You just bought equipment from Silver Island Media. You will receive a cash rebate of $2,700 from Silver Island Media in 4 years, pay $19,300 to Silver Island Media in 8 years, receive a cash rebate of $2,400 from Silver Island Media in 11 years, and pay $4,300 to Silver Island Media in 16 years. The discount rate is 17.93 percent per year. What is the present value of the cash flows associated with this transaction? Note: the correct answer is less than zero.



To calculate the present value (PV) of cash flows, we can use the formula for the present value of future cash flows:

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

Where:
- $C$ = Cash flow at time $t$
- $r$ = Discount rate (17.93% or 0.1793)
- $t$ = Time in years

### Cash flows:
1. Receive $ +2,700 $ in 4 years.
2. Pay $ -19,300 $ in 8 years.
3. Receive $ +2,400 $ in 11 years.
4. Pay $ -4,300 $ in 16 years.

### Step-by-step calculation:
1. **PV of $2,700 in 4 years:**

\[
PV_1 = \frac{2,700}{(1 + 0.1793)^4}
\]

2. **PV of $19,300 in 8 years:**

\[
PV_2 = \frac{-19,300}{(1 + 0.1793)^8}
\]

3. **PV of $2,400 in 11 years:**

\[
PV_3 = \frac{2,400}{(1 + 0.1793)^11}
\]

4. **PV of $4,300 in 16 years:**

\[
PV_4 = \frac{-4,300}{(1 + 0.1793)^16}
\]

Now, let's calculate the total present value of all the cash flows.The present value of the cash flows associated with this transaction is approximately $-3,679.12$. Since the present value is negative, it indicates a net cost when discounted at the rate of 17.93%.

Would you like more details or have any questions?

Here are 5 related questions to consider:
1. How does the choice of discount rate affect the present value?
2. What happens if you receive cash flows earlier or later in this example?
3. How would the calculation change if the discount rate were compounded monthly instead of annually?
4. What is the break-even discount rate where the present value becomes zero?
5. How could the future value of these cash flows be calculated?

**Tip:** When dealing with time value of money, always ensure the discount rate and time period are in the same units (e.g., both in years).

You just bought equipment from Silver Island Media. You will receive a cash rebate of $2,700 from Silver Island Media in 4 years, pay $19,300 to Silver Island Media in 8 years, receive a cash rebate of $2,400 from Silver Island Media in 11 years, and pay $4,300 to Silver Island Media in 16 years. The discount rate is 17.93 percent per year. What is the present value of the cash flows associated with this transaction? Note: the correct answer is less than zero.

Learn how to calculate the present value of future cash flows in a financial transaction involving payments and rebates over several years, with a 17.93% discount rate. Understand key concepts like the present value formula and the time value of money. Suitable for undergraduate finance students or advanced high school math learners.

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