) ii.What changesc.Coupon Bonds Summary13.P = F / (1+i)i.i = (F-P) /Pii.When n =1a.P = F / (1+i)^ni.When n > 1b.Price is almost always less than face valuei.US treasury Bills in US, maturity date of one year or lessii.Summaryc.Discount Bond (zero coupon bond)14.Sum of infinite series a.Y = 1 +x + x^2….i.Consider b.Then sum is infinitei.If x > 1c.Then sum converges to 1/ (1-x)i.If x< 1d.No end date to a bondi.Or i = C/Pa)Simplifies to P = C/i1)ii.When maturity = 20 years or more1)Price of coupon bond is close to face value2)Yield on Consol approx. to coupon bondiii.Consol Bondse.Consol15.Today: \$1000Inflation 7%1 year later: 1000(1+.07) = 10705 yrs later: 1000(1.07)^5Value today = PV discounted value of all income streams M&B lecture notes[Conflict] Page 2Amount of fundsa.Principal1.Date to be repaida.Maturity date2.a.For the nth yearb.Present Discounted Value3.Interest rate equals yield to maturityi.Simple loana.Principal + interest every set time periodi.Make today's present value of the loan equal to sum of PV's of cash flows1)2)Loan value, fixed payments, n are known3)Find i 4)YTMii.Fixed payment loan (fully amortized loan)b.Pay fixed interest paymenti.Final face value is paid at endii.% of face value that is paid each period1)Coupon rateiii.1)Find i 2)YTMiv.i = ca)When P = FV, YTM = coupon rate1)P and YTM are negatively related2)i > ca)YTM > c, when FV > P3)Facts about the YTMv.Coupon Bondc.No maturity datei.No repayment of principalii.iii.Consol or Perpetuity d.Face value repaid at maturity i.Discount bond e.Credit Market Instruments4.Ch 4 - ExpandedSaturday, February 15, 20143:10 PM M&B lecture notes[Conflict] Page 3Face value repaid at maturity i.Use discounting present value formulaii.Interest rate that equates PV of all cash flows to todaya.Yield to Maturity 5.Coupon payment / purchase pricea.FV / Pb.Current yield6.Coupon + ∆Price i.For any security, payments to owner plus change in is value expressed as a fraction of its purchase pricea.Does not necessarily equal YTMb.Return, from holding bond from t to t+1i.Current yield (i) + rate of capital gainii.iii.Calculate all future values to last year, pulling the reinvested coupon payments1)Set that equal to starting 2)3)Alternative way to calculateiv.c.Rate of Return7.a.b.Annualized Holding Period Return 8.If time to maturity = holding period, return = initial YTMa.Etcb.Facts about Bonds9.Prices and returns for long term bondsa.Interest Rate Risk10. M&B lecture notes[Conflict] Page 4Total resources owned, including assets1)+2)Wealthi.On one asset relative to alternative assets1)+2)Expected returnii.Degree of uncertainty associated with return1)-2)Riskiii.Ease and speed with which asset can be turned into cash1)+2)Liquidity iv.Determined bya.Asset Demand1.Easier to analyze effects from changes in expected inflationa.i.ii.Since price and the interest rate/expected return is inversely relatediii.As price falls, demand upiv.+a)Wealth1)-a)Expected interest rate2)-a)Expected inflation3)-a)Risk4)+a)Liquidity5)Shifts in the demand for bondsv.Demand curveb.Bond Market Supply and Demand2.Ch 5Saturday, February 15, 20145:20 PM M&B lecture notes[Conflict] Page 5vi.Higher price means lower interest ratea.More people want to supply bondsb.In

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NYU ECON-UA 231 - Chapter 4

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