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Question
Machine A costs ₹ 15,000 and machine B costs ₹ 20,000. The annual income from A and B are ₹ 4,000 and ₹ 7,000 respectively. Machine A has a life of 4 years and B has a life of 7 years. Find which machine may be purchased. (Assume discount rate 8% p.a) [(1.08)–4 = 0.7350, (1.08)–7 = 0.5835]
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Solution
For Machine A:
Present value of outflow = ₹ 15,000
a = ₹ 4000, i = 8% = 0.08, n = 4
P = `"a"/"i" [1 - (1 + "i")^"n"]`
= `4000/0.08 [1 - (1 + 0.08)^4]`
= `4000/0.08 [1 - (1.08)^4]`
= `4000/0.08 [1 - 0.7350]`
= 50,000 (0.265)
= ₹ 13,250
For Machine B:
Present value of outflow = ₹ 20,000
a = ₹ 7000, i = 8% = 0.08, n = 7
P = `"a"/"i" [1 - (1 + "i")^"n"]`
= `7000/0.08 [1 - (1 + 0.08)^7]`
= `7000/0.08 [1 - (1.08)^7]`
= `7000/0.08 [1 - 0.5835]`
= 87,500 (0.4165)
= ₹ 36443.75
Machine B is more than Machine A, Machine B may be purchased.
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