document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1171213>Question 1171213</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Cricket World Cup (CWC) is considering a project proposal which requires an initial investment of $72,625 and it is expected to have net cash flows of $15,000 per year for 8 years. The firm cash flows are discounted at a rate of 12 percent.<BR>\n" );
document.write( "a. What is the project’s Net Present Value (NPV)? (Rounded to 2 decimal places) <BR>\n" );
document.write( "b. What is the project’s discounted payback period? (Rounded to 2 decimal places) <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850977 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=850977\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Absolutely! Let's calculate the NPV and discounted payback period for the CWC project proposal.\r<BR>\n" );
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document.write( "**a) Net Present Value (NPV)**\r<BR>\n" );
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document.write( "To find the NPV, we need to discount each year's cash flow back to its present value and then sum them up, subtracting the initial investment.\r<BR>\n" );
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document.write( "* **Year 0 (Initial Investment):** -$72,625<BR>\n" );
document.write( "* **Years 1-8 (Annual Cash Flows):** $15,000 per year\r<BR>\n" );
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document.write( "We use the present value formula: PV = CF / (1 + r)^n\r<BR>\n" );
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document.write( "Where:\r<BR>\n" );
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document.write( "* PV = Present Value<BR>\n" );
document.write( "* CF = Cash Flow<BR>\n" );
document.write( "* r = Discount Rate (12% or 0.12)<BR>\n" );
document.write( "* n = Year\r<BR>\n" );
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document.write( "Let's do the calculations:\r<BR>\n" );
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document.write( "* **Year 1:** $15,000 / (1.12)^1 = $13,392.86<BR>\n" );
document.write( "* **Year 2:** $15,000 / (1.12)^2 = $11,957.91<BR>\n" );
document.write( "* **Year 3:** $15,000 / (1.12)^3 = $10,676.71<BR>\n" );
document.write( "* **Year 4:** $15,000 / (1.12)^4 = $9,532.78<BR>\n" );
document.write( "* **Year 5:** $15,000 / (1.12)^5 = $8,511.41<BR>\n" );
document.write( "* **Year 6:** $15,000 / (1.12)^6 = $7,599.47<BR>\n" );
document.write( "* **Year 7:** $15,000 / (1.12)^7 = $6,785.24<BR>\n" );
document.write( "* **Year 8:** $15,000 / (1.12)^8 = $6,058.25\r<BR>\n" );
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document.write( "Now, sum these present values and subtract the initial investment:\r<BR>\n" );
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document.write( "NPV = -$72,625 + $13,392.86 + $11,957.91 + $10,676.71 + $9,532.78 + $8,511.41 + $7,599.47 + $6,785.24 + $6,058.25 = $1,889.63\r<BR>\n" );
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document.write( "Therefore, the NPV is approximately $1,889.63.\r<BR>\n" );
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document.write( "**b) Discounted Payback Period**\r<BR>\n" );
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document.write( "The discounted payback period is the time it takes for the discounted cash flows to recover the initial investment.\r<BR>\n" );
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document.write( "1.  **Year 0:** -$72,625<BR>\n" );
document.write( "2.  **Year 1:** -$72,625 + $13,392.86 = -$59,232.14<BR>\n" );
document.write( "3.  **Year 2:** -$59,232.14 + $11,957.91 = -$47,274.23<BR>\n" );
document.write( "4.  **Year 3:** -$47,274.23 + $10,676.71 = -$36,597.52<BR>\n" );
document.write( "5.  **Year 4:** -$36,597.52 + $9,532.78 = -$27,064.74<BR>\n" );
document.write( "6.  **Year 5:** -$27,064.74 + $8,511.41 = -$18,553.33<BR>\n" );
document.write( "7.  **Year 6:** -$18,553.33 + $7,599.47 = -$10,953.86<BR>\n" );
document.write( "8.  **Year 7:** -$10,953.86 + $6,785.24 = -$4,168.62<BR>\n" );
document.write( "9.  **Year 8:** -$4,168.62 + $6,058.25 = $1,889.63\r<BR>\n" );
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document.write( "From the above calculations, we see that the discounted payback occurs in year 8.\r<BR>\n" );
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document.write( "Therefore:\r<BR>\n" );
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document.write( "* **a) NPV:** $1,889.63<BR>\n" );
document.write( "* **b) Discounted Payback Period:** 8 years.<BR>\n" );
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