You will receive $100 at the end of year one, $200 at the end of year two, and $300 at the end of year three. What is the present value of these cash flows today if the discount rate is 13 percent annually?

To calculate the **present value (PV)** of these cash flows, we need to discount each future payment back to today using the given discount rate of 13% annually.

The present value of each cash flow can be calculated using the formula:

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

Where:
- $ PV $ = present value
- $ C $ = future cash flow
- $ r $ = discount rate (in decimal form)
- $ n $ = number of years in the future

We will calculate the present value for each year’s cash flow and then sum them up.

### Year 1:
\[
PV_1 = \frac{100}{(1 + 0.13)^1} = \frac{100}{1.13} \approx 88.50
\]

### Year 2:
\[
PV_2 = \frac{200}{(1 + 0.13)^2} = \frac{200}{(1.13)^2} \approx \frac{200}{1.2769} \approx 156.61
\]

### Year 3:
\[
PV_3 = \frac{300}{(1 + 0.13)^3} = \frac{300}{(1.13)^3} \approx \frac{300}{1.4436} \approx 207.79
\]

### Total Present Value:
\[
PV_{\text{total}} = PV_1 + PV_2 + PV_3 \approx 88.50 + 156.61 + 207.79 = 452.90
\]

So, the present value of the cash flows today is approximately **$452.90**.

Would you like further details or have any questions?

Here are some related questions you might consider:
1. How does the discount rate affect the present value of future cash flows?
2. What would the present value be if the discount rate was lower, say 10%?
3. How does the time period (n) affect the present value calculation?
4. Can the present value calculation be applied to uneven cash flows over time?
5. What happens if the payments occur more frequently, like semi-annually?

**Tip:** The higher the discount rate, the lower the present value of future cash flows.

Learn how to calculate the present value of future cash flows of $100, $200, and $300 over 3 years using a 13% discount rate. This step-by-step solution covers key finance concepts such as discounting and the time value of money. Suitable for undergraduate finance or economics students.

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