Machine costs a company 1 million and its effective life is estimated to be 20 years. if the scrap is expected to realize 50000 only. the sum to be invested every year at 13.25% compounded annually for 20 years to replace the machine which would cost 30% more than its present value
To calculate the sum to be invested every year, we need to find the present value of the machine and then calculate the annual investment needed to replace it.
1. Calculate the future value of the machine at the end of its effective life:
Future Value = Scrap Value = $50,000
2. Calculate the present value of the machine:
Present Value = Future Value / (1 + interest rate)^n
Where n is the number of years
Present Value = $50,000 / (1 + 0.1325)^20
Present Value ≈ $7,442.31
3. Calculate the cost of replacing the machine, which is 30% more than its present value:
Replacement Cost = Present Value + (Present Value * 0.30)
Replacement Cost = $7,442.31 + ($7,442.31 * 0.30)
Replacement Cost ≈ $9,679.00
4. Calculate the annual investment needed to replace the machine over 20 years:
Annual Investment = Replacement Cost / ((1 + interest rate)^n - 1) / interest rate
Annual Investment = $9,679 / ((1 + 0.1325)^20 - 1) / 0.1325
Annual Investment ≈ $328.83
Therefore, the sum to be invested every year at a compounded annual interest rate of 13.25% for 20 years to replace the machine that would cost 30% more than its present value is approximately $328.83.
To calculate the sum to be invested every year at a rate of 13.25% compounded annually for 20 years, we need to find the future value of the machine plus the scrap value after 20 years.
1. Calculate the future value of the machine:
Present Value = $1,000,000
Interest Rate = 13.25% (compounded annually)
Number of years = 20
Future Value of machine = Present Value × (1 + Interest Rate)^Number of years
Future Value of machine = $1,000,000 × (1 + 0.1325)^20
2. Calculate the total cost of replacement machine:
Total cost = Future Value of machine + Scrap value
Total cost = Future Value of machine + $50,000
3. Calculate the amount to be invested every year for 20 years:
Amount to be invested = Total cost ÷ (1 + 0.3)^20
Note: The present value of the machine is not accounted for in this calculation, as we are assuming the entire cost needs to be accumulated over 20 years.
Let's calculate the values step by step:
Step 1: Calculate the future value of the machine:
Future Value of machine = $1,000,000 × (1 + 0.1325)^20
Future Value of machine ≈ $7,011,910.34
Step 2: Calculate the total cost of replacement machine:
Total cost = $7,011,910.34 + $50,000
Total cost ≈ $7,061,910.34
Step 3: Calculate the amount to be invested every year for 20 years:
Amount to be invested = $7,061,910.34 ÷ (1 + 0.3)^20
Amount to be invested ≈ $96,192.61
Therefore, the sum to be invested every year at a rate of 13.25% compounded annually for 20 years to replace the machine, which would cost 30% more than its present value, is approximately $96,192.61.