Question

You+have+purchased+a+canning+machine+for+$5,000.+you+expect+the+machine+to+save+your+company+$3,325+each+year+for+the+next+10+years.+what+is+the+npv+of+the+machine?+use+a+discount+rate+of+10.8%.

Answer 1

The NPV of the canning machine involves discounting the expected yearly savings at a rate of 10.8% and then subtracting the initial cost of the machine to evaluate if the investment is worthwhile.

Step-by-step explanation:

The student has purchased a canning machine for $5,000 and expects it to save the company $3,325 each year for the next 10 years. To calculate the net present value (NPV) of the machine using a discount rate of 10.8%, we apply the NPV formula which accounts for the time value of money. This formula will discount the future savings back to their present value and then subtract the initial investment.

The NPV calculation involves finding the present value of each year's savings and then adding them up before subtracting the cost of the machine. A financial calculator or spreadsheet software can be used to perform this calculation efficiently.

NPV = Σ (P / (1+i)^n) - C

Where:

• P is the annual savings ($3,325)
• i is the discount rate (10.8% or 0.108)
• n is the year number
• C is the initial cost of the machine ($5,000)

Once all the present values for the 10 years are summed and the initial cost is subtracted, we obtain the NPV of the canning machine, which allows the company to decide whether the investment is financially viable or not.

Answer 2

The NPV of the machine is calculated by summing the present values of future savings over 10 years at a discount rate of 10.8% and then subtracting the initial cost of the machine, which is $5,000.

Step-by-step explanation:

To calculate the net present value (NPV) of the canning machine, we need to discount the future savings to the present using the given discount rate of 10.8%. The initial cost of the machine is $5,000, and it is expected to save the company $3,325 each year for the next 10 years.

Here is the step-by-step calculation:

1. First, calculate the present value of the annual savings for each year using the formula: Present Value = Future Value / (1 + r)^n, where r is the discount rate and n is the year.
2. Second, sum these present values to get the total present value of future savings.
3. Finally, subtract the initial cost of the machine from the total present value of future savings to get the NPV.

The NPV formula is: NPV = ∑(Future Cash Flows / (1 + r)^n) - Initial Investment, where the sum is from n=1 to n=number of periods.