document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1179443>Question 1179443</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A Php 100,000, 10% bond, pays a dividend every quarter for 8 years. The bond is priced at par and is redeemable at 110% of the par value. Find the yield to maturity. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850232 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850232\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To calculate the yield to maturity (YTM) of the bond, we can use the following formula:\r<BR>\n" );
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document.write( "```<BR>\n" );
document.write( "YTM = (C + (FV - PV) / N) / ((FV + PV) / 2)<BR>\n" );
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document.write( "Where:\r<BR>\n" );
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document.write( "* C = Annual coupon payment<BR>\n" );
document.write( "* FV = Face value of the bond<BR>\n" );
document.write( "* PV = Present value of the bond<BR>\n" );
document.write( "* N = Number of years to maturity\r<BR>\n" );
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document.write( "In this case:\r<BR>\n" );
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document.write( "* C = 100,000 * 10% = 10,000 Php (annual coupon payment)<BR>\n" );
document.write( "* FV = 100,000 Php (face value)<BR>\n" );
document.write( "* PV = 100,000 Php (priced at par)<BR>\n" );
document.write( "* N = 8 years (number of years to maturity)\r<BR>\n" );
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document.write( "However, since the bond is redeemable at 110% of the par value, we need to adjust the FV accordingly:\r<BR>\n" );
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document.write( "* FV = 100,000 * 110% = 110,000 Php (redeemable value)\r<BR>\n" );
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document.write( "Now, we can plug these values into the YTM formula:\r<BR>\n" );
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document.write( "```<BR>\n" );
document.write( "YTM = (10,000 + (110,000 - 100,000) / 8) / ((110,000 + 100,000) / 2)<BR>\n" );
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document.write( "YTM = (10,000 + 1,250) / 105,000<BR>\n" );
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document.write( "YTM = 11,250 / 105,000<BR>\n" );
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document.write( "YTM ≈ 0.1071 or 10.71%<BR>\n" );
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document.write( "Therefore, the yield to maturity of the bond is approximately **10.71%**.\r<BR>\n" );
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document.write( "Note that this is just an approximate YTM, as it doesn't take into account the quarterly coupon payments. To get a more precise YTM, you would need to use a financial calculator or spreadsheet software that can handle the time value of money calculations with quarterly compounding. </SPAN>\n" );
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