Payback period
Formula:
[ \text{Payback Period} = \text{Years before final year} + \left( \frac{\text{Investment remaining in final year}}{\text{Cash flow in final year}} \right) ]
Some Practice Questions for Payback Period with Answers.
??? Question
## Question:
A Firm is considering purchase two machinery, P and Q, given the following cash flows and an initial investment of ₹200,000 for each.Calculate it by payback period?
**Cash Flows:**
| Year | Machine P | Machine Q |
|------|-----------|-----------|
| 1 | 60,000 | 20,000 |
| 2 | 80,000 | 60,000 |
| 3 | 100,000 | 80,000 |
| 4 | 60,000 | 120,000 |
| 5 | 40,000 | 80,000 |
## Answer:
### Steps for Calculating Payback Period:
1. Calculate cumulative cash flow for each year until it equals or exceeds the initial investment.
2. Identify the year in which the cumulative cash flow first exceeds the initial investment.
3. Calculate the fraction of the year needed to pay back the remainder of the investment.
### Steps for Machine P:
**Formula:**
\[ \text{Payback Period} = \text{Years before final year} + \left( \frac{\text{Investment remaining at start of final year}}{\text{Cash flow in final year}} \right) \]
**Calculation:**
- Year 1: 60,000
- Year 2: 60,000 + 80,000 = 140,000
- Year 3: 140,000 + 100,000 = 240,000
At the start of Year 3, 60,000 is needed to recover the full investment.
\[ \text{Payback Period for P} = 2 + \frac{60,000}{100,000} = 2.6 \text{ years} \]
### Steps for Machine Q:
**Calculation:**
- Year 1: 20,000
- Year 2: 20,000 + 60,000 = 80,000
- Year 3: 80,000 + 80,000 = 160,000
- Year 4: 160,000 + 120,000 = 280,000
At the start of Year 4, 40,000 is needed to recover the full investment.
\[ \text{Payback Period for Q} = 3 + \frac{40,000}{120,000} \approx 3.33 \text{ years} \]
### Conclusion:
- The payback period for Machine P is approximately **2.6 years**.
- The payback period for Machine Q is approximately **3.33 years**.
so Machine P is better than Machine Q which has less payback period for the same investment.
??? Question ## Question:
Neeraj Books Ltd. is considering the purchase of a new machine. There are two alternative models X and Y. Prepare a statement of profitability showing the payback period from the following information:
| Particulars | Machine X | Machine Y |
|----------------------------------------------|-----------|-----------|
| Cost of machine | 1,80,000 | 3,00,000 |
| Estimated life in Years | 10 yrs | 15 yrs |
| Estimated savings in scrap per year | 12,000 | 15,000 |
| Additional cost of supervision per year | 14,400 | 19,200 |
| Additional cost of maintenance per year | 8,400 | 13,200 |
| Cost of indirect material per year | 7,200 | 9,600 |
| Estimated savings in wages: | | |
| Workers not required | 150 | 200 |
| Wages per worker per year | 720 | 720 |
Assume tax at 50% of profit.
Which model would you recommend?
##**Answer:**
| Particulars | Machine X | Machine Y |
|----------------------------------------------|------------|------------|
| Estimated Savings in scrap | 12,000 | 18,000 |
| Estimated Savings in wages (720 * Workers) | 1,08,000 | 1,44,000 |
| **Total savings (A)** | **1,20,000** | **1,52,000** |
| Estimated cost of Additional materials | 7,200 | 9,600 |
| Cost of supervision | 14,400 | 19,200 |
| Additional cost of Maintenance | 8,400 | 13,200 |
| **Total additional cost (B)** | **30,000** | **42,000** |
| Annual Cash inflow (A-B) | 90,000 | 1,20,000 |
| Less: Depreciation (Cost/Life) | 18,000 | 20,000 |
| **Profit before tax** | **72,000** | **100,000** |
| Less: Tax (50% of profit) | 36,000 | 50,000 |
| **Profit after tax** | **36,000** | **50,000** |
| Add: Depreciation | 18,000 | 20,000 |
| Profit after tax and depreciation (Annual Cash inflow) | 54,000 | 70,000 |
| Payback period (Original Investment/Annual Cash inflow) | 180,000/54,000 | 300,000/70,000 |
| **Payback period** | **3.33 years** | **4.28 years** |
Considering the profit after tax, Machine Y seems more profitable in the long run even though it has a higher initial cost.