Answer :
Answer: To calculate the payback period based on the given information:
1. **Identify the Relevant Data:**
- Cost of the project (initial investment): Rs. 22,84,000
- Annual annuity (cash inflow): Rs. 8,00,000 per year
- Useful life of the project: 5 years
2. **Calculate Annual Cash Inflow:**
Since the annuity is given as Rs. 8,00,000 per year, this is the cash inflow each year.
3. **Calculate Cumulative Cash Flow:**
Determine the cumulative cash flow over the years until the initial investment is recovered.
Year 1: Rs. 8,00,000
Year 2: Rs. 8,00,000 (Cumulative: Rs. 16,00,000)
Year 3: Rs. 8,00,000 (Cumulative: Rs. 24,00,000)
Year 4: Rs. 8,00,000 (Cumulative: Rs. 32,00,000)
Year 5: Rs. 8,00,000 (Cumulative: Rs. 40,00,000)
4. **Determine the Payback Period:**
- The payback period is the time it takes for the cumulative cash inflows to equal the initial investment.
Payback Period = Number of years until cumulative cash inflow ≥ Initial Investment
From the cumulative cash flow calculation:
- At the end of Year 4, the cumulative cash flow is Rs. 32,00,000.
- At the end of Year 5, the cumulative cash flow is Rs. 40,00,000.
Since the initial investment is Rs. 22,84,000, and the cumulative cash flow reaches Rs. 22,84,000 within the first 3 years (Rs. 24,00,000 at the end of Year 3), the payback period is approximately 3 years.
Therefore, the payback period for this project is approximately 3 years.
Calculating the payback period for a project with the given information requires considering the initial cost, annual annuity benefit, and ignoring the project's useful life. Here's how to find the payback period:
* Divide the initial cost by the annual annuity benefit:
Payback Period = Initial Cost / Annual Annuity Benefit
Payback Period = ₹2,28,40,000 / ₹8,00,000
Payback Period = 28.55 years
Since the payback period (28.55 years) is greater than the project's useful life (5 years), the project might not recover its initial cost within its functional lifespan. It's advisable to perform a more comprehensive analysis considering the project's cash flows throughout its useful life to determine its financial viability.
* Divide the initial cost by the annual annuity benefit:
Payback Period = Initial Cost / Annual Annuity Benefit
Payback Period = ₹2,28,40,000 / ₹8,00,000
Payback Period = 28.55 years
Since the payback period (28.55 years) is greater than the project's useful life (5 years), the project might not recover its initial cost within its functional lifespan. It's advisable to perform a more comprehensive analysis considering the project's cash flows throughout its useful life to determine its financial viability.