Problem sets Recitation most questions will be covered 1 question required 2 pick 1 question you make up Ch 4 Wednesday January 29 2014 11 01 AM 1 2 Outline a b c d e Present Discounted Value Bonds Yield to Maturity Mortgages Yield vs Return Comparing income streams a Today vs future 1000 i Inflation 1 2 ii Investment Depreciates purchasing power over time Rate percentage rate in prices 1 2 Interest from investing now Compensation for delaying gratification 3 Present Discounted Value a b c d n number of periods in the future PV today s present value in today s dollars CF future cash flow in future dollars i interest rate nominal r e i Always assume nominal interest rate e CF PV 1 i n i ii Future Value Present Value 1 i n Example 1 2 1000 today if i 5 what will you have in 7 years X 1000 1 05 7 f PV CF 1 i n i ii Present value of a future value Example 1 2 Interest rate or yield to maturity 4 Expect 1000 two years from now if i 3 then what is it worth today X2 1000 1 03 2 THE interest rate that equates the present value of cash glow payments associated with a debt instrument with its value today Discounting Just the interest rate that you associate with the present value of cash flows b Classical Theory of asset pricing Equate the value of an asset today with the present value of the future income benefit stream generated by the asset 5 Application of PDV Fixed Payment Loans Mortgages a Mortgage is a loan for buying a house a YTM i ii iii i i b Components i fp fixed payment 1 2 Dollar amount per period is the same Includes effectively the principal interest rate a b ii iii i interest rate on mortgage n maturity date on the loan 6 Examples Mortgage Rates and House Prices 7 Mortgage Types a b c a b Costs 1mm Down payment 10 100 000 Pay 50 000 a year Traditional fixed rate 30 years Interest rate is fixed Adjustable Rate Mortgage ARM i i ii Rate is fixed for some time and then flexible 7 1 ARM for 7 years its fixed then resets every 1 year 8 Bonds a b c d Maturity Date n Face Value F Coupon Payment C Coupon rate c i Price P e c 100 x C F 9 Bond Types a Coupon Bond i Most common M B lecture notes Conflict Page 1 Today 1000 Today 1000 Inflation 7 1 year later 1000 1 07 1070 5 yrs later 1000 1 07 5 Value today PV discounted value of all income streams a b THE interest rate that equates the PV of cash flow payments associated with a debt instrument with its value today Coupon Bond i Price P e c 100 x C F 9 Bond Types a Coupon Bond i ii iii iv Most common Coupon payment 0 Maturity date known Price can be greater or less than face value b Discount bond zero coupon bond No coupon payments Price face value Less given now for more later i ii iii c Consol annuity i ii No maturity date P C i d Inflation Indexed Bonds TIPS in US i ii iii All info on bond is in real terms Nominal coupon payments C indexed to inflation Face value indexed to inflation 10 Interest Rate or Yield to Maturity i Coupon payment 1 2 Always derived from the face value A percentage of the face value 11 YTM as bond price changes As P i a 12 Bond Price and YTM a Relationship between P and I i Negative relationship b c When P F i c When P F i c i When P F i c 13 Coupon Bonds Summary a b Bond is a debt instrument so a way of borrowing Unchanging info i ii iii Coupon payment C or coupon rate c C F Face Value always 1000 Maturity date c What changes i ii Price of the bond P Yield i 14 Discount Bond zero coupon bond a When n 1 i ii P F 1 i i F P P P F 1 i n b When n 1 c i Summary i ii 15 Consol a b Y 1 x x 2 Sum of infinite series Consider i If x 1 i If x 1 i Then sum is infinite c d e Consol Bonds i No end date to a bond Then sum converges to 1 1 x ii iii 1 Simplifies to P C i Or i C P a Yield on Consol approx to coupon bond When maturity 20 years or more Price of coupon bond is close to face value 1 2 Price is almost always less than face value US treasury Bills in US maturity date of one year or less M B lecture notes Conflict Page 2 Ch 4 Expanded Saturday February 15 2014 3 10 PM 1 Principal a Amount of funds 2 Maturity date a Date to be repaid 3 Present Discounted Value a b For the nth year Credit Market Instruments 4 a Simple loan i Interest rate equals yield to maturity Fixed payment loan fully amortized loan b i ii Principal interest every set time period YTM 1 Make today s present value of the loan equal to sum of PV s of cash flows 3 4 Loan value fixed payments n are known Find i c Coupon Bond Pay fixed interest payment Final face value is paid at end Coupon rate of face value that is paid each period 2 i ii iii iv 1 YTM 1 2 Find i v Facts about the YTM 1 When P FV YTM coupon rate a i c 2 3 P and YTM are negatively related YTM c when FV P i c Consol or Perpetuity a d i ii No maturity date No repayment of principal iii e Discount bond i Face value repaid at maturity M B lecture notes Conflict Page 3 i ii Yield to Maturity 5 Face value repaid at maturity Use discounting present value formula a Interest rate that equates PV of all cash flows to today 6 Current yield 7 Rate of Return Coupon payment purchase price FV P For any security payments to owner plus change in is value expressed as a fraction of its purchase price i Coupon Price b Does not necessarily equal YTM i ii Return from holding bond from t to t 1 Current yield i rate of capital gain iv Alternative way to calculate 1 2 Calculate all future values to last year pulling the reinvested coupon payments Set that equal to starting a b a c a b iii 3 8 Annualized Holding Period Return 9 Facts about Bonds a b If time to maturity holding period return initial YTM Etc Interest Rate Risk 10 a Prices and returns for long term bonds M B lecture notes Conflict Page 4 Ch 5 Saturday February 15 2014 5 20 PM 1 …