A company was adding a new product line that required $80,000 worth of Class 43 equipment (CCA rate = 30%) and initial working capital of $55,000. The working capital requirement would increase at 18% a year. The product would have production costs of $79,000 a year and annual revenues of

Question

A company was adding a new product line that required [latex]\$80,000[/latex] worth of Class 43 equipment [latex](CCA rate = 30\%)[/latex] and initial working capital of [latex]\$55,000[/latex]. The working capital requirement would increase at [latex]18\%[/latex] a year. The product would have production costs of [latex]\$79,000[/latex] a year and annual revenues of [latex]\$167,000[/latex]. The product would be manufactured for five years and then discontinued; then the working capital would be recovered and the equipment sold for [latex]\$5,000[/latex]. Find the EUAW with [latex]MARR = 10\% [/latex] and [latex]t = 29\%[/latex].

Accepted Answer

The after-tax diagram shows the initial working capital going in at Time 0. Then there are the annual additions to ensure that there is enough working capital to meet the increasing requirements. Since the initial working capital remains throughout the project, it is necessary only to add an amount annually to cover the percentage increase.

Working Capital Requirement Increasing at [latex]18\%[/latex]

Year	Working Capital at Beginning of Year	Amount Added at End of Year	Total Available for Next Year
1	[latex]\$ 55,000[/latex]	[latex]\$55,000 × 18\% = \$9,900[/latex]	[latex]\$ 64,900[/latex]
2	[latex]\$ 64,900[/latex]	[latex](\$55,000 ×18\%)(1 + 18\%) = \$11,682[/latex]	[latex]\$ 76,582[/latex]
3	[latex]\$ 76,582[/latex]	[latex](\$55,000 × 18\%)(1 + 18\%)^{2} = \$13,785[/latex]	[latex]\$ 90,376[/latex]
4	[latex]\$ 90,376[/latex]	[latex](\$55,000 × 18\%)(1 + 18\%) ^{3}= \$16,266[/latex]	[latex]\$106,633[/latex]
5	[latex]\$ 106,633[/latex]		[latex]\$106,633[/latex]

The increasing working capital thus forms an n - 1 long geometric series as shown on the cash flow diagram.

The annual equivalent formula on the after-tax cash flows is the same as in Example 12-9 but with the addition of a geometric series term for four periods and an increased amount of working capital recovered at the end of Period 5.

CTF [latex]= 1 - [(0.29 × 0.30)/(0.1 + 0.30)](1.05/1.1) = 0.7924[/latex]
CSF =[latex] 1 - [(0.29 × 0.30)/(0.1 + 0.30)] = 0.7825[/latex]
EUAW =[latex] -[\$80,000 × CTF + \$55,000 + (\$55,000 × 0.18)(P/A, 18\%, 10\%, 4)](A/P, 10\%, 5\%)[/latex]
+[latex] (\$167,000 - \$79,000)(1 - 0.40) + (\$5,000 × CSF + \$106,033)(A/F, 10\%, 5)[/latex]
= [latex]-\$41,815 +\$62,480 + \$18,107[/latex]
= [latex]\$38,772 \cong \$38,800[/latex]

Year	Working Capital at Beginning of Year	Amount Added at End of Year	Total Available for Next Year
1	$\$ 55,000$	$\$55,000 × 18\% = \$9,900$	$\$ 64,900$
2	$\$ 64,900$	$(\$55,000 ×18\%)(1 + 18\%) = \$11,682$	$\$ 76,582$
3	$\$ 76,582$	$(\$55,000 × 18\%)(1 + 18\%)^{2} = \$13,785$	$\$ 90,376$
4	$\$ 90,376$	$(\$55,000 × 18\%)(1 + 18\%) ^{3}= \$16,266$	$\$106,633$
5	$\$ 106,633$		$\$106,633$

Question 12.10: A company was adding a new product line that required $80,00...

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