Question

X Company is considering the replacement of an existing machine. The new machine costs $1.8 million and requires installation costs of $250,000. The existing machine can be sold currently for $125,000 before taxes. The existing machine is 3 years old, cost $1 million when purchased, and has a $290,000 book value and a remaining useful life of 5 years. It was being depreciated under MACRS using a 5-year recovery period. If it is held for 5 more years, the machine’s market value at the end of year 5 will be zero. Over its 5-year life, the new machine should reduce operating costs by $650,000 per year, and will be depreciated under MACRS using a 5-year recovery period. The new machine can be sold for $150,000 net of removal and cleanup costs at the end of 5 years. A $30,000 increase in net working capital will be required to support operations if the new machine is acquired. The firm has adequate operations against which to deduct any losses experienced on the sale of the existing machine. The firm has a 15% cost of capital, is subject to a 40% tax rate and requires a 42-month payback period for major capital projects.

5-Year MACRS

Year 1　 20%

Year 2    32%

Year 3 19%

Year 4 12%

Year 5 12%

Year 6 5%

1. Should they accept or reject the proposal to replace the machine?

2. What is the NPV?

3. What is the IRR?

4. What is the payback period?

Answer 1

Answer for Question 1. The company is to reject the proposal to replace the machine, because the NPV is negative, which means the Present value of incremental cash inflow is not sufficient to meet incremental cash outlay.

Answer for Question 2. NPV is -187540.239076755, rounded to two decimal is -187540.24

Cost of capital is 15%, it is presumed that this 15% is after tax cost of Capital,

It is presumed that tax savings on loss of old asset is get at the end of the year.

Here NPV = Present value of incremental cash inflow - incremental cash outlay,

Present value of incremental cash inflow = Annual incremental cash inflow x Discount Factor ( or PV factor),

Discount Factor ( or PV factor) = 1/(1+i)^n, here i is cost of capital = 15% or 0.15, n = respective number of year upto and including 5. example, for year 1 = 1/(1.15^1), =0.869565217391304, year 2 =1/(1.15^2), = 0.756143667296787 like that upto year 5 it is shown in calculation table. the relevant computaions are given below

Step 1, compute outlay on new machine

	New Machine			Amount in $
Cost of new machine				18,00,000.00
Installation cost of new				2,50,000.00
Total cost of New Machine				20,50,000.00
Increase in Working Capital				30,000.00
Total outlay				20,80,000.00
Less: Sale value of old Machine				1,25,000.00
	Incremental cash outlay			19,55,000.00

Dpreciation is to be worked out on Total cost of New Machine.

	Old Machine		Amount in $
Original cost			10,00,000.00
Depreciation till date			7,10,000.00
Current book value			2,90,000.00
Sale value			1,25,000.00
loss on sale			1,65,000.00

The tax saved on loss of asset is cosidered for computing profit before tax

Step 2

Calculation of incremental depreciation of new machine over old machine
Depreciation on New Machine			Depre on old Machine
year	Rate	Depreciation	Rate	Depreciation	Incremental Depreciation
1	20%	4,10,000.00	12%	1,20,000.00	2,90,000.00
2	32%	6,56,000.00	12%	1,20,000.00	5,36,000.00
3	19%	3,89,500.00	5%	50,000.00	3,39,500.00
4	12%	2,46,000.00	0%	-	2,46,000.00
5	12%	2,46,000.00	0%	-	2,46,000.00

These incremental depreciatios are considered for computation of profit befor tax and cash flow after tax.

Step 3,

Profit on sale of Asset after 5 years
Book value of new machine after 5 years				1,02,500.00
Sale value of new machine after 5 years				1,50,000.00
Profit on sale of Asset after 5 years				47,500.00

This Profit on sale of Asset after 5 years considered for Computing profit before tax of year 5

Step 4

Calculation of Annual Incremental Cash Inflow, Discount factor and present value of Annual Incremental Cash Inflow
		Years	1	2	3	4	5
Reduction in operating Costs			$6,50,000	$6,50,000	$6,50,000	$6,50,000	$6,50,000
Less incremental depreciation			$2,90,000	$5,36,000	$3,39,500	$2,46,000	$2,46,000
(-) Loss /(+)profit on sale of asset			-$1,65,000	-	-	-	$47,500
Incremental profit before tax			$1,95,000	$1,14,000	$3,10,500	$4,04,000	$4,51,500
Less : Tax @ 40%			$78,000	$45,600	$1,24,200	$1,61,600	$1,80,600
Incremental profit after tax			$1,17,000	$68,400	$1,86,300	$2,42,400	$2,70,900
Add: incremental Depreciation			$2,90,000	$5,36,000	$3,39,500	$2,46,000	$2,46,000
Sale value of New Machine after 5 years							$1,50,000
Incremental Cash inflow after tax			$4,07,000	$6,04,400	$5,25,800	$4,88,400	$6,66,900
Discount factor @ cost of capital 15%			0.869565217391	0.756143667297	0.657516232432	0.571753245593	0.497176735298
Present Value of incremental cashflow			$3,53,913.043478261	$4,57,013.232514178	$3,45,722.035012739	$2,79,244.285147637	$3,31,567.164770429

Step 5 Calculation of NPV

Total PV of icremental Cash inflow of 5 years			$17,67,459.760923240
Initial incremental Cash outlay			$19,55,000.000000000
Net Present Value			-$1,87,540.239076755
NPV rounded to two decimal			-1,87,540.24

Answer for Question 3. IRR is 11.10% (rounded to two decimal ) relevant calculation and formula as below

Formula for IRR = LR + ((NPV @LR / NPV @LR - NPV @HR)x (HR - LR), First we have to identify lowest rate (LR) in which we will get a positive NPV and we have to identify Highest rate (HR) in which we will get a negative NPV. Here HR = 12%, and LR = 10% and relevant calculations are as follows, here also

NPV = Present value of incremental cash inflow - incremental cash outlay,

Present value of incremental cash inflow = Annual incremental cash inflow x Discount Factor ( or PV factor),

Discount Factor ( or PV factor) = 1/(1+i)^n, here i is LR = 10% or 0.10, n = respective number of year upto and including 5.

year	Icremental Cash inflow	Disc. Factor @ 10%	PV of Icremnt. Cash inflow
1	4,07,000.00	0.909090909090909	$3,70,000.000000000
2	6,04,400.00	0.826446280991735	$4,99,504.132231405
3	5,25,800.00	0.751314800901578	$3,95,041.322314050
4	4,88,400.00	0.683013455365071	$3,33,583.771600300
5	6,66,900.00	0.620921323059155	$4,14,092.430348150
	Total PV of Icremntal Cash inflow		$20,12,221.656493910
	Initial incremental Cash outlay		$19,55,000.000000000
		NPV @ LR	$57,221.656493905

NPV = Present value of incremental cash inflow - incremental cash outlay,

Present value of incremental cash inflow = Annual incremental cash inflow x Discount Factor ( or PV factor),

Discount Factor ( or PV factor) = 1/(1+i)^n, here i is HR = 12% or 0.12, n = respective number of year upto and including 5. calculations are as follows

year	Icremental Cash inflow	Disc. Factor @ 12%	PV of Icremnt. Cash inflow
1	$4,07,000	0.892857142857143	$3,63,392.857142857
2	$6,04,400	0.797193877551020	$4,81,823.979591837
3	$5,25,800	0.711780247813411	$3,74,254.054300291
4	$4,88,400	0.635518078404831	$3,10,387.029492920
5	$6,66,900	0.567426855718599	$3,78,416.970078734
	Total PV of Icremntal Cash inflow		$19,08,274.890606640
	Initial incremental Cash outlay		$19,55,000.000000000
		NPV @ HR	-$46,725.109393361

Next step applying values in the formula LR + ((NPV @LR / NPV @LR - NPV @HR)x (HR - LR),

10% +(($57,221.656493905/($57,221.656493905-^-$46,725.109393361) x(12-10) = 10% +1.10098002579443% = 11.10098002579443%, rounded to two decimal = 11.10%

Answer for Question 4. Pay back period is 3 years and 312.24 days reounded

Pay back period is the time at which the investments are recovered. Here the cash flow are not same in all years, so we have to compute cumulative cash flow to identify in which year the cash inflows crossing the initial outlay, calculations are as follows

year	Icremental Cash inflow	Cumulative Cash flow
1	4,07,000.00	4,07,000.00
2	6,04,400.00	10,11,400.00
3	5,25,800.00	15,37,200.00
4	4,88,400.00	20,25,600.00
5	6,66,900.00	26,92,500.00

We know that 4^th year the cash inflows crossing the initial outlay. we have to identify exact period in 4th year at which cash inflows are crossing the initial outlay, here initial outlay is 1955000 which is computed in step 1 of answer 2

formula xact period in 4th year at which cash inflows are crossing the initial outlay, = (how much will need to cross the initial outlay / 4^th year cashflow) x 365 =

how much will need to cross the initial outlay =1955000-1537200 =417800

So ( 417800/ 488400) x 365 = 312.23791973792, Pay back period = 3 years +312.23791973792 days,

3 years and 312.24 days

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