What is the present value of the following set of cash​ flows, discounted at 15 % per​ year? year 1= $102, Year 2=-102, Year 3 = 200, Year 4=-200

The present value (PV) of a set of cash flows is calculated using the formula:

\[
PV = \frac{{C_1}}{{(1 + r)^1}} + \frac{{C_2}}{{(1 + r)^2}} + \frac{{C_3}}{{(1 + r)^3}} + \dots + \frac{{C_n}}{{(1 + r)^n}}
\]

Where:
- $C_t$ is the cash flow in year $t$,
- $r$ is the discount rate (15% or 0.15 in this case),
- $t$ is the year number.

Given:
- Year 1: $C_1 = 102$,
- Year 2: $C_2 = -102$,
- Year 3: $C_3 = 200$,
- Year 4: $C_4 = -200$,
- Discount rate: $r = 0.15$.

Now, let's calculate the present value (PV) for each year.

### Step-by-step calculation:

\[
PV_1 = \frac{{102}}{{(1 + 0.15)^1}} = \frac{{102}}{{1.15}}
\]
\[
PV_2 = \frac{{-102}}{{(1 + 0.15)^2}} = \frac{{-102}}{{(1.15)^2}}
\]
\[
PV_3 = \frac{{200}}{{(1 + 0.15)^3}} = \frac{{200}}{{(1.15)^3}}
\]
\[
PV_4 = \frac{{-200}}{{(1 + 0.15)^4}} = \frac{{-200}}{{(1.15)^4}}
\]

Summing these values will give us the total present value. I'll calculate this for you.The total present value (PV) of the given cash flows, discounted at 15% per year, is approximately **$28.72**.

Would you like further details or have any questions?

Here are some related questions to deepen your understanding:
1. How does changing the discount rate affect the present value of cash flows?
2. What is the future value of these cash flows, assuming the same discount rate?
3. How would the present value change if one of the cash flows were delayed by a year?
4. What is the significance of negative cash flows in present value calculations?
5. How do you calculate the present value for irregularly spaced cash flows?

**Tip:** Understanding the time value of money is key to making informed financial decisions, as future cash flows are worth less today due to inflation and opportunity costs.

What is the present value of the following set of cash​ flows, discounted at 15 % per​ year? Year 1 = $102, Year 2 = -$102, Year 3 = $200, Year 4 = -$200

Calculate the present value of cash flows of $102 in year 1, -$102 in year 2, $200 in year 3, and -$200 in year 4, using a 15% discount rate. Understand the Time Value of Money and how discounting affects cash flow valuation.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation