The manager of Automated Products is thinking to purchasea new machine that will cost 300,000 and has a usefullife of five years. The machine will yield (year-end) cost reductions to Automated Products of 50,000 in year1,T60,000 in year 2, 75,000 in year 3, and 790,000 in year 4 and 90,000 in year 5.a) What is the present value of the cost savings of the machine if the interest rate is 8 percent?b) Should the manager purchase the machine? State your answer with the calculation of Net Present Value.
Question
The manager of Automated Products is thinking to purchasea new machine that will cost 300,000 and has a usefullife of five years. The machine will yield (year-end) cost reductions to Automated Products of 50,000 in year1,T60,000 in year 2, 75,000 in year 3, and 790,000 in year 4 and 90,000 in year 5.a) What is the present value of the cost savings of the machine if the interest rate is 8 percent?b) Should the manager purchase the machine? State your answer with the calculation of Net Present Value.
Solution
To answer this question, we need to calculate the present value of the cost savings for each year and then sum them up. The formula for present value is:
PV = FV / (1 + r)^n
where:
- PV is the present value
- FV is the future value (the cost savings in this case)
- r is the interest rate
- n is the number of years
a) The present value of the cost savings:
- Year 1: PV = 50,000 / (1 + 0.08)^1 = 46,296.30
- Year 2: PV = 60,000 / (1 + 0.08)^2 = 51,440.33
- Year 3: PV = 75,000 / (1 + 0.08)^3 = 59,479.53
- Year 4: PV = 790,000 / (1 + 0.08)^4 = 614,462.14
- Year 5: PV = 90,000 / (1 + 0.08)^5 = 62,150.29
The total present value of the cost savings is the sum of these, which is 833,828.59.
b) To decide whether the manager should purchase the machine, we need to calculate the Net Present Value (NPV). The NPV is the total present value of the cost savings minus the cost of the machine.
NPV = Total PV - Cost of machine = 833,828.59 - 300,000 = 533,828.59
Since the NPV is positive, the manager should purchase the machine. It means that the machine will generate more savings than its cost, considering the time value of money.
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