Question

Caspian Sea Drinks is considering buying the J-Mix 2000. It will allow them to make and sell more product. The machine cost $1.95 million and create incremental cash flows of $657,598.00 each year for the next five years. The cost of capital is 10.95%. What is the net present value of the J-Mix 2000?

Answer 1

To find the Net Present Value (NPV) of the J-Mix 2000 machine, we need to calculate the present value of the future cash flows and then subtract the initial investment.

**Given:**
- Cost of the machine = $1,950,000
- Incremental cash flows per year = $657,598
- Number of years = 5
- Cost of capital (discount rate) = 10.95%

**Step 1: Calculate the Present Value (PV) of the cash flows.**

The formula for the present value of an annuity is:

\[
PV = C \times \left( \frac{1 - (1 + r)^{-n}}{r} \right)
\]

Where:
- \( C \) is the cash flow per period ($657,598),
- \( r \) is the discount rate (10.95% or 0.1095),
- \( n \) is the number of periods (5 years).

Now, we can plug in the values:

\[
PV = 657,598 \times \left( \frac{1 - (1 + 0.1095)^{-5}}{0.1095} \right)
\]

Calculating the term \((1 + 0.1095)^{-5}\):

\[
1 + 0.1095 = 1.1095
\]
\[
(1.1095)^{-5} \approx 0.5907
\]

Now substituting back into the formula:

\[
PV = 657,598 \times \left( \frac{1 - 0.5907}{0.1095} \right)
\]
\[
PV = 657,598 \times \left( \frac{0.4093}{0.1095} \right)
\]
\[
PV = 657,598 \times 3.7374 \approx 2,457,330.80
\]

**Step 2: Calculate the NPV.**

Now that we have the present value of cash flows, we can calculate the NPV:

\[
NPV = PV - \text{Initial Investment}
\]
\[
NPV = 2,457,330.80 - 1,950,000 = 507,330.80
\]

**Conclusion:**
The net present value (NPV) of the J-Mix 2000 is approximately **$507,330.80**.