Question

Relevant cash flows - No terminal value Central Laundry and Cleaners is considering replacing an existing piece of machinery with a more sophisticated machine. The old machine was purchased 3 years ago at a cost of $53,400​, and this amount was being depreciated under MACRS using a​ 5-year recovery period. The machine has 5 years of usable life remaining. The new machine that is being considered costs $75,900 and requires $3,700 in installation costs. The new machine would be depreciated under MACRS using a​ 5-year recovery period. The firm can currently sell the old machine for $54,800 without incurring any removal or cleanup costs. The firm is subject to a tax rate of 40%. The revenues and expenses​ (excluding depreciation and​ interest) associated with the new and the old machines for the next 5 years are given in the table (Table contains the applicable MACRS depreciation​ percentages.) Note: The new machine will have no terminal value at the end of 5 years. a. Calculate the initial investment associated with replacement of the old machine by the new one. b. Determine the incremental operating cash inflows associated with the proposed replacement.​ (Note: Be sure to consider the depreciation in year​ 6.) c. Depict on a time line the relevant cash flows found in parts ​(a​) and ​(b​) associated with the proposed replacement decision.

   New machine           Old machine  
Year   Revenue   Expenses
(excluding depreciation and interest)       Revenue   Expenses
(excluding depreciation and interest)
1   $750,800    $719,400       $674,000   $659,200
2   750,800   719,400       676,000   659,200
3   750,800   719,400       680,000   659,200
4   750,800   719,400       678,000   659,200
5   750,800   719,400       674,000   659,200

Rounded Depreciation Percentages by Recovery Year Using MACRS for
First Four Property Classes              
   Percentage by recovery year*          
Recovery year    3 years    5 years    7 years    10 years
1 33%   20%   14%   10%
2 45%   32%   25%   18%
3 15%   19%   18%   14%
4 7% 12%   12%   12%
5 12% 9% 9%
6    5% 9% 8%
7      9%   7%
8     4%   6%
9     6%
10 6%
11 4%
Totals 100%   100%   100%   100%
              

Answer 1

a)
Installed cost of new asset
Cost of new asset	$  75,900.00
Add: Installation costs	$    3,700.00
Total cost of new asset		$    79,600.00
Less : After-tax proceeds from sale of old asset
Proceeds from sale of old asset	$ (54,800.00)
Add:  Tax on sale of old Asset (see below)	$  15,725.60	$   (39,074.40)
Total proceeds, sale of old asset		$    40,525.60
Initial investment
Book value of old machine: [1 - (0.20 + 0.32 + 0.19)]  x  $53,400	$15,486
Gain on Assets = $54,800 - $15,486	$39,314
Tax on recaptured depreciation ( $53,400 - $15486) x  0.40	$15,166
Tax on  capital gain = ($39,314 - (53,400 - 15486) x  0.40	$       560.00
Total tax on sale of asset	$15,726
b)
Calculation of Operating Cash Flow
Year	1	2	3	4	5	6
Old Machine
Profit Before Depreciation and tax	$  14,800.00	$    16,800.00	$ 20,800.00	$ 18,800.00	$14,800.00
Depreciation	$    6,408.00	$      6,408.00	$   2,670.00
Net Profit before tax	$    8,392.00	$    10,392.00	$ 18,130.00	$ 18,800.00	$14,800.00
Taxes @ 40%	$    3,356.80	$      4,156.80	$   7,252.00	$   7,520.00	$  5,920.00
Net Profit after tax	$    5,035.20	$      6,235.20	$ 10,878.00	$ 11,280.00	$  8,880.00
Depreciation	$    6,408.00	$      6,408.00	$   2,670.00	$              -	$             -
Cash flow	$  11,443.20	$    12,643.20	$ 13,548.00	$ 11,280.00	$  8,880.00
New Machine
Profit Before Depreciation and tax	$  31,400.00	$    31,400.00	$ 31,400.00	$ 31,400.00	$31,400.00
Depreciation	$  15,920.00	$    25,472.00	$ 15,124.00	$   9,552.00	$  9,552.00	$  3,980.00
Net Profit before tax	$  15,480.00	$      5,928.00	$ 16,276.00	$ 21,848.00	$21,848.00	$ (3,980.00)
Taxes @ 40%	$    6,192.00	$      2,371.20	$   6,510.40	$   8,739.20	$  8,739.20	$ (1,592.00)
Net Profit after tax	$    9,288.00	$      3,556.80	$   9,765.60	$ 13,108.80	$13,108.80	$ (2,388.00)
Depreciation	$  15,920.00	$    25,472.00	$ 15,124.00	$   9,552.00	$  9,552.00	$  3,980.00
Cash flow	$  25,208.00	$    29,028.80	$ 24,889.60	$ 22,660.80	$22,660.80	$  1,592.00
Incremental After-tax cash flows	$  13,764.80	$    16,385.60	$ 11,341.60	$ 11,380.80	$13,780.80	$  1,592.00
c)
Year	Cash flows
0	$ (40,525.60)
1	$  13,764.80
2	$  16,385.60
3	$  11,341.60
4	$  11,380.80
5	$  13,780.80
6	$    1,592.00

Cash flows Chart Area 23,764. 16,385. 11,341.6 11,380. 13,780. 4 5 10,525.60)


4 (excluding depreciation and interest) Revenue Exper New Machine Old machine 5 (excluding depreciation and interest) 6 1 72 8 3 Revenue 750800 750800 750800 750800 750800 Expenses (excluding depreciation and interest) 719400 719400 719400 719400 719400 Revenue 674000 676000 680000 678000 674000 Expenses (excluding depreciation and interest) 659200 659200 659200 659200 659200 5 10 11 12 a) 75900 3700 =B14+B15 13 Installed cost of new asset 14 Cost of new asset 15 Add: Installation costs 16 Total cost of new asset 17 Less : After-tax proceeds from sale of old asset 18 Proceeds from sale of old asset 19 Add: Tax on sale of old Asset (see below) 20 Total proceeds, sale of old asset 21 Initial investment -54800 =B27 =B18+B19 =C16+C19 22 23 Book value of old machine: (1 - (0.20 + 0.32 + 0.19)] x $ =53400*(1-(20%+32%+19%)) 24 Gain on Assets = $54,800 - $15,486 =-B18-B23 Tax on recaptured depreciation ($53,400 - $15486) X 25 0.40 =(53400-B23)*40% Tax on capital gain = ($39,314 - (53,400 - 15486) X 26 0.40 =(B24-(53400-B23)*40% 27 Total tax on sale of asset =B25+B26 28 29 b) 30 Calculation of Operating Cash Flow 31 Year 32 Old Machine 33 Profit Before Depreciation and tax =E6-F6 34 Depreciation =53400*12% 35 Net Profit before tax =B33-B34 36 Taxes @ 40% =B3540% 37 Net Profit after tax =B35-B36 38 Depreciation =B34 39 Cash flow =B37+B38 40 3 4 56 =E9-F9 =E10-F10 =E7-F7 =53400*12% =C33-C34 =C3540% =C35-C36 =C34 =C37+C38 =E8-F8 =53400'5% =D33-D34 =D35*40% =D35-D36 =D34 =D37+D38 =E33-E34 -E35*40% =E35-E36 =E34 =E37+E38 =F33-F34 -F35*40% =F35-F36 =F34 =F37+F38

Ε F G A 41 New Machine 42 Profit Before Depreciation and tax 43 Depreciation 44 Net Profit before tax 45 Taxes @ 40% 46 Net Profit after tax 47 Depreciation 48 Cash flow 49 Incremental After-tax cash flows 50 51 c) 52 Year 53 0 54 1 55 2 =B6-C6 =$C$16'20% =B42-B43 =B44*40% =B44-B45 =B43 =B46+B47 =B48-B39 =B7-C7 =$C$16*32% =C42-C43 =C44*40% =C44-C45 =C43 =C46+C47 =C48-C39 =B8-CB =$C$ 16*19% =D42-043 =D44*40% =D44-045 =D43 =D46+D47 =D48-D39 =B9-C9 =$C$16*12% =E42-E43 -E44-40% =E44-E45 =E43 =E46+E47 =E48-E39 =B10-C10 =$C$1612% =F42-F43 -F44-40% =F44-F45 =F43 =F46+F47 =F48-F39 =$C$16'5% =G42-G43 =G44-40% =G44-G45 =G43 =G46+G47 =G48-G39 Cash flows =-C20 =B49 =C49 =D49 =E49 =F49 =G49 Cash flows 13,764.8 16,385.6 13,780.8 11,341.6 11,380.8