Question

Caspian Sea Drinks is considering buying the J-Mix 2000. It will allow them to make and sell more product. The machine cost $1.74 million and create incremental cash flows of $649,115.00 each year for the next five years. The cost of capital is 9.56%. What is the profitability index for the J-Mix 2000?

Answer 1

To calculate the profitability index (PI), we first need to calculate the present value of the incremental cash flows from the J-Mix 2000, then we can use the formula for the profitability index.

Step 1: Determine the Present Value of Cash Flows

The cash flows are $649,115 per year for 5 years. The formula to calculate the present value (PV) of an annuity is:

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

where:

• \( C \) = annual cash flow ($649,115)
• \( r \) = cost of capital (9.56% or 0.0956)
• \( n \) = number of years (5)

Substituting the values into the formula:

\[ PV = 649,115 \times \frac{1 - (1 + 0.0956)^{-5}}{0.0956} \]

Calculating the factor:

1. Calculate \( (1 + r)^{-n} \): \[ (1 + 0.0956)^{-5} \approx (1.0956)^{-5} \approx 0.6256 \]
2. Calculate \( 1 - (1 + r)^{-n} \): \[ 1 - 0.6256 = 0.3744 \]
3. Now calculate \( \frac{0.3744}{0.0956} \): \[ \frac{0.3744}{0.0956} \approx 3.914 \]
4. Finally, calculate the present value: \[ PV = 649,115 \times 3.914 \approx 2,543,517.76 \]

Step 2: Calculate the Profitability Index

The profitability index is calculated using the formula:

\[ PI = \frac{PV \text{ of cash flows}}{\text{initial investment}} \]

Where the initial investment for the J-Mix 2000 is $1.74 million.

Substituting the values:

\[ PI = \frac{2,543,517.76}{1,740,000} \approx 1.465 \]

Conclusion

The profitability index for the J-Mix 2000 is approximately 1.465.

Answer 2

Is PV of cash flow the same as NPV?

Answer 3

The Present Value (PV) of cash flows and Net Present Value (NPV) are related concepts, but they are not the same. Here’s a breakdown of the differences:

Present Value (PV)

• PV refers to the current worth of future cash flows discounted at a specific rate. It represents the value of expected cash flows from an investment, discounted back to the present to account for the time value of money.
• When calculating PV, you typically look only at the cash inflows (or the expected financial benefits) from the investment.

Net Present Value (NPV)

• NPV takes the concept of PV a step further. It is calculated by subtracting the initial investment cost from the total present value of the future cash flows.
• The formula for NPV is: \[ NPV = PV \text{ of Cash Inflows} - \text{Initial Investment} \]
• NPV gives you a more complete picture of the profitability of an investment, as it incorporates both the cash inflows from the investment and the outflow (the initial investment cost).

Summary

• PV is a measure of the value of future cash flows.
• NPV measures the profitability of an investment by taking into account the initial investment cost.

In the context of your earlier question about the J-Mix 2000, we calculated the present value of the cash flows generated by the machine. If we wanted to calculate the NPV, we would take that PV and subtract the initial cost of the machine ($1.74 million):

\[ NPV = PV - \text{Initial Investment} = 2,543,517.76 - 1,740,000 \approx 803,517.76 \]

This NPV would indicate how much value is added (or lost) by making the investment in the J-Mix 2000.