Facility A estimates that building a $16,000,000 manufacturing facility can enable it to handle its overhauling...

Facility A estimates that building a $16,000,000 manufacturing facility can enable it to handle its overhauling work by replacing its current contract of $55,000 per machine per year with Facility B. it is estimated that the new facility will have a life of 20 years, a salvage value of $150,000 at the end of its life and handle the overhauling costs at $40,000 per machine per year. Annual costs (for both cases) are expected to increase 3.5% per year. Assuming an interest rate of 12%, find the least number of machines that Facility A must operate to economically justify building its own facility.

I need to know the lowest number of machines required to be able to justify running Facility A. I've been trying to work this out in an excel spreadsheet but cant get my formulas correct. if you could please show your work that would be greatly appreciated it!

Expert Solution

	Initial investment		=	$16,000,000

1)	Annual saving(per machine)		=	$55000-$40000
			=	$15,000 (
2)
	Let no. of machines be x(total saving=15000*x for year 1 & so on)
					*(abc)[please keep 'x' in separate cell for applying formula]*

		(a)	(b)	©
		annual saving		PVF@ 12%	Discounted savings
	1	15000	x	0.8929	$13,392.8571	x
	2	15525	x	0.7972	$12,376.4349	x
	3	16068.38	x	0.7118	$11,437.1519	x
	4	16630.77	x	0.6355	$10,569.1538	x
	5	17212.85	x	0.5674	$9,767.0305	x
	6	17815.29	x	0.5066	$9,025.7827	x
	7	18438.83	x	0.4523	$8,340.7902	x
	8	19084.19	x	0.4039	$7,707.7838	x
	9	19752.14	x	0.3606	$7,122.8181	x
	10	20443.46	x	0.3220	$6,582.2471	x
	11	21158.98	x	0.2875	$6,082.7015	x
	12	21899.55	x	0.2567	$5,621.0679	x
	13	22666.03	x	0.2292	$5,194.4690	x
	14	23459.34	x	0.2046	$4,800.2459	x
	15	24280.42	x	0.1827	$4,435.9416	x
	16	25130.23	x	0.1631	$4,099.2853	x
	17	26009.79	x	0.1456	$3,788.1788	x
	18	26920.13	x	0.1300	$3,500.6831	x
	19	27862.34	x	0.1161	$3,235.0063	x
	20	28837.52	x	0.1037	$2,989.4924	x
				Total discounted savings	$140,069.1221	x
				Total discounted savings

	PV of terminal value		=	150,000*0.103666
			=	15550

	By equation of NPV,no. of machine is
		Initial investment	=	PV of discounted cashflow+PV of salavge value

		16,000,000	=	(140069.12*x)+15555
		15984445	=	140069.12 *x
		114.1183	=	x


	So the no.of machines is 114.1183 or 115 mchines.
	Theres may be minor difference due to decimal places.Please do not downvote answer on that basis

Verification of answer

		annual saving		PVF@ 12%	Discounted savings
	1	15000	114.118	0.8929	$1,528,370.0893
	2	15525	114.118	0.7972	$1,412,377.7164
	3	16068.38	114.118	0.7118	$1,305,188.3362
	4	16630.77	114.118	0.6355	$1,206,133.8642
	5	17212.85	114.118	0.5674	$1,114,596.9192
	6	17815.29	114.118	0.5066	$1,030,006.9744
	7	18438.83	114.118	0.4523	$951,836.8023
	8	19084.19	114.118	0.4039	$879,599.1878
	9	19752.14	114.118	0.3606	$812,843.8923
	10	20443.46	114.118	0.3220	$751,154.8469
	11	21158.98	114.118	0.2875	$694,147.5594
	12	21899.55	114.118	0.2567	$641,466.7178
	13	22666.03	114.118	0.2292	$592,783.9759
	14	23459.34	114.118	0.2046	$547,795.9063
	15	24280.42	114.118	0.1827	$506,222.1098
	16	25130.23	114.118	0.1631	$467,803.4675
	17	26009.79	114.118	0.1456	$432,300.5258
	18	26920.13	114.118	0.1300	$399,492.0038
	19	27862.34	114.118	0.1161	$369,173.4142
	20	28837.52	114.118	0.1037	$341,155.7890
				Total discounted savings	$15,984,450.0985
				Total discounted savings


		Discounted salavage value		=	15550
		Equation
		Initial investment		=	Discounted savings+discounted salvage value
				=	15,984,450+15550
		16,000,000		=	$16,000,000

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