Suppose there is a cash flow stream that has an inflow of $286 one period from now.  After that, the inflows will grow at the rate of 2% every period after that forever.  The risk-free rate is 6%.  Calculate the PV of the cash flow stream.  Round your final answer to the nearest dollar.

To calculate the present value (PV) of the given cash flow stream, we can use the formula for the present value of a growing perpetuity. The formula is:

\[
PV = \frac{C}{r - g}
\]

Where:
- $ C $ is the cash flow one period from now ($286).
- $ r $ is the risk-free rate (6% or 0.06).
- $ g $ is the growth rate of the cash flows (2% or 0.02).

### Step-by-step calculation:

1. **Identify the values:**
   \[
   C = 286,\quad r = 0.06,\quad g = 0.02
   \]

2. **Apply the formula:**
   \[
   PV = \frac{286}{0.06 - 0.02} = \frac{286}{0.04}
   \]

3. **Calculate the result:**
   \[
   PV = 7150
   \]

Thus, the present value of the cash flow stream is **$7,150**.

Let me know if you want further details or have any questions.

Here are 5 related questions:
1. How would the present value change if the risk-free rate increases to 8%?
2. What happens to the PV if the growth rate increases to 3%?
3. How is this formula for a growing perpetuity different from a regular perpetuity?
4. Can the formula be applied if the growth rate exceeds the risk-free rate?
5. How would you calculate the PV if the inflows stopped after a certain number of periods?

**Tip:** In a growing perpetuity, the growth rate must always be less than the discount rate for the formula to work!

Suppose there is a cash flow stream that has an inflow of $286 one period from now. After that, the inflows will grow at the rate of 2% every period after that forever. The risk-free rate is 6%. Calculate the PV of the cash flow stream. Round your final answer to the nearest dollar.

Learn how to calculate the present value of a growing perpetuity with an initial cash flow of $286, a growth rate of 2%, and a risk-free rate of 6%. This step-by-step guide walks you through the formula and provides a clear explanation for students in finance and business courses.

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