Question

Caspian Sea Drinks is considering buying the J-Mix 2000. It will allow them to make and sell more product. The machine cost $1.84 million and create incremental cash flows of $522,368.00 each year for the next five years. The cost of capital is 10.27%. What is the net present value of the J-Mix 2000?

Answer 1

To calculate the Net Present Value (NPV) of the J-Mix 2000, we can use the following formula:

\[
NPV = \sum \frac{C_t}{(1 + r)^t} - C_0
\]

Where:
- \( C_t \) = cash flow at time t
- \( r \) = discount rate (cost of capital)
- \( t \) = time period
- \( C_0 \) = initial investment

Given:
- Initial investment \( C_0 = 1,840,000 \)
- Annual cash flow \( C_t = 522,368 \)
- Cost of capital \( r = 10.27\% = 0.1027 \)
- Number of years = 5

Let's calculate the present value of the cash flows for each of the five years:

\[
PV = \sum_{t=1}^{5} \frac{522,368}{(1 + 0.1027)^t}
\]

Calculating each term:

1. For \( t = 1 \):
\[
PV_1 = \frac{522,368}{(1 + 0.1027)^1} = \frac{522,368}{1.1027} \approx 473,033.11
\]

2. For \( t = 2 \):
\[
PV_2 = \frac{522,368}{(1 + 0.1027)^2} = \frac{522,368}{1.2161} \approx 429,053.34
\]

3. For \( t = 3 \):
\[
PV_3 = \frac{522,368}{(1 + 0.1027)^3} = \frac{522,368}{1.3404} \approx 389,021.79
\]

4. For \( t = 4 \):
\[
PV_4 = \frac{522,368}{(1 + 0.1027)^4} = \frac{522,368}{1.4815} \approx 352,722.65
\]

5. For \( t = 5 \):
\[
PV_5 = \frac{522,368}{(1 + 0.1027)^5} = \frac{522,368}{1.6416} \approx 318,906.54
\]

Now, summing all the present values:

\[
\text{Total PV} = PV_1 + PV_2 + PV_3 + PV_4 + PV_5
\]
\[
\text{Total PV} \approx 473,033.11 + 429,053.34 + 389,021.79 + 352,722.65 + 318,906.54 \approx 1,962,737.43
\]

Finally, we can find the NPV:

\[
NPV = \text{Total PV} - C_0
\]
\[
NPV = 1,962,737.43 - 1,840,000 \approx 122,737.43
\]

Thus, the Net Present Value (NPV) of the J-Mix 2000 is approximately **$122,737.43**.