document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1165407>Question 1165407</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A company is considering a project which requires an investment of Rs. 1,200,000<BR>\n" );
document.write( "now and Rs. 300,000 at the end of the 1st year. It will earn Rs. 200,000 at the end of<BR>\n" );
document.write( "2nd year and thereafter it will earn a fixed annual amount up to the 7th year.<BR>\n" );
document.write( "If interest rate is 11%, find the amount that the project should earn annually i.e.<BR>\n" );
document.write( "from year 3 to year 7 if the company desires to earn a net present value of<BR>\n" );
document.write( "Rs. 100,000 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #789894 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=789894\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> take the first 2 years.<BR>\n" );
document.write( "the cash flow is:<BR>\n" );
document.write( "end of year 0 = -1,200,000<BR>\n" );
document.write( "end of year 1 = -300,000<BR>\n" );
document.write( "end of year 2 = +200,000<BR>\n" );
document.write( "find the present value of the cash flow at 11% per year.<BR>\n" );
document.write( "you will get present value of cash flow (NPV) = -$1,307,945.78<BR>\n" );
document.write( "you want a present value of cash flow of +100,000.<BR>\n" );
document.write( "the difference is 1,407,945.78<BR>\n" );
document.write( "that's in year 0.<BR>\n" );
document.write( "multiply that by 1.11^3 to get a present value of cash flow (NPV) at the end of year 3 =  1,925,550.295.<BR>\n" );
document.write( "your cash flow becomes:<BR>\n" );
document.write( "end of year 0 = -1,200,000<BR>\n" );
document.write( "end of year 1 = -300,000<BR>\n" );
document.write( "end of year 2 = +200,000<BR>\n" );
document.write( "end of year 3 = +1,925,550.295<BR>\n" );
document.write( "find the present value of the cash flow at 11.5% per year.<BR>\n" );
document.write( "you would get present value of cash flow (NPV) = +100,000.<BR>\n" );
document.write( "this tells you the present value of cash flow at the end of year 3 is good.<BR>\n" );
document.write( "now you want to change that to an annuity that has a present value of that at the end of year 3.<BR>\n" );
document.write( "you would use a financial calculator to give you the annual payment at the end of year 3 to the end of year 7 that will give you a present value of 1,925,550.295 at the end of year 3.<BR>\n" );
document.write( "in this calculation, the payments would be made at the beginning of each year.<BR>\n" );
document.write( "the calculator will tell you that the annual payment would be 469,366.4318 at the end of year 3 going to the end of year 7.<BR>\n" );
document.write( "you would plug that into your cash flow and find that the present value of that cash flow is equla to 100,000.<BR>\n" );
document.write( "this is the figure you wanted so you're ok.\r<BR>\n" );
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document.write( "i used excel and the ti-ba-ii financial calculator.\r<BR>\n" );
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document.write( "the excel takes the annual cash flow and brings it back to the end of year 0 at 11% per year.\r<BR>\n" );
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document.write( "the financial calculator finds the annual payments from a present value for 5 years.<BR>\n" );
document.write( "the inputs to the calculator are:<BR>\n" );
document.write( "present value = -1925550.295 at the end of year 3.<BR>\n" );
document.write( "future value = 0<BR>\n" );
document.write( "interest rate per year = 11%<BR>\n" );
document.write( "number of years = 5 (from end of year 3 to end of year 7 = 5 years of payments).<BR>\n" );
document.write( "payments are made at the beginning of each year.<BR>\n" );
document.write( "this means the first payment is made at the end of year 3.<BR>\n" );
document.write( "the output of that calculator was annual payments of 469,366.43 starting at the end of the third year and going to the end of the 7th year.\r<BR>\n" );
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document.write( "the output of the online financial calculator agrees with the output of the ti-ba-ii.\r<BR>\n" );
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document.write( "here's a display of the excel spreadsheet used.\r<BR>\n" );
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document.write( "the left table is using the present value calculated for end of year 3.<BR>\n" );
document.write( "the right table is using the annuity generated from that present value with payments from end of year 3 to end of year 7.\r<BR>\n" );
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document.write( "here's a display of an online calculator that does pretty much the same thing that the ti-ba-ii does, only it rounds the answer for you.\r<BR>\n" );
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document.write( "input\r<BR>\n" );
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document.write( "output\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/092106.jpg\" >\r<BR>\n" );
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document.write( "note that the annuity calculation could have been done 2 ways.\r<BR>\n" );
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document.write( "when the initial investment is at the end of year 3, the calculations shown above apply.\r<BR>\n" );
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document.write( "if you assume the initial investment was at the beginning of year 3 (same as the end of year 2), then the present value would be -1925550.295 divided by 1.11 = -1,734,729.996.<BR>\n" );
document.write( "the annuity calculations would then be made assuming end of year payments.<BR>\n" );
document.write( "the payment at the end of each year would be the same as the payments at the beginning of each year in the above calculations.\r<BR>\n" );
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document.write( "here is the display of the annuity calculations assuming end of year payments.\r<BR>\n" );
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document.write( "in both cases, the first payment is made at the end of year 3.\r<BR>\n" );
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document.write( "the online calculator that i used that performs the same functions as the ti-ba-ii can be found at <a  rel=nofollow HREF= \"https://arachnoid.com/finance/index.html\" target = \"_blank\">https://arachnoid.com/finance/index.html</a><BR>\n" );
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