What is the payback period for the following set of cash flows?  
Year	Cash Flow
0	−$ 4,300
1	1,200
2	2,800
3	1,200
4	1,400

To calculate the payback period, we need to determine how many years it takes for the initial investment to be recovered through the cumulative cash flows.

Here’s the set of cash flows:

- Initial Investment at Year 0: $ -4,300 $
- Year 1: $ 1,200 $
- Year 2: $ 2,800 $
- Year 3: $ 1,200 $
- Year 4: $ 1,400 $

### Step-by-Step Calculation

1. **Year 1**: The cumulative cash flow after Year 1 is:
   \[
   -4,300 + 1,200 = -3,100
   \]
   Still negative, so the payback period is not yet reached.

2. **Year 2**: The cumulative cash flow after Year 2 is:
   \[
   -3,100 + 2,800 = -300
   \]
   Still negative, so the payback period is not yet reached.

3. **Year 3**: The cumulative cash flow after Year 3 is:
   \[
   -300 + 1,200 = 900
   \]
   Now the cumulative cash flow is positive, so the payback period is somewhere between Year 2 and Year 3.

### Finding the Fraction of Year Needed

- After Year 2, we still need to recover $300.
- In Year 3, the cash flow is $1,200. Therefore, it will take a fraction of Year 3 to recover the remaining $300.
- The fraction is:
   \[
   \frac{300}{1,200} = 0.25
   \]

### Payback Period

The payback period is:
\[
\text{Payback Period} = 2 + 0.25 = 2.25 \text{ years}
\]

So, the payback period is **2.25 years**.

---

Would you like further details or have any questions?

Here are 5 related questions:
1. How is the discounted payback period different from the regular payback period?
2. Can payback period be a good metric for evaluating long-term projects?
3. What happens when the payback period is longer than the project's life?
4. How can you modify the cash flow if taxes or other costs are involved?
5. What is the impact of inflation on the payback period calculation?

**Tip**: Payback period is useful for understanding liquidity, but it doesn't account for the time value of money or cash flows beyond the payback point.

What is the payback period for the following set of cash flows? Year: 0, Cash Flow: -$4,300; Year: 1, Cash Flow: $1,200; Year: 2, Cash Flow: $2,800; Year: 3, Cash Flow: $1,200; Year: 4, Cash Flow: $1,400.

Find the payback period for a set of cash flows, including fractional recovery in Year 3. Learn the step-by-step process of calculating cumulative cash flows and determining the payback period for an investment of $4,300, with annual cash flows of $1,200, $2,800, $1,200, and $1,400. Suitable for finance students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation