Unformatted text preview: 6/26/2006 Chapter 5. Solution to Ch 05 P24 Build a Model Rework Problem 512 using a spreadsheet. After completing questions a through d, answer the new question. A 10year 12 percent semiannual coupon bond, with a par value of $1,000, may be called in 4 years at a call price of $1,060. The bond sells for $1,100. (Assume that the bond has just been issued.) Work parts a through d with a spreadsheet. You can also work these parts with a calculator to check your spreadsheet answers if you aren't confidient of your spreadsheet solution. You must then go on to work the remaining parts with the spreadsheet. a. What is the bond's yield to maturity? Basic Input Data: Years to maturity: Periods per year: Periods to maturity: Coupon rate: Par value: Periodic payment: Current price Call price: Years till callable: Periods till callable: YTM = 10.37% 10 2 20 12% $1,000 $60 $1,100 $1,060 4 8 This is a nominal rate, not the effective rate. Nominal rates are generally quoted. b. What is the bond's current yield? Current yield = Ann. Coupon $120 10.91% / / Price $1,100 c. What is the bond's capital gain or loss yield? Cap. Gain/loss yield = YTM 10.37% 0.54% Current yield 10.91% Note that this is an economic loss, not a loss for tax purposes. d. What is the bond's yield to call? Here we can again use the Rate function, but with data related to the call. YTC = This is a nominal rate, not the effective rate. Nominal rates are generally quoted. The YTC is lower than the YTM because if the bond is called, the buyer will lose the difference between the call price and the current price in just 4 years, and that loss will offset much of the interest imcome. Note too that the bond is likely to be called and replaced, hence that the YTC will probably be earned. 10.15% The YTC is lower than the YTM because if the bond is called, the buyer will lose the difference between the call price and the current price in just 4 years, and that loss will offset much of the interest imcome. Note too that the bond is likely to be called and replaced, hence that the YTC will probably be earned. NOW ANSWER THE FOLLOWING NEW QUESTIONS: e. How would the price of the bond be affected by changing interest rates? (Hint: Conduct a sensitivity analysis of price to changes in the yield to maturity, which is also the going market interest rate for the bond. Assume that the bond will be called if and only if the going rate of interest falls below the coupon rate. That is an oversimplification, but assume it anyway for purposes of this problem.) Nominal market rate, r: Value of bond if it's not called: Value of bond if it's called: 12% $1,000.00 $1,037.64 The bond would not be called unless r<coupon rate = 12%. We can use the two valuation formulas to find values under different r's, in a 2output data table, and then use an IF statement to determine which value is appropriate: Value of Bond If: Actual value, Not called Called considering $1,000.00 $1,037.64 call likehood: $2,200.00 $1,540.00 $1,540.00 $1,902.28 $1,437.99 $1,437.99 $1,654.06 $1,344.23 $1,344.23 $1,446.32 $1,257.96 $1,257.96 $1,271.81 $1,178.50 $1,178.50 $1,124.62 $1,105.24 $1,105.24 $1,000.00 $1,037.64 $1,000.00 $894.06 $975.21 $894.06 $803.64 $917.48 $803.64 $726.14 $864.07 $726.14 $659.46 $814.59 $659.46 Hint: Use function Wizard and pick IF function. Rate, r 0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20% We can graph the above data to get another idea of the bond's price sensitivity. 12% If you study the graph, you will see that the "not called" situation shows the greatest price sensitivity, the "called" the least sensitivity, and the "modified" falls somewhere in between. Actually, the modified situation, which is representative of most actual bonds because most bonds are callable, shows that bondholders will not win big if rates fall because then the bond will be called, but they do lose big if rates rise because then the bonds will not be called. In terms of the graph, the sensitivity line is not steep where we want it to be steep, to the left of the 12% coupon rate, but it is steep where we do not want it to be steep, to the right of 12%. The clear conclusion is that callable bonds are riskier than noncallable bonds, and their risk is asymmetric. If you study the graph, you will see that the "not called" situation shows the greatest price sensitivity, the "called" the least sensitivity, and the "modified" falls somewhere in between. Actually, the modified situation, which is representative of most actual bonds because most bonds are callable, shows that bondholders will not win big if rates fall because then the bond will be called, but they do lose big if rates rise because then the bonds will not be called. In terms of the graph, the sensitivity line is not steep where we want it to be steep, to the left of the 12% coupon rate, but it is steep where we do not want it to be steep, to the right of 12%. The clear conclusion is that callable bonds are riskier than noncallable bonds, and their risk is asymmetric. f. Now assume the date is 10/25/2007. Assume further that our 12%, 10year bond was issued on 7/1/2007, is callable on 7/1/2011 for $1,060, will mature on 7/1/2017, pays interest semiannually (January 1 and July 1), and sells for $1,100. Use your spreadsheet to find (a) the bond’s yield to maturity and (b) its yield to call. Refer to the Ch 09 Tool Kit for information about how to use Excel's bond valuation functions. The model finds the price of a bond, but the procedures for finding the yield are similar. Begin by setting up the input data as shown below: Basic info: Call info: Settlement (today) 10/25/2007 Same Maturity 7/1/2017 7/1/2011 True maturity for YTM, call date for YTC Coupon rate 12% Same Current price (% of par) 110 Same Redemption (% of par value) 100 106 Par for YTM, Call price for YTC Frequency (for semiannual) 2 Same Basis (360 or 365 day year) 0 Same With the input data set, put the pointer on D133 and then click fx, Financial, YIELD, OK to get the yield menu. Fill in the menu by using the pointandclick procedure, and then click OK to get the bond's yield, 10.34%: Yield to Maturity: 10.92% The completed menu is shown below. Tip: Use Yield function. For dates, either refer to cells D122 and D123, or enter the date in quotes, such as "10/25/2007". To find the yield to call, use the YIELD function, but with the call price rather than par value as the redemption Yield to call: 10.92% You could also use Excel's "Price" function to find the value of a bond between interest payment dates. ...
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This note was uploaded on 01/27/2009 for the course FI FI515 taught by Professor Fi515 during the Spring '09 term at Dominican.
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