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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.

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