# Ch07sol - H7.1 Solution to Problem 7.2 7.2 Interpreting...

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H7.1. Solution to Problem 7.2. n 7.2. Interpreting Bond Yields: Suppose you buy an 8% coupon, 15-year bond today when it’s first issued. If interest rates suddenly rise to 14%, what happens to the value of your bond? Why? 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 parvalue, 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.

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H7.2. Solution to Problem 7.4 n 7.4. Bond Yields: Aragorn Co. has 10% coupon bonds on the market with nine years left to maturity. The bonds make annual payments. If the bond currently sells for S 884.50, what is its YTM? Here we need to find the YTM of a bond. The equation for the bond price is: P = £884.50 = £100(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 = 12.18% 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. That still leaves a lot of interest rates to check.
H7.3. Solution to Problem 7.4 One way to get a starting point is to use the following equation, which will give you an approximation of the YTM: Approximate YTM = [Annual interest payment + (Price difference from par / Years to maturity)] / [(Price + Par value) / 2] Solving for this problem, we get: Approximate YTM = [£100 + (£115.50 / 9)] / [(£884.50 + 1,000) / 2] = 11.97% This is not the exact YTM, but it is close, and it will give you a place to start.

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H7.4. Solution to Problem 7.5 n 7.5. Coupon Rates: Ultra Soft Diapers has bonds on the market making annual payments, with 16 years to maturity, and selling for \$870. At this price, the bonds yield 6.8%. What must the coupon rate be on Ultra’s bonds? Here we need to find the coupon rate of the bond. All we need to do is to set up the bond pricing equation and solve for the coupon payment as follows: P = \$870 = C (PVIFA6.8%,16) + \$1,000(PVIF6.8%,16) Solving for the coupon payment, we get: C = \$54.42 The coupon payment is the coupon rate times par value. Using this relationship, we get: Coupon rate = \$54.42 / \$1,000 = 5.44%
H7.5. Solution to Problem 7.6. n 7.6. Bond Prices: Severa Limited has 8% coupon bonds on the market that have 10 years left to maturity. The bonds make annual payments.

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## This note was uploaded on 04/13/2010 for the course TECHNOLOGY 032913 taught by Professor Hong during the Spring '08 term at 서울대학교.

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Ch07sol - H7.1 Solution to Problem 7.2 7.2 Interpreting...

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