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A machine cost rs. 6000. Operating cost of the machine is rs. 10000for each of the first five years and thereafter increasing every year by rs. 3000 from sixth and subsequent year. If discount rate is 10 percnetwhen should the machine be replaced ?
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A machine cost rs. 6000. Operating cost of the machine is rs. 10000for...
Introduction:
In this problem, we need to determine when a machine should be replaced based on its cost and operating cost.
Given Data:
- Cost of Machine (C) = Rs. 6000
- Operating Cost (O) = Rs. 10000 for each of the first five years
- Operating Cost increases by Rs. 3000 from the sixth year and so on.
- Discount Rate (D) = 10%
Calculations:
To determine when the machine should be replaced, we need to calculate the Present Value (PV) of costs and compare it with the PV of benefits.
PV of Costs:
- Cost of Machine (C) = Rs. 6000
- Operating Cost (O) = Rs. 10000 for each of the first five years
- Operating Cost increases by Rs. 3000 from the sixth year and so on.
- Use the formula: PV = C + (O/1+D)^t
Year 1: PV = 10000/1.1 + 6000 = Rs. 15909.09
Year 2: PV = 10000/1.1^2 + 6000/1.1 = Rs. 25289.26
Year 3: PV = 10000/1.1^3 + 6000/1.1^2 = Rs. 34504.77
Year 4: PV = 10000/1.1^4 + 6000/1.1^3 = Rs. 43659.78
Year 5: PV = 10000/1.1^5 + 6000/1.1^4 = Rs. 52758.86
Year 6: PV = 13000/1.1^6 + 6000/1.1^5 = Rs. 55877.49
Year 7: PV = 16000/1.1^7 + 6000/1.1^6 = Rs. 59071.45
Year 8: PV = 19000/1.1^8 + 6000/1.1^7 = Rs. 62341.88
Year 9: PV = 22000/1.1^9 + 6000/1.1^8 = Rs. 65689.18
Year 10: PV = 25000/1.1^10 + 6000/1.1^9 = Rs. 69113.03
PV of Benefits:
- Assume that the machine will be replaced after 10 years.
- Cost of New Machine (Cn) = Rs. 6000
- Salvage Value (S) = Rs. 2000
- Use the formula: PV = S/1+D^t - Cn/1+D^t
PV of Benefits = 2000/1.1^10 - 6000/1.1^10 = Rs. 2712.18
Decision:
- PV of Costs after 10 years = Rs. 69113.03
- PV of Benefits after 10 years = Rs. 2712.18
- Since the PV of Costs is much higher than the PV of Benefits, it is not beneficial
In this problem, we need to determine when a machine should be replaced based on its cost and operating cost.
Given Data:
- Cost of Machine (C) = Rs. 6000
- Operating Cost (O) = Rs. 10000 for each of the first five years
- Operating Cost increases by Rs. 3000 from the sixth year and so on.
- Discount Rate (D) = 10%
Calculations:
To determine when the machine should be replaced, we need to calculate the Present Value (PV) of costs and compare it with the PV of benefits.
PV of Costs:
- Cost of Machine (C) = Rs. 6000
- Operating Cost (O) = Rs. 10000 for each of the first five years
- Operating Cost increases by Rs. 3000 from the sixth year and so on.
- Use the formula: PV = C + (O/1+D)^t
Year 1: PV = 10000/1.1 + 6000 = Rs. 15909.09
Year 2: PV = 10000/1.1^2 + 6000/1.1 = Rs. 25289.26
Year 3: PV = 10000/1.1^3 + 6000/1.1^2 = Rs. 34504.77
Year 4: PV = 10000/1.1^4 + 6000/1.1^3 = Rs. 43659.78
Year 5: PV = 10000/1.1^5 + 6000/1.1^4 = Rs. 52758.86
Year 6: PV = 13000/1.1^6 + 6000/1.1^5 = Rs. 55877.49
Year 7: PV = 16000/1.1^7 + 6000/1.1^6 = Rs. 59071.45
Year 8: PV = 19000/1.1^8 + 6000/1.1^7 = Rs. 62341.88
Year 9: PV = 22000/1.1^9 + 6000/1.1^8 = Rs. 65689.18
Year 10: PV = 25000/1.1^10 + 6000/1.1^9 = Rs. 69113.03
PV of Benefits:
- Assume that the machine will be replaced after 10 years.
- Cost of New Machine (Cn) = Rs. 6000
- Salvage Value (S) = Rs. 2000
- Use the formula: PV = S/1+D^t - Cn/1+D^t
PV of Benefits = 2000/1.1^10 - 6000/1.1^10 = Rs. 2712.18
Decision:
- PV of Costs after 10 years = Rs. 69113.03
- PV of Benefits after 10 years = Rs. 2712.18
- Since the PV of Costs is much higher than the PV of Benefits, it is not beneficial
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A machine cost rs. 6000. Operating cost of the machine is rs. 10000for each of the first five years and thereafter increasing every year by rs. 3000 from sixth and subsequent year. If discount rate is 10 percnetwhen should the machine be replaced ?
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