document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1191944>Question 1191944</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The forward price of a forward contract on a stock maturing in 3 years is $70. The stock is expected to pay a dividend of $1 twice: in 6 months and in a year from now. Solve for the current stock price if the continuous compounding interest rate is 6%. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849142 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1987)</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=849142\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to solve for the current stock price:\r<BR>\n" );
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document.write( "**1. Understand the Formula:**\r<BR>\n" );
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document.write( "The forward price (F) of a stock with dividends is calculated as:\r<BR>\n" );
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document.write( "F = (S - PV of dividends) * e^(rT)\r<BR>\n" );
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document.write( "Where:\r<BR>\n" );
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document.write( "* F = Forward price<BR>\n" );
document.write( "* S = Current stock price (what we want to find)<BR>\n" );
document.write( "* PV of dividends = Present value of all dividends paid during the life of the forward contract<BR>\n" );
document.write( "* r = Continuously compounded interest rate<BR>\n" );
document.write( "* T = Time to maturity of the forward contract (in years)\r<BR>\n" );
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document.write( "**2. Calculate the Present Value of Dividends:**\r<BR>\n" );
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document.write( "* **Dividend 1 (in 6 months):** PV1 = $1 * e^(-0.06 * 0.5) = $1 * e^(-0.03) ≈ $0.9704<BR>\n" );
document.write( "* **Dividend 2 (in 1 year):** PV2 = $1 * e^(-0.06 * 1) = $1 * e^(-0.06) ≈ $0.9418\r<BR>\n" );
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document.write( "Total PV of dividends = PV1 + PV2 ≈ $0.9704 + $0.9418 ≈ $1.9122\r<BR>\n" );
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document.write( "**3. Plug Values into the Formula and Solve for S:**\r<BR>\n" );
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document.write( "We know:\r<BR>\n" );
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document.write( "* F = $70<BR>\n" );
document.write( "* r = 0.06<BR>\n" );
document.write( "* T = 3 years<BR>\n" );
document.write( "* PV of dividends ≈ $1.9122\r<BR>\n" );
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document.write( "Now, plug these values into the formula:\r<BR>\n" );
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document.write( "$70 = (S - $1.9122) * e^(0.06 * 3)<BR>\n" );
document.write( "$70 = (S - $1.9122) * e^(0.18)<BR>\n" );
document.write( "$70 = (S - $1.9122) * 1.1972<BR>\n" );
document.write( "$70 / 1.1972 = S - $1.9122<BR>\n" );
document.write( "$58.47 = S - $1.9122<BR>\n" );
document.write( "S = $58.47 + $1.9122<BR>\n" );
document.write( "S ≈ $60.38\r<BR>\n" );
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document.write( "**Therefore, the current stock price is approximately $60.38.**<BR>\n" );
document.write( " </SPAN>\n" );
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