Question

In: Finance

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!

Solutions

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)
(a*b*c)[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
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
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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