You just bought equipment from Orange Cave Furniture. You will receive a cash rebate of $1,400 from Orange Cave Furniture in 2 years, pay $24,300 to Orange Cave Furniture in 7 years, receive a cash rebate of $3,700 from Orange Cave Furniture in 12 years, and pay $2,900 to Orange Cave Furniture in 17 years. The discount rate is 15.40 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 the cash flows, we need to discount each cash flow back to the present using the given discount rate of 15.40% per year. The formula to discount a future cash flow is:

\[
PV = \frac{\text{Future Value}}{(1 + r)^t}
\]

Where:
- $ r $ is the discount rate (15.40% or 0.154),
- $ t $ is the time period in years,
- Future Value is the cash flow at time $ t $.

Let’s break it down for each cash flow:

1. **Cash rebate of $1,400 in 2 years**:
\[
PV_1 = \frac{1,400}{(1 + 0.154)^2}
\]

2. **Payment of $24,300 in 7 years**:
\[
PV_2 = \frac{-24,300}{(1 + 0.154)^7}
\]

3. **Cash rebate of $3,700 in 12 years**:
\[
PV_3 = \frac{3,700}{(1 + 0.154)^12}
\]

4. **Payment of $2,900 in 17 years**:
\[
PV_4 = \frac{-2,900}{(1 + 0.154)^17}
\]

The total present value is the sum of the individual PVs:

\[
PV_{\text{total}} = PV_1 + PV_2 + PV_3 + PV_4
\]

Now let's calculate these values.The present value of the cash flows associated with this transaction is approximately $-\$7,455.34$, which is less than zero as expected.

Would you like more details or have any questions?

Here are five related questions to consider:

1. How does changing the discount rate affect the present value?
2. What if one of the cash flows occurred at a different time—how would that change the result?
3. How can future cash flows be planned to avoid a negative present value?
4. What impact does the frequency of compounding (e.g., quarterly vs annually) have on the present value calculation?
5. How does inflation influence the real value of future cash flows?

**Tip**: A higher discount rate decreases the present value of future cash flows, making future benefits appear less valuable today.

You just bought equipment from Orange Cave Furniture. You will receive a cash rebate of $1,400 from Orange Cave Furniture in 2 years, pay $24,300 to Orange Cave Furniture in 7 years, receive a cash rebate of $3,700 from Orange Cave Furniture in 12 years, and pay $2,900 to Orange Cave Furniture in 17 years. The discount rate is 15.40 percent per year. What is the present value of the cash flows associated with this transaction? Note: the correct answer is less than zero.

This problem involves calculating the present value of cash flows with a discount rate of 15.40% per year. Learn how to discount future cash flows back to the present and understand the time value of money. The cash flows include rebates and payments spread over 2, 7, 12, and 17 years.

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