Chapter 13, Problem 56P

To determine

The best alternative.

Answer to Problem 56P

The alternative C should be selected.

Explanation of Solution

Alternative A :

Calculate the present value for alternative A.

Year	Operating expense after tax(A)	Cash flow(B)	Discount $10\%$ (C)	Present value $\left(A\times C\right)$
$0$	$-\$44000\times 0.6=-\$26400$		$1$	$-\$26400$
Net				$-\$26400$

Alternative B :

Calculate the present value for alternative B.

Year	Operating expense after tax(A)	Depreciation tax benefits(B)	Purchase Of Equipment(C)	Cash flow(D) $\left(A+B+C\right)$	Discount rate @ $10\%$ (E) $\left(\frac{1}{{\left(1+i\right)}^n}\right)$	Present Worth $\left(D\times E\right)$
	$\begin{array}{c}=\$7000\times 0.6\\ =\$4200\end{array}$	$\begin{array}{l}=\frac{\$49000\times 0.4}{7}\\ =\$2800\end{array}$
$0$			$-\$49000$	$-\$49000$	$1$	$-\$49000$
$1$	$\$4200$	$\$2800$		$\$7000$	$0.91$	$\$6370$
$2$	$\$4200$	$\$2800$		$\$7000$	$0.83$	$\$5810$
$3$	$\$4200$	$\$2800$		$\$7000$	$0.75$	$\$5250$
$4$	$\$4200$	$\$2800$		$\$7000$	$0.68$	$\$4760$
$5$	$\$4200$	$\$2800$		$\$7000$	$0.62$	$\$4340$
$6$	$\$4200$	$\$2800$		$\$7000$	$0.56$	$\$3920$
$7$	$\$4200$	$\$2800$		$\$7000$	$0.51$	$\$3570$
Total						$-\$14980$

Alternative C :

Calculate the depreciation for alternative C.

Year	Value of asset(A)	Remaining estimated useful life at the beginning of the year.	Applicable %(B)	Annual depreciation(C) $\left(A\times B\right)$	Depreciation tax benefits $\left(C\times 0.4\right)$
$1$	$\$56000$	$7$	$\frac{7}{28}$	$\$14000$	$\$5600$
$2$	$\$56000$	$6$	$\frac{6}{28}$	$\$12000$	$\$4800$
$3$	$\$56000$	$5$	$\frac{5}{28}$	$\$10000$	$\$4000$
$4$	$\$56000$	$4$	$\frac{4}{28}$	$\$8000$	$\$3200$
$5$	$\$56000$	$3$	$\frac{3}{28}$	$\$6000$	$\$2400$
$6$	$\$56000$	$2$	$\frac{2}{28}$	$\$4000$	$\$1600$
$7$	$\$56000$	$1$	$\frac{1}{28}$	$\$2000$	$\$800$
Total		$28$		$\$56000$

Calculate the present worth for alternative C.

Year	Operating expense after tax(A)	Depreciation tax benefits(B)	Purchase Of Equipment(C)	Cash flow(D) $\left(A+B+C\right)$	Discount rate @ $10\%$ (E) $\left(\frac{1}{{\left(1+i\right)}^n}\right)$	Present Worth $\left(D\times E\right)$
	$\begin{array}{c}=\$12000\times 0.6\\ =\$7200\end{array}$
$0$			$-\$56000$	$-\$56000$	$1$	$-\$56000$
$1$	$\$7200$	$\$5600$		$\$12800$	$0.91$	$\$11648$
$2$	$\$7200$	$\$4800$		$\$12000$	$0.83$	$\$9960$
$3$	$\$7200$	$\$4000$		$\$11200$	$0.75$	$\$8400$
$4$	$\$7200$	$\$3200$		$\$10400$	$0.68$	$\$7072$
$5$	$\$7200$	$\$2400$		$\$9600$	$0.62$	$\$5952$
$6$	$\$7200$	$\$1600$		$\$8800$	$0.56$	$\$4928$
$7$	$\$7200$	$\$800$		$\$8000$	$0.51$	$\$4080$
Total						$-\$3960$

Alternative D :

Calculate the present value for alternative D.

Year	Operating expense after tax(A)	Depreciation tax benefits(B)	Purchase Of Equipment(C)	Cash flow(D) $\left(A+B+C\right)$	Discount rate @ $10\%$ (E) $\left(\frac{1}{{\left(1+i\right)}^n}\right)$	Present Worth $\left(D\times E\right)$
	$\begin{array}{c}=\$8000\times 0.6\\ =\$4800\end{array}$	$\begin{array}{l}=\frac{\$49000\times 0.4}{7}\\ =\$2800\end{array}$
$0$			$-\$49000$	$-\$49000$	$1$	$-\$49000$
$1$	$\$4800$	$\$2800$		$\$7600$	$0.91$	$\$6916$
$2$	$\$4800$	$\$2800$		$\$7600$	$0.83$	$\$6308$
$3$	$\$4800$	$\$2800$		$\$7600$	$0.75$	$\$5700$
$4$	$\$4800$	$\$2800$		$\$7600$	$0.68$	$\$5168$
$5$	$\$4800$	$\$2800$		$\$7600$	$0.62$	$\$4712$
$6$	$\$4800$	$\$2800$		$\$7600$	$0.56$	$\$4256$
$7$	$\$4800$	$\$2800$		$\$7600$	$0.51$	$\$3876$
Total						$-\$12064$

Conclusion:

Therefore, the alternative C should be selected as it has the lowest negative net present value.