document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=591561>Question 591561</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You are the owner of an apartment building that is being offered for sale for $1,500,000. You receive an offer from a prospective buyer who wants to pay you $500,000 now, $500,000 in 6 months, and $500,000 in 1 year.\r<BR>\n" );
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document.write( "a. What is the actual present value of this offer, considering you can earn 12% interest compounded monthly on your money?\r<BR>\n" );
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document.write( "b. If another buyer offers to pay you $1,425,000 cash now, which is a better deal?\r<BR>\n" );
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document.write( "c. Because you understand the \"time value of money\" concept, you have negotiated a deal with the original buyer from part a, whereby you will accept the three-payment offer but will charge 12% interest, compounded monthly, on the two delayed payments. Calculate the total purchase price under this new agreement.\r<BR>\n" );
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document.write( "d. Now, calculate the present value of the new deal, to verify that you will receive the original asking price of $1,500,000 for your apartment building. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #375679 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=375679\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the present value of 1.5 million is equal to 1.5 million if it is all payed up front.<BR>\n" );
document.write( "the present value of 1.425 million is equal to 1.425 million if it is all payed up front.<BR>\n" );
document.write( "the present value of .5 million payed up front and .5 million payed in 6 months and .5 million payed in 12 months would be equal to:<BR>\n" );
document.write( ".5 million plus .5 million / (1.01)^6 plus .5 million / (10.1)^12 which would be equal to:<BR>\n" );
document.write( ".5 million plus .4710226176 million plus .4437246126 which is equal to:<BR>\n" );
document.write( "1.41474723 million.<BR>\n" );
document.write( "the best you're going to do is if the 1.5 million is payed up front.<BR>\n" );
document.write( "the next best you're going to do is if you accept the 1.425 million offer.<BR>\n" );
document.write( "the last best you're going to do is if you accept the 3 payment plan and don't charge interest on the deferred payments.<BR>\n" );
document.write( "if you accept the deferred payment offer but charge 12% interest compounded monthly on the deferred payments, then you will make the following:<BR>\n" );
document.write( ".5 million on the part that is paid up front.<BR>\n" );
document.write( ".5 million * (1.01)^6 on the part that is paid in 6 months.<BR>\n" );
document.write( ".5 million * (1.01)^12 on the part that is paid in 12 months.<BR>\n" );
document.write( "the present value of that is equal to:<BR>\n" );
document.write( ".5 million on the first part.<BR>\n" );
document.write( "plus .5 million * (1.01)^6 / (1.01)^6 = .5 million on the second part.<BR>\n" );
document.write( "plus .5 million * (1.01)^6 / (1.01)^12 = .5 million on the third part><BR>\n" );
document.write( "this will total 1.5 million which is the original asking price.<BR>\n" );
document.write( "the payment of 1.5 million up front is equivalent to paying in 3 parts with interest being charged for the 3 parts, so you will make the same money.<BR>\n" );
document.write( "the bottom line is:<BR>\n" );
document.write( "1.5 million up front is a present value of 1.5 million.<BR>\n" );
document.write( "1.5 million in 3 payments and being charged 1% per month for the deferred payments still gives you a present value of 1.5 million.<BR>\n" );
document.write( "1.425 million present value is next in line.<BR>\n" );
document.write( "1.41 million present value is next in line.<BR>\n" );
document.write( "the deferred payment plan that charges 1% interest for each deferred month of payment is equivalent to 1.5 million up front and is the preferred plan if deferred payments are to be considered.<BR>\n" );
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