To calculate the Net Present Value (NPV) of the J-Mix 2000, we need to find the present value of the incremental cash flows generated from the machine and then subtract the initial investment.
Step 1: Calculate the Present Value of Cash Flows
The formula to calculate the present value (PV) of cash flows is:
\[ PV = \frac{CF}{(1 + r)^t} \]
where:
- \( CF \) = cash flow for the year,
- \( r \) = discount rate (cost of capital),
- \( t \) = year.
In this case, the cash flow \( CF \) is $697,085, the discount rate \( r \) is 10.97% (or 0.1097), and \( t \) varies from 1 to 5.
We will sum the present value of cash flows for each of the 5 years.
Year 1:
\[ PV_1 = \frac{697085}{(1 + 0.1097)^1} = \frac{697085}{1.1097} \approx 629,834.74 \]
Year 2:
\[ PV_2 = \frac{697085}{(1 + 0.1097)^2} = \frac{697085}{(1.1097)^2} = \frac{697085}{1.2375} \approx 563,541.02 \]
Year 3:
\[ PV_3 = \frac{697085}{(1 + 0.1097)^3} = \frac{697085}{(1.1097)^3} = \frac{697085}{1.3762} \approx 507,025.92 \]
Year 4:
\[ PV_4 = \frac{697085}{(1 + 0.1097)^4} = \frac{697085}{(1.1097)^4} = \frac{697085}{1.5333} \approx 454,752.72 \]
Year 5:
\[ PV_5 = \frac{697085}{(1 + 0.1097)^5} = \frac{697085}{(1.1097)^5} = \frac{697085}{1.7095} \approx 407,843.59 \]
Step 2: Total Present Value of Cash Flows
Now, we find the total present value of cash flows from year 1 to year 5:
\[ PV_{total} = PV_1 + PV_2 + PV_3 + PV_4 + PV_5 \] \[ PV_{total} \approx 629,834.74 + 563,541.02 + 507,025.92 + 454,752.72 + 407,843.59 \approx 2,563,998.99 \]
Step 3: Calculate the Net Present Value (NPV)
Now, we subtract the initial investment from the total present value of cash flows:
\[ NPV = PV_{total} - \text{Initial Investment} \] \[ NPV = 2,563,998.99 - 1,160,000 \approx 1,403,998.99 \]
Final Result
Thus, the Net Present Value (NPV) of the J-Mix 2000 is approximately $1,403,998.99.
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