A financial asset has just paid a cash flow of $2.18 million. The cash flow is expected to grow by 3.68% per year for 25 years. After that the cash flows will stay constant in perpetuity. The required rate of return on the asset is 14%. What should the price of the asset be today?
 
$21.90 million
 
$20.60 million
 
$19.86 million
 
$21.31 million

To determine the price of the asset today, we need to calculate the present value (PV) of the expected cash flows. The cash flows are divided into two phases:

1. **Growth phase (Years 1 to 25):** Cash flows grow at 3.68% annually.
2. **Perpetual phase (Year 26 onward):** Cash flows remain constant.

### Step 1: Calculate the present value of cash flows during the growth phase

The cash flow for year $ t $ can be calculated as:
\[
CF_t = CF_0 \times (1 + g)^{t}
\]
where:
- $ CF_0 = 2.18 $ million (initial cash flow)
- $ g = 0.0368 $ (growth rate)
- $ t $ is the year number

The present value of these cash flows is the sum of the discounted cash flows from year 1 to 25:
\[
PV_{\text{growth}} = \sum_{t=1}^{25} \frac{CF_0 \times (1 + g)^t}{(1 + r)^t}
\]
where $ r = 0.14 $ is the required rate of return.

### Step 2: Calculate the present value of the perpetuity starting from year 26

The cash flow from year 26 onward will remain constant at the level of $ CF_{26} = CF_0 \times (1 + g)^{25} $. The present value of this perpetuity as of year 25 is:
\[
PV_{\text{perpetuity\ as\ of\ year\ 25}} = \frac{CF_{26}}{r}
\]

Then, discount this value back to today (year 0):
\[
PV_{\text{perpetuity\ today}} = \frac{CF_0 \times (1 + g)^{25}}{r \times (1 + r)^{25}}
\]

### Step 3: Calculate the total present value

The total price of the asset today is the sum of the present values of the two phases:
\[
\text{Price today} = PV_{\text{growth}} + PV_{\text{perpetuity\ today}}
\]

Now let's compute this.The calculated price of the asset today is approximately **$21.31 million**.

Thus, the correct answer is **$21.31 million**.

Would you like further details or have any questions? Here are some related questions you might find interesting:

1. How would the asset's price change if the required rate of return were lower?
2. What would be the effect of a higher growth rate on the asset's price?
3. How do perpetual cash flows impact the valuation of long-term assets?
4. How is the present value of a growing annuity calculated?
5. What are the risks associated with assuming a constant growth rate in asset valuation?

**Tip:** When valuing financial assets, small changes in the discount rate can have a significant impact on the asset's price, especially over long periods.

A financial asset has just paid a cash flow of $2.18 million. The cash flow is expected to grow by 3.68% per year for 25 years. After that, the cash flows will stay constant in perpetuity. The required rate of return on the asset is 14%. What should the price of the asset be today? 
Options:
 $21.90 million
 $20.60 million
 $19.86 million
 $21.31 million

Determine the price of a financial asset today that pays an initial cash flow of $2.18 million, growing annually by 3.68% for 25 years, with a perpetual constant cash flow thereafter. Using present value and perpetuity formulas, find the correct price given a 14% required rate of return.

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