Using a discount rate of 5%, what are the PV of the following CFs? 
Year 1: $20,000
Year 2: $25,000
Year 3: ($40,000)

To calculate the **Present Value (PV)** of the cash flows, we'll use the formula for the present value of each individual cash flow:

\[
PV = \frac{CF}{(1 + r)^t}
\]

Where:
- $CF$ is the cash flow in each year,
- $r$ is the discount rate (5% or 0.05),
- $t$ is the year in which the cash flow occurs.

### Cash Flows:
- Year 1: $20,000
- Year 2: $25,000
- Year 3: ($40,000)

#### Step-by-step calculation:

1. **Year 1**: $ CF = 20,000 $
\[
PV_1 = \frac{20,000}{(1 + 0.05)^1} = \frac{20,000}{1.05} \approx 19,047.62
\]

2. **Year 2**: $ CF = 25,000 $
\[
PV_2 = \frac{25,000}{(1 + 0.05)^2} = \frac{25,000}{1.1025} \approx 22,679.62
\]

3. **Year 3**: $ CF = -40,000 $
\[
PV_3 = \frac{-40,000}{(1 + 0.05)^3} = \frac{-40,000}{1.157625} \approx -34,555.23
\]

#### Total Present Value:

\[
PV_{\text{total}} = PV_1 + PV_2 + PV_3
\]
\[
PV_{\text{total}} = 19,047.62 + 22,679.62 - 34,555.23 \approx 7,172.01
\]

### The total present value of the cash flows is approximately **$7,172.01**.

Would you like more details or have any questions? 

Here are 5 related questions to explore further:
1. How does changing the discount rate affect the present value of future cash flows?
2. How would the PV change if the cash flow in Year 3 was positive?
3. Can you explain why the third cash flow results in a negative present value?
4. What happens to the PV when future cash flows are larger than initial cash flows?
5. How would we calculate the Net Present Value (NPV) if an initial investment was included?

**Tip**: Always keep in mind that as the discount rate increases, the present value of future cash flows decreases!

Using a discount rate of 5%, what are the PV of the following CFs? Year 1: $20,000 Year 2: $25,000 Year 3: ($40,000)

Learn how to calculate the present value of cash flows using a 5% discount rate. This example includes cash flows of $20,000, $25,000, and ($40,000) over three years, demonstrating the application of the time value of money concept. Ideal for students in Grades 11-12 or college.

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