You just bought equipment from Orange Ocean Furniture. You will receive a cash rebate of $4,100 from Orange Ocean Furniture in 3 years, pay $26,500 to Orange Ocean Furniture in 8 years, receive a cash rebate of $4,200 from Orange Ocean Furniture in 12 years, and pay $4,400 to Orange Ocean Furniture in 14 years. The discount rate is 14.10 percent per year. What is the value of the cash flows associated with this transaction? Round to the nearest dollar for your answer.

To find the value of the cash flows associated with this transaction, we need to calculate the **present value (PV)** of each cash flow using the given discount rate of **14.10%** per year.

The formula for calculating the present value of a future cash flow is:

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

Where:
- $ C $ = the future cash flow
- $ r $ = the discount rate (14.10% = 0.141)
- $ t $ = the number of years until the cash flow occurs

### Step-by-step calculations:

1. **Cash rebate in 3 years (receive $4,100):**
   \[
   PV = \frac{4100}{(1 + 0.141)^3}
   \]

2. **Payment in 8 years (pay $26,500):**
   \[
   PV = \frac{-26500}{(1 + 0.141)^8}
   \]

3. **Cash rebate in 12 years (receive $4,200):**
   \[
   PV = \frac{4200}{(1 + 0.141)^12}
   \]

4. **Payment in 14 years (pay $4,400):**
   \[
   PV = \frac{-4400}{(1 + 0.141)^14}
   \]

Let me calculate the present value for each of these cash flows.The present values of the individual cash flows are:

1. **Cash rebate in 3 years ($4,100):** $2,760
2. **Payment in 8 years (-$26,500):** -$9,225
3. **Cash rebate in 12 years ($4,200):** $863
4. **Payment in 14 years (-$4,400):** -$694

When these present values are summed up, the total present value of the cash flows is **- $6,296**.

This means the overall value of the transaction is negative, indicating that in today's terms, you are paying more than you are receiving.

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the importance of calculating the present value in financial decisions?
2. How does the discount rate affect the present value of cash flows?
3. What would happen if the discount rate was lower, say 10%?
4. How do these cash flows compare in value at different time periods?
5. Can you use the present value to compare different investment opportunities?

**Tip:** The further into the future a cash flow occurs, the smaller its present value will be when discounted.

Learn how to calculate the present value of future cash flows from a purchase made at Orange Ocean Furniture. This problem involves receiving rebates and making payments over several years, with a discount rate of 14.10%. Understand the steps to calculate present value and assess financial decisions.

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