Bonds. Describe Bonds. Define Key Words. Created 2007 By Michael Worthington Elizabeth City State University

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1 Bonds OBJECTIVES Describe bonds Define key words Explain why bond prices fluctuate Compute interest payments Calculate the price of bonds Created 2007 By Michael Worthington Elizabeth City State University Describe Bonds Bonds = debts Buy bonds = lend Issue or sell bonds = borrow money Semiannual (2 per year) interest payments Maturity = end of bond term Face Value paid at maturity to bondholders Define Key Words Face or Par Value or Maturity Value = amount paid to bondholders at end of bond s term Term = number of years until the maturity value (face value or par value) is paid to bondholders Maturity = end of the bond s term Coupon Rate or Nominal Rate = rate used to compute amount of semiannual interest payments Market Rate or Effective Rate = actual rate of interest which determines the price of the bond Discount or Premium = difference between the bond s price and its face value (or par value) 1

2 Describe relationship between bond prices and interest rates Rate Price Bond s price and effective interest rate are inversely related -- when one goes up, the other goes down -- and visa-versa Compute Semiannual Interest Divide annual nominal rate (or coupon rate) by half since payments are made twice a year Payments = face value times ½ nominal rate Nominal rate only used to compute payments Effective rate only used to compute the present value (price) of bond -- NOT payments Semiannual Payments One Year January December 1 st Payment 2 nd Payment Semiannual payments divide year in two parts So divide interest rates into two parts Example: 10% Annual Percentage Rate January December 5% for 6 months 5% for 6 months 2

3 Calculate Interest Payments 8% $10,000 Bond Multiply face value by ½ nominal rate Compute Bond Price of a bond equals: (1) present value of interest payments PLUS (2) present value of the maturity payment (face value paid at end of bond s term) effective interest of 8% Multiply face value by ½ nominal rate $100,000 x (.06 x ½ ) = $3,000 semiannual interest payments for 2 years (4 payments) 3

4 Issue Bond effective rate of 8% 1 st semiannual interest payment TIMELINE 2 nd semiannual interest payment End of 3 rd semiannual one year interest payment 4 th semiannual interest payment End of two years Maturity Payment effective interest rate of 8% January 1, 00 July 1, 00 December 31, 00 July 1, 01 December 31, 01 December 31, 01 Issue Bond $100,000 maturity payment Interest = ordinary annuity interest rate of 8% ½ of the effective rate = 4% semiannually 4 semiannual payments over two years PV of Ordinary Annuity Table N 1% 2% 3% 4% 5%

5 effective interest rate of 8% $3,000 semiannual interest payments times factor off PV of Annuity Table $10,890 Present Value of effective interest rate of 8% The face value is paid to the bondholders when the bond matures (end of term) Since this maturity payment is only paid ONCE, use PV of Sum of $1 Table to compute its Present effective interest of 8% ½ of the effective rate = 4% semiannually 4 semiannual payments over two years N % PV of Sum of $1 2% 3% 4% %

6 effective interest of 8% $100,000 Maturity Value times.855 factor off PV of $1 Table $85,500 Present Value of Maturity Payment effective rate of 8% $10,890 Present Value of Interest Payments Plus $85,500 Present Value of Maturity Payment $96,390 Price (Present Value of Bond) Interest rate ROSE from 6% nominal rate to 8% effective rate, so the price FELL from $100,000 to $96, rates and prices move opposite directions SUMMARY Interest Payments = face value x ½ nominal rate Compute present value using ½ effective rate and twice the term (2 payments per year) Calculate present value of interest payments using PV of Ordinary Annuity Table Calculate present value of maturity value using PV of $1 Table PV of Interest Payments + PV of Maturity Value equals the bond price Bond prices and interest rates move in opposite directions -- when rates go up, prices go down, and visa versa 6