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Unformatted text preview: CHAPTER 7 INTEREST RATES AND BOND VALUATION Solutions to Questions and Problems NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each problem is found without rounding during any step in the problem. Basic 1. The yield to maturity is the required rate of return on a bond expressed as a nominal annual interest rate. For noncallable bonds, the yield to maturity and required rate of return are interchangeable terms. Unlike YTM and required return, the coupon rate is not a return used as the interest rate in bond cash flow valuation, but is a fixed percentage of par over the life of the bond used to set the coupon payment amount. For the example given, the coupon rate on the bond is still 10 percent, and the YTM is 8 percent. 2. Price and yield move in opposite directions; if interest rates rise, the price of the bond will fall. This is because the fixed coupon payments determined by the fixed coupon rate are not as valuable when interest rates rise—hence, the price of the bond decreases. NOTE: Most problems do not explicitly list a par value for bonds. Even though a bond can have any par value, in general, corporate bonds in the United States will have a par value of $1,000. We will use this par value in all problems unless a different par value is explicitly stated. 3. The price of any bond is the PV of the interest payment, plus the PV of the par value. Notice this problem assumes an annual coupon. The price of the bond will be: P = $75({1 – [1/(1 + .0875)] 10 } / .0875) + $1,000[1 / (1 + .0875) 10 ] = $918.89 We would like to introduce shorthand notation here. Rather than write (or type, as the case may be) the entire equation for the PV of a lump sum, or the PVA equation, it is common to abbreviate the equations as: PVIF R,t = 1 / (1 + r) t which stands for P resent V alue I nterest F actor PVIFA R,t = ({1 – [1/(1 + r) ] t } / r ) which stands for P resent V alue Interest F actor of an A nnuity These abbreviations are short hand notation for the equations in which the interest rate and the number of periods are substituted into the equation and solved. We will use this shorthand notation in remainder of the solutions key. 4. Here we need to find the YTM of a bond. The equation for the bond price is: P = $934 = $90(PVIFA R% ,9 ) + $1,000(PVIF R %,9 ) Notice the equation cannot be solved directly for R . Using a spreadsheet, a financial calculator, or trial and error, we find: R = YTM = 10.15% If you are using trial and error to find the YTM of the bond, you might be wondering how to pick an interest rate to start the process. First, we know the YTM has to be higher than the coupon rate since the bond is a discount bond....
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This note was uploaded on 06/16/2011 for the course FIN 521 taught by Professor Varney during the Spring '11 term at Andrew Jackson.

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