In: Finance
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!
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 | ||||||