Chapter 12, Problem 59P

1.

To determine

Determine the amount of difference in cost for the two systems.

Explanation of Solution

Compute the amount of difference in cost for the two systems:

Particulars	Present                                                           Value	Year 1	Year 2	Year 4	Year 5	Year 6	Year 7	Year 8	Year 9	Year 10	Year 11
Initial investment	$400,000
After-tax paint cost (1)		$228,000	$228,000	$228,000	$228,000	$228,000	$228,000	$228,000	$228,000	$228,000	$0
After-tax environ. costs (3)		$383,845	$383,845	$383,845	$383,845	$383,845	$383,845	$383,845	$383,845	$383,845
Total after-tax cash costs		$611,845	$611,845	$611,845	$611,845	$611,845	$611,845	$611,845	$611,845	$611,845
Depreciation (MACRS) (2)		$40,000	$72,000	$46,080	$36,880	$29,480	$26,200	$26,200	$26,240	$26,200	$13,120
Tax savings on depreciation		$16,000	$28,800	$18,432	$14,752	$11,792	$10,480	$10,480	$10,496	$10,480	$5,248
Net after-tax cash costs	$3,360,365	$595,845	$583,045	$593,413	$597,093	$600,053	$601,365	$601,365	$601,349	$601,365	-$5,248
Total cost	$3,760,365
Powder-Paint System
Initial investment	$1,200,000
After-tax paint cost (4)		$240,000	$240,000	$240,000	$240,000	$240,000	$240,000	$240,000	$240,000	$240,000	$0
Depreciation (MACRS)		$120,000	$216,000	$138,240	$110,640	$88,440	$78,600	$78,600	$78,720	$78,600	$39,360
Tax saving on depreciation		$48,000	$86,400	$55,296	$44,256	$35,376	$31,440	$31,440	$31,488	$31,440	$15,744
Net after-tax cash costs	$1,064,182	$192,000	$153,600	$184,704	$195,744	$204,624	$208,560	$208,560	$208,512	$208,560	-$15,744
Total cost (B)	$2,264,182
Difference in total cost (A-B)	$1,496,183

Working notes:

Determine the amount of annual tax:

$\begin{array}{c}\text{Annual tax}\}\text{ = }\left(\begin{array}{l}\text{Paint cost per unit}\times \text{Annual cost}\\ \text{on disposal of machine}\times (\text{1}-\text{Tax rate}\end{array}\right)\\ =\text{\$0}\text{.19 × 2,000,000 × }\left(\text{1 - 0}\text{.40}\right)\\ =\$380,000\text{×}0.60\\ =\$228,000\end{array}$

Determine the amount of annual tax of “P”:

$\begin{array}{c}\text{Annual tax}\}\text{ = }\left(\begin{array}{l}\text{Amortization cost per unit}\\ \times \text{Annual cost}\\ \text{on disposal of machine}\times (\text{1}-\text{Tax rate}\end{array}\right)\\ =\text{\$0}\text{.20 × 2,000,000 × }\left(\text{1 - 0}\text{.40}\right)\\ =\$400,000\text{×}0.60\\ =\$240,000\end{array}$

2.

To determine

Determine the amount of the firm that should be willing to pay for “P” process.

Explanation of Solution

$\begin{array}{c}\text{Amount paid by firm}\}\text{ = }\left[\begin{array}{l}\text{Original estimated amount }\\ \text{+ Difference in PVs of costs}\\ \end{array}\right]\\ \text{=\$1,200,000+\$1,496,183}\\ \text{=\$2,696,183}\end{array}$

Therefore, it is increased by 125% over the original price.