Chapter7solutions - CHAPTER 7 INTEREST RATES AND BOND...

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CHAPTER 7 INTEREST RATES AND BOND VALUATION Answers to Concepts Review and Critical Thinking Questions 1. No. As interest rates fluctuate, the value of a Treasury security will fluctuate. Long-term Treasury securities have substantial interest rate risk. 3. No. If the bid price were higher than the ask price, the implication would be that a dealer was willing to sell a bond and immediately buy it back at a higher price. How many such transactions would you like to do? 6. Bond issuers look at outstanding bonds of similar maturity and risk. The yields on such bonds are used to establish the coupon rate necessary for a particular issue to initially sell for par value. Bond issuers also simply ask potential purchasers what coupon rate would be necessary to attract them. The coupon rate is fixed and simply determines what the bond’s coupon payments will be. The required return is what investors actually demand on the issue, and it will fluctuate through time. The coupon rate and required return are equal only if the bond sells for exactly at par. 8. Companies pay to have their bonds rated simply because unrated bonds can be difficult to sell; many large investors are prohibited from investing in unrated issues. Solutions to Questions and Problems 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. 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
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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. That still leaves a lot of interest rates to check. One way to get a starting point is to use the following equation, which will give you an approximation of the YTM:
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This note was uploaded on 07/01/2010 for the course ECON 393 taught by Professor D during the Summer '10 term at Rutgers.

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Chapter7solutions - CHAPTER 7 INTEREST RATES AND BOND...

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