Chapter 13, Problem 48P

To determine

The firm whether keeps its old forklift truck for the present or replace it now with the new one.

Answer to Problem 48P

The company should not replace the truck.

Explanation of Solution

Calculate the net present value of old truck.

Year	Cost of maintenance(A)	Tax saving $\begin{array}{c}\left(B\right)\\ \left(A\times 0.4\right)\end{array}$	After tax cash flow $\begin{array}{c}\left(C\right)\\ \left(A-B\right)\end{array}$	Discount rate $8\%$ (D) $\left(\frac{1}{{\left(1+i\right)}^n}\right)$	Net present value $\left(C\times D\right)$
$0$
$1$	$\$400$	$\$160$	$\$240$	$0.9259$	$\$222.216$
$2$	$\$600$	$\$240$	$\$360$	$0.8573$	$\$308.628$
$3$	$\$800$	$\$320$	$\$480$	$0.7938$	$\$381.024$
$4$	$\$1000$	$\$400$	$\$600$	$0.7350$	$\$441$
$5$	$\$1400$	$\$560$	$\$840$	$0.6806$	$\$571.704$
$6$	$\$1400$	$\$560$	$\$840$	$0.6301$	$\$529.284$
$7$	$\$1400$	$\$560$	$\$840$	$0.5835$	$\$490.14$
$8$	$\$1400$	$\$560$	$\$840$	$0.5403$	$\$453.852$
$9$	$\$1400$	$\$560$	$\$840$	$0.5002$	$\$420.168$
$10$	$\$1400$	$\$560$	$\$840$	$0.4632$	$\$389.088$
Total NPV					$\$4206$

Write the equation for straight line depreciation.

$\text{Depreciation}=\frac{B-S}{N}$ ...... (I)Here, total cost is B, salvage value is S, and life is N.

Substitute $\$6500$ for B, $\$0$ for S, and $10$ years for N in Equation (I).

$\begin{array}{c}\text{Depreciation}=\frac{\$6500-0}{10}\\ =\$650\end{array}$

Calculate the net present value of New truck.

Year	Cost of maintenance(A)	Depreciation(B)	Total cost(C)	Tax saving $\begin{array}{c}\left(D\right)\\ \left(C\times 0.4\right)\end{array}$	After tax cash flow $\begin{array}{c}\left(E\right)\\ \left(C-D\right)\end{array}$	Cash out flow $\begin{array}{c}\left(F\right)\\ \left(E-B\right)\end{array}$	Discount rate $8\%$ (G) $\left(\frac{1}{{\left(1+i\right)}^n}\right)$	Net present value $\left(F\times G\right)$
$0$								$\$6500$
$1$	$\$50$	$\$650$	$\$700$	$\$280$	$\$420$	$\$230$	$0.9259$	$\$213$
$2$	$\$50$	$\$650$	$\$700$	$\$280$	$\$420$	$\$230$	$0.8573$	$\$197.2$
$3$	$\$50$	$\$650$	$\$700$	$\$280$	$\$420$	$\$230$	$0.7938$	$\$182.6$
$4$	$\$50$	$\$650$	$\$700$	$\$280$	$\$420$	$\$230$	$0.7350$	$\$169$
$5$	$\$50$	$\$650$	$\$700$	$\$280$	$\$420$	$\$230$	$0.6806$	$\$156.5$
$6$	$\$50$	$\$650$	$\$700$	$\$280$	$\$420$	$\$230$	$0.6301$	$\$145$
$7$	$\$50$	$\$650$	$\$700$	$\$280$	$\$420$	$\$230$	$0.5835$	$\$134.2$
$8$	$\$50$	$\$650$	$\$700$	$\$280$	$\$420$	$\$230$	$0.5403$	$\$124.3$
$9$	$\$50$	$\$650$	$\$700$	$\$280$	$\$420$	$\$230$	$0.5002$	$\$115$
$10$	$\$50$	$\$650$	$\$700$	$\$280$	$\$420$	$\$230$	$0.4632$	$\$106.5$
Total NPV								$-\$4957$

Hence, the NPV of New truck is negative. So, it is not economically beneficial to replace the truck.

Conclusion:

Therefore, the company should not replace the truck.