Chapter 12, Problem 59P

1.

To determine

Determine the total cost value of “S” paint system.

Explanation of Solution

Compute the total cost value of “S” paint system:

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	$3,359,719	$595,845	$583,045	$593,413	$597,093	$600,053	$601,365	$601,365	$601,349	$601,365	-$5,248
Total cost	$3,759,719

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 total cost value of “P” paint system.

Explanation of Solution

Compute the total cost value of “P” paint system:

Particulars	Present                                                           Value	Year 1	Year 2	Year 4	Year 5	Year 6	Year 7	Year 8	Year 9	Year 10	Year 11
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	$1,064,021	$192,000	$153,600	$184,704	$195,744	$204,624	$208,560	$208,560	$208,512	$208,560	-$15,744
Total cost (B)	$2,264,021

3.

To determine

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

Explanation of Solution

$\begin{array}{c}\text{Amount paid by firm}\}\text{ = }\left[\begin{array}{l}\text{Original estimated amount }\\ \text{+ Difference in PVs of costs}\\ \end{array}\right]\\ \text{=\$1,200,000+\$1,495,698}\\ \text{=\$2,695,698}\end{array}$

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