Bond Definitions & Formulas PDF

DEFINITION OF TERMS IN RELATION TO BONDS MATH PRESENTATION Bond An interest-bearing security which promises to pay a stated amount of money on the maturity date, and regular interest payments called coupons. Coupon The periodic interest payment that the bondholder receives...

DEFINITION OF TERMS IN RELATION TO BONDS MATH PRESENTATION Bond An interest-bearing security which promises to pay a stated amount of money on the maturity date, and regular interest payments called coupons. Coupon The periodic interest payment that the bondholder receives during the time between purchase date and maturity date; usually received semi- annually. Coupon Rate The rate per coupon payment period; denoted by r. Price of a Bond The price of the bond at purchase time; denoted by P. Par Value or Face Value The amount payable on the maturity date; denoted by F. If P = F, the bond is purchased at par. If P < F, the bond is purchased at a discount. If P > F, the bond is purchased at premium. Term of a Bond The fixed period of time (in years) at which the bond is redeemable as stated in the bond certificate; number of years from time of purchase to maturity date. Fair Price of a Bond The present value of all cash inflows to the bondholder.  EXAMPLE Determine the amount of the semi-annual coupon for a bond with a face value of P300,000 that pays 10%, payable semi- annually for its coupons. WHAT ARE THE GIVEN? Face Value F = 300000 Coupon rate r = 10% FIND: Amount of the semi-annual coupon. SOLUTION Semi-annual coupon amount: = Face Value F(1/2) =30000(1/2) = 15000  NOTE The coupon rate is used only for computing the coupon amount, usually paid semi- annually. It is not the rate at which money grows. Instead current market conditions are reflected by the market rate, and is used to compute the present value of future payments.  ANOTHER EXAMPLE Suppose that a bond has a face value of P100,000 and its maturity date is 10 years from now. The coupon rate is 5% payable semi-annually. Find the fair price of this bond, assuming that the annual market rate is 4%. WHAT ARE THE GIVEN? Coupon rate r = 5% Payable semi-annually Face Value = 100,000 Time to maturity = 10 years Number of periods = 2(10) = 20 Market rate = 4% FIND: The fair price of this bond. SOLUTION FORMULAS IN SOLVING To find semi-annually coupon: (Face Value F)(1/2) Annually coupon: (Face Value F)(r) FORMULAS IN SOLVING To find fair price: First: P= F. (1+j)^n Second: (1+r)¹ = (1+j)^m Final: P= 1-(1+j)^-n R... j STEP FIVE USE THE MODEL TO SOLVE THE PROBLEM With the linear equation, you can now use it to make predictions or answer questions. For example, you can find the profit when 50 tickets are sold by substituting T=50 into the equation: P = 5T + 200 P = 5(50) + 200 = 250 + 200 = 450 So, if you sell 50 tickets, you can expect a total profit of $450.  YOUR TURN Your school is holding a bake sale, and you want to model the total profit ($) you can make by selling cookies. You decide to use a linear equation to represent the relationship between the number of cookies sold and the profit earned.