1297279973576_Chapter6_Instructor_Notes

1297279973576_Chapter6_Instructor_Notes - CHAPTER 6: BONDS,...

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______________________________________________________________________________________ 1 CHAPTER 6: BONDS, BOND PRICES, AND THE DETERMINATION OF INTEREST RATES A. T HE B ASICS Chapter 6 shows how the work done in Chapter 4 on present values can be used to determine the prices of various kinds of bonds. Looking beyond just bonds, Chapter 6 lays the foundation for pricing a wide variety of other financial assets as well. Core Principle 1 that time has value is the key concept used in establishing prices of the various financial assets. Equation (3) on text page 127, reproduced below, uses the present value concept to illustrate the price of a coupon bond, CB P . Importantly, it can be easily modified to show the prices of zero-coupon bonds, fixed payment loans, and consols. By understanding this particular result you can learn quickly other, related results. n n 2 ) i 1 ( Value Face ) i 1 ( Payment Coupon ) i 1 ( Payment Coupon ) i 1 ( Payment Coupon P Specifically, to find the price of a zero coupon bond (also called a discount bond), simply set the coupon payments to zero: n COUPON ZERO ) i 1 ( Face P . Or, consider the price of a fixed payment loan, in which n fixed payments are made to retire the loan. Each of the fixed payments is part principal repayment and part interest payment. Accordingly, set the face value term to zero since principal repayment is directly included as part of the fixed payment, and change the terminology from “coupon payment” to “fixed payment,” obtaining n 2 PAYMENT FIXED ) i 1 ( Payment Fixed ) i 1 ( Payment ) i 1 ( Payment P Or, finally, to find the price of the consol, let the number of years, n, until return of principal grow arbitrarily large (in mathematical lingo, let n → ∞). For a given face value, this makes the denominator of the last term in the coupon bond expression arbitrarily large (pick an interest rate, even as low as 1%, and compute 1/(1+i) n using a large value of n, such 1,000 or 10,000, and see what you obtain). So, n 2 CONSOL ) i 1 ( Payment Coupon ) i 1 ( Payment Coupon ) i 1 ( Payment Coupon P
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Chapter 6: Bonds, Bond Prices, and the Determination of Interest Rates ______________________________________________________________________________________ 2 where the sum goes on forever. (You learned to evaluate this expression in the appendix to chapter 4, text pages 94-95; if you don’t remember the details, they are worth reviewing.) In addition, notice that for any of these expressions for a given value for n, 1. if you know the price of the asset and the payments, which are known when the bond or loan is issued, you can solve for the interest rate; 2. if you know the interest rate and the payments, you can find the price; and 3. the interest rate is always in the denominator, which implies that a rise in the interest rate must imply a fall in the price of the asset and vice versa.
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1297279973576_Chapter6_Instructor_Notes - CHAPTER 6: BONDS,...

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