https://file.aiquickdraw.com/mathbot/file/1727363641634cqdb1akw.jpg

To solve the problem presented in the image, we need to calculate two things: 

1. **Payback Period**
2. **Profitability**

### 1. **Payback Period**
The payback period is the time it takes for the initial investment to be recovered through the project's profits. 

#### Given:
- Initial Investment: Rs 6,00,000
- Profits after tax for each year:
  - Year 1: Rs 2,20,000
  - Year 2: Rs 1,50,000
  - Year 3: Rs 2,00,000
  - Year 4: Rs 1,50,000
  - Year 5: Rs 1,75,000

#### Calculation:
We sum the profits year by year until the total equals or exceeds the initial investment of Rs 6,00,000.

- **Year 1:** Rs 2,20,000
- **Year 2:** Rs 2,20,000 + Rs 1,50,000 = Rs 3,70,000
- **Year 3:** Rs 3,70,000 + Rs 2,00,000 = Rs 5,70,000
- **Year 4:** Rs 5,70,000 + Rs 1,50,000 = Rs 7,20,000

The investment is recovered in **Year 4**. 

**Payback Period = 3 years + \( \frac{(6,00,000 - 5,70,000)}{1,50,000} \)**
                   = 3 years + 2 months

So, the **Payback Period is 3 years and 2 months**.

### 2. **Profitability**
Profitability can be measured using various methods. A common method is the **Profitability Index (PI)**, which is calculated as the ratio of the present value of future cash flows to the initial investment. However, since this question does not provide a discount rate, we can estimate the overall profit generated relative to the investment.

#### Total Profit:
- Sum of all profits over 5 years:
  - Rs 2,20,000 + Rs 1,50,000 + Rs 2,00,000 + Rs 1,50,000 + Rs 1,75,000 = Rs 8,95,000
- Profitability (Net Profit) = Total Profits - Initial Investment
  - Rs 8,95,000 - Rs 6,00,000 = Rs 2,95,000

Therefore, the profitability in terms of net profit over the 5-year period is Rs **2,95,000**.

### Summary:
1. **Payback Period:** 3 years and 2 months
2. **Profitability (Net Profit):** Rs 2,95,000

Would you like any further details or have any questions?

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Here are five related questions:
1. What would be the impact on the payback period if the profits in Year 3 were lower?
2. How would you calculate the Payback Period if the cash flows were discounted?
3. What is the significance of the Payback Period in investment decision-making?
4. How can the Profitability Index be used to compare different projects?
5. What other methods can be used to measure the profitability of an investment?

**Tip:** The Payback Period is a simple and intuitive method but does not consider the time value of money, which can be crucial in long-term investments.

A company is considering a new project with an initial investment of Rs 6,00,000, salvage value Rs 50,000, and a project life of 5 years. The company needs to determine the payback period and profitability based on profits after tax over the years.

Learn how to calculate the payback period and profitability for an investment of Rs 6,00,000 with annual profits after tax over a 5-year period. This problem involves understanding investment analysis, payback period formulas, and basic profitability calculations.

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