document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1181198>Question 1181198</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A piece of machine is purchased for $1,000,000. Accountants of the firm decided to use straight line<BR>\n" );
document.write( "method with the machine being depreciated in 12 years and have an estimated salvage value of<BR>\n" );
document.write( "$123,000. Letting V is equal to the book value of the machine and t is the age of machine,<BR>\n" );
document.write( "a) Determine the function V = f(t)<BR>\n" );
document.write( "b) Determine the book value of machine after 8 years & 11.5 years by using the function<BR>\n" );
document.write( "determined in part a </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850072 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=850072\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to determine the function for the book value and calculate the book value after 8 and 11.5 years:\r<BR>\n" );
document.write( "\n" );
document.write( "**a) Determine the function V = f(t):**\r<BR>\n" );
document.write( "\n" );
document.write( "1. **Calculate the annual depreciation:**\r<BR>\n" );
document.write( "\n" );
document.write( "*   Depreciable amount = Purchase price - Salvage value<BR>\n" );
document.write( "*   Depreciable amount = $1,000,000 - $123,000 = $877,000<BR>\n" );
document.write( "*   Annual depreciation = Depreciable amount / Useful life<BR>\n" );
document.write( "*   Annual depreciation = $877,000 / 12 years = $73,083.33 per year (approximately)\r<BR>\n" );
document.write( "\n" );
document.write( "2. **Write the function:**\r<BR>\n" );
document.write( "\n" );
document.write( "Since we're using straight-line depreciation, the book value decreases linearly over time.  The function will be in the form:\r<BR>\n" );
document.write( "\n" );
document.write( "V(t) = Initial book value - (Annual depreciation * t)\r<BR>\n" );
document.write( "\n" );
document.write( "V(t) = $1,000,000 - $73,083.33t\r<BR>\n" );
document.write( "\n" );
document.write( "**b) Determine the book value after 8 years and 11.5 years:**\r<BR>\n" );
document.write( "\n" );
document.write( "Using the function V(t) = $1,000,000 - $73,083.33t:\r<BR>\n" );
document.write( "\n" );
document.write( "*   **After 8 years:**<BR>\n" );
document.write( "    V(8) = $1,000,000 - ($73,083.33 * 8)<BR>\n" );
document.write( "    V(8) = $1,000,000 - $584,666.64<BR>\n" );
document.write( "    V(8) = $415,333.36\r<BR>\n" );
document.write( "\n" );
document.write( "*   **After 11.5 years:**<BR>\n" );
document.write( "    V(11.5) = $1,000,000 - ($73,083.33 * 11.5)<BR>\n" );
document.write( "    V(11.5) = $1,000,000 - $840,458.295<BR>\n" );
document.write( "    V(11.5) = $159,541.705\r<BR>\n" );
document.write( "\n" );
document.write( "**Answers:**\r<BR>\n" );
document.write( "\n" );
document.write( "*   a) The function V = f(t) is:  V(t) = $1,000,000 - $73,083.33t<BR>\n" );
document.write( "*   b) The book value after 8 years is approximately $415,333.36.<BR>\n" );
document.write( "*   b) The book value after 11.5 years is approximately $159,541.71.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );