Suppose a software development company has undertaken a project that is expected to cost £160,000 to execute and the expected inflow is £25,000 per quarter for the first year, £30,000 per quarter thereafter. What is the payback period for the project?

To find the payback period, we need to determine how long it will take for the cumulative cash inflows to equal the initial investment of £160,000.

### Breakdown of the Cash Flows

1. **Initial Investment**: £160,000
2. **Cash Inflows**:
   - **First year**: £25,000 per quarter (4 quarters)  
   - **After the first year**: £30,000 per quarter

Let's calculate the cumulative cash inflows over time to see when they reach the initial investment amount.

### Year 1 (Quarters 1-4)
- Quarterly inflow = £25,000
- Total inflow for the first year = \( 25,000 \times 4 = 100,000 \)

After the first year, the cumulative inflow is **£100,000**. This does not yet cover the initial investment of £160,000.

### Year 2 (Quarters 5-8)
Starting in the second year, the quarterly inflow increases to £30,000.

1. **Quarter 5**:  
   Cumulative inflow after Quarter 5 = £100,000 + £30,000 = £130,000

2. **Quarter 6**:  
   Cumulative inflow after Quarter 6 = £130,000 + £30,000 = £160,000

At **Quarter 6**, the cumulative inflow reaches exactly **£160,000**, matching the initial investment.

### Conclusion
The payback period for the project is **1 year and 2 quarters (or 1.5 years)**.

Would you like more details on this calculation, or do you have other questions?

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Here are some related questions for further exploration:

1. How would the payback period change if the initial cost were different?
2. What if the quarterly inflow increased by a certain percentage each year?
3. How would a delay in receiving the quarterly payments affect the payback period?
4. What if the cash inflows varied each quarter rather than being constant?
5. How would incorporating a discount rate impact the payback period?

**Tip**: When calculating payback periods, always separate cash inflows by time periods to ensure accuracy in cumulative summing.

Learn how to calculate the payback period for a project with an initial investment of £160,000 and quarterly cash inflows of £25,000 in the first year and £30,000 thereafter. Follow a step-by-step breakdown of cumulative cash flow analysis to find when the initial investment is recouped. Suitable for students at the high school or college level.

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