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 $46,800​, 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 $3,600 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 $55,900 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

New machine			Old machine
Year	Revenue	Expenses ​(excluding depreciation and​ interest)		Revenue	Expenses ​(excluding depreciation and​ interest)
1	$749,600	$720,600		$674,700	$660,400
2	749,600	720,600		676,700	660,400
3	749,600	720,600		680,700	660,400
4	749,600	720,600		78,700	660,400
5	749,600	720,600		674,700	660,400

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​%

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.

Answer 1

a. Calculate the initial investment associated with replacement of the old machine by the new one.

Purchase cost of New Machine	$75,900
Installation cost	$3,600
Total cost of new machine 75900 + 3600 (outflow)		($ 79500)
Cash inflow from sale of old machine		$55,900
Tax expe. On gain from old machine sale		(16931)
Net initial investment		40531

Sale of old machine = 55900

Purchase cost =46800

Accumulated dep = 33228

Book value of old mechine = 46800-33228 = 13572

Taxable gain from = 55900 - 13572 = 42328

Tax on gain = 42328*40% = 16931

Depreciation schedule

Year and MACRS rate(for new)	Y1 = 20%	Y2= 32%	Y3 = 19%	Y4=12%	Y5=12%	Y6=5%
New machine Cost = 79500	=79500*20% =15900	=25440	=15105	=9540	=9540	3975
Year and rate (old) (3 year already depreciated) =20%+32%+19% = 71%	Year 4 12%	Year 5 12%	Year 6 5%
Old machine cost= 46800 Acc. Dep = 46800*71%=33228	46800*12% =5616	=5616	2340
Incremental depreciation	15900- 5616 = 10284	=19824	=12765	=9540	9540	=3975
Depreciation Tax shield = Incre. Dep * Tax rate(40%)	10284*40% =4114	19824*40% =7930	12765*40% =5106	9540*40% =3816	9540*40% =3816

b. Determine the incremental operating cash inflows associated with the proposed replacement.​

Incremental operating cash flow

Net increase (decrease) in operating revenue
∓ Net (increase) decrease in operating expenses, excluding depreciation
= Net incremental operating cash flow before taxes
∓ Net (increase) decrease in income taxes on operating cash flow
= Net incremental operating cash flow after taxes
± Depreciation tax shield: net increase (decrease) in depreciation expense for
tax purposes × tax rate
= Incremental net cash flow for the period

	Year 1	Year	Year 3	Year 4	Year 5
Net increase in operating revenue	749600 - 674700 = 74900	749,600- 676,700 =72900	749,600- 680,700 =68900	749,600- 678700 =70900	749,600- 674700 =74900
- Net increase in operating expenses, excluding depreciation	720,600- 660,400 =60200	720,600- 660,400 =60200	720,600- 660,400 =60200	720,600- 660,400 =60200	720,600- 660,400 =60200
= Net incremental operating cash flow before taxes	=14700	=12700	=8700	=10700	=14700
- Net increase in income taxes on operating cash flow Tax =40%	14700*40% =5880	=5080	3480	4280	5880
= Net incremental operating cash flow after taxes (excluding dep.)	=8820	=7620	=5220	=6420	=8820
+ Depreciation tax shield: net increase in depreciation expense for tax purposes × tax rate(see above dep table)	4114	7930	5106	3816	3816
= Incremental net operating cash flow for the period	=12934	=15550	=10326	=10236	12636

+There is no terminal value for new machine, so we take = 0

The carrying value at end of year 5(6th year depr.) = 3975

No salvage value, so the full amt of $ 3975 is loss from disposal of asset

+Tax savings on loss from disposal of asset = 3975* 40% = 1590 (inflow)

=  Final year’s incremental net cash flow = Incremental net operating cash flow for the period + Tax savings on loss from disposal of asset

= 12636 + 1590 = $ 14226

c. c. Depict on a time line the relevant cash flows found in parts​(a​) and ​(b​) associated with the proposed replacement decision.