A company was adding a new product line that needed [latex]\$80,000[/latex] of Class 43 equipment [latex](CCA rate = 30\%)[/latex] and initial working capital of [latex]\$55,000[/latex]. 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, and then the working capital would be recovered and the equipment sold for [latex]\$5,000[/latex]. Find the equivalent uniform annual worth with [latex]MARR = 10\%[/latex] and [latex]t = 29\%[/latex].

The after-tax diagram shows the working capital going in at Time 0, and coming back at the end of Year 5. Now we use the annual worth formula on the after-tax cash flows. 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)(A/P, 10\%, 5) + (\$167,000 - \$79,000)(1 - 0.29)[/latex] +[latex] (\$5,000 × CSF + \$55,000)(A/F, 10\%, 5)[/latex] = [latex]-\$31,251 + \$62,480 + \$9,650[/latex] =[latex] \$40,898 \cong \$41,000[/latex]

Question 12.9: A company was adding a new product line that needed $80,000 ...

Engineering Economic Analysis

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

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The after-tax diagram shows the working capital going in at Time 0, and coming back at the end of Year 5.

Now we use the annual worth formula on the after-tax cash flows.

CTF = $1 - [(0.29 \times 0.30)/(0.1 + 0.30)](1.05/1.1) = 0.7924$
CSF = $1 - [(0.29 \times0.30)/(0.1 + 0.30)] = 0.7825$
EUAW = $-(\$80,000 × CTF + \$55,000)(A/P, 10\%, 5) + (\$167,000 – \$79,000)(1 – 0.29)$
+ $(\$5,000 × CSF + \$55,000)(A/F, 10\%, 5)$
= $-\$31,251 + \$62,480 + \$9,650$
= $\$40,898 \cong \$41,000$