Use the following information for your bond: 11% coupon, Starting YTM of 11%, an

Question

Use the following information for your bond: 11% coupon, Starting YTM of 11%, and 24 years to maturity. Assume a $1000 par value and annual coupon payments.

Create a column of increasing YTM’s from 0% to 24% in increments of 1%.

Using a data table approach, calculate the price of the bond at each YTM.

Calculate the percentage price change in the bond based on changes in YTM. So, you would have a price change with an increase in YTM from 0% to 1%, and so on. Note: there will not be a price change for the 0% YTM.

Calculate the modified duration of the bond at the Starting YTM (11%), using the MDURATION function. You must use the bond functions for duration calculations. You can use a settlement date of September 24, 2015 and a maturity date of September 24, 2039.

Note: only calculate one value for duration based on the Starting YTM…do not calculate duration for the range of YTM created in Step 1 (above).

To the right of your calculations for the 24 year bond, calculate the predicted percentage price change of the bond (according to duration) at each level of YTM.

The formula for predicted percentage price change is:

= - modified duration * (change in YTM)

= - modified duration * (New YTM - Starting YTM)

So, for example, at the new yield of 0% and a Starting YTM of 11%, the change in YTM is (0%-11%), and the change in price is –MDURATION *(0%-11%). So, if the modified duration is 7 (and it’s not), the change in price would be calculated as: -7*(-.11) = 77% (using cell references and not absolute values, of course).

Be sure to use absolute references for your MDURATION value and your starting YTM as you copy the formula down.

Now, calculate the predicted price to the right of your predicted percentage price change. Multiply (1+% Change in Price) by the bond price at 11%. The starting price is $1000, so the new price would be $1000*(1.77) = $1770.

Now plot the bond prices you obtained in Step 2 along with the predicted prices you calculated in Step 6 in a line graph. Be sure to label the axes, create a title, and use appropriate legend labels.

Question: Briefly discuss why duration predicts a more incorrect price change as the “new” yield gets further from the starting yield?

***SHOW ALL FORMULAS USED IN THE CHART FOR BOND PRICE, % CHANGE, %PRICE CHANGE (DURATION), AND PREDICTED PRICE OF BOND

Explanation / Answer

Solution:

`YTM 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% 21% 22% 23% 24% Face Value 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 Coupon Payments 110 110 110 110 110 110 110 110 110 110 110 110 110 110 PVAF @ for 24 years 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% 21% 22% 23% 24% 8.348 7.7843 7.282 6.835 6.434 6.072 5.746 5.4509 5.1822 4.937 4.7128 4.507 4.318 4.1428 918.28 856.273 801.02 751.85 707.74 667.92 632.06 599.599 570.042 543.07 518.408 495.77 474.98 455.708 PVIF @ for 24 years 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% 21% 22% 23% 24% 0.0817 0.0659 0.0532 0.0431 0.0349 0.0284 0.0231 0.0188 0.0154 0.0126 0.0103 0.0085 0.007 0.0057 81.7 65.9 53.2 43.1 34.9 28.4 23.1 18.8 15.4 12.6 10.3 8.5 7 5.7 Price of Bond = Present Value of Coupon Payments + Present value of Face Value 999.98 922.173 854.22 794.95 742.64 696.32 655.16 618.399 585.442 555.67 528.708 504.27 481.98 461.408 Percentage change in price -7.78% -7.37% -6.94% -6.58% -6.24% -5.91% -5.61% -5.33% -5.09% -4.85% -4.62% -4.42% -4.27%

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