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📘 IRR & Payback Period in Mining – DGMS Exam Notes 

 Financial evaluation is a vital component of mine management. Before starting or expanding a mine, project managers and owners must assess whether the investment will yield satisfactory returns. Two major financial indicators are used:

1. Payback Period (PBP) – how long it takes to recover the investment.
2. Internal Rate of Return (IRR) – the rate at which the project’s Net Present Value (NPV) becomes zero.

These tools help determine whether a mining project is economically viable, ensuring that mine managers take rational, data-based decisions — an important competency for DGMS Management & Legislation papers.

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💰 Internal Rate of Return (IRR)

Definition:
IRR is the discount rate at which the Net Present Value (NPV) of a project’s cash inflows equals the initial investment.
Mathematically:
[
NPV = 0 = \sum \frac{R_t}{(1 + r)^t} - C_0
]
where

• ( R_t ) = Cash inflow at time t
• ( C_0 ) = Initial investment
• ( r ) = IRR (discount rate)

🔹 Concept:

• Higher IRR = More profitable project.
• If IRR > Cost of capital → Accept project.
• If IRR < Cost of capital → Reject project.

🔹 Example: A mine invests ₹10 crore and expects ₹3 crore per year for 5 years.
By trial and error or financial calculator, if the discount rate that gives NPV = 0 is 14%,
→ IRR = 14%. 🔹 Advantages:

• Considers time value of money.
• Easy to compare projects.
• Used for long-term mining investments.

🔹 Limitations:

• Assumes constant cash flow pattern.
• Difficult for uneven inflows.
• May show multiple IRRs if sign changes in cash flow.

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⏳ Payback Period (PBP) 

  Definition:
The time required for cumulative cash inflows to equal the initial investment. [
\text{Payback Period} = \frac{\text{Initial Investment}}{\text{Annual Cash Inflow}}
] 🔹 Example: If a mining company invests ₹8 crore and earns ₹2 crore annually,
[
PBP = 8 / 2 = 4 \text{ years.}
] 🔹 Decision Rule:

• Shorter PBP = Better liquidity.
• Used for quick decision-making in risk-prone mining projects.

🔹 Advantages:

• Simple and easy to compute.
• Highlights project liquidity risk.

🔹 Limitations:

• Ignores time value of money.
• Doesn’t measure profitability after recovery.

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⚙️ Mining Project Examples 🔸 Example 1 – Coal Washing Plant:

Year	Cash Flow (₹ Cr)	Discount @ 12%	PV
0	-10	—	-10
1	+3	0.893	2.68
2	+3	0.797	2.39
3	+3	0.712	2.14
4	+3	0.636	1.91
5	+3	0.567	1.70

Total PV = ₹10.82 Cr → NPV ≈ 0 → IRR ≈ 12.5%. 🔸 Example 2 – Haulage System Upgrade: Initial cost ₹4 crore, return ₹1 crore/year.
→ PBP = 4 years.
If cost of capital = 10% and IRR = 13%, project is accepted.

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📊 DGMS Exam Applications 

 DGMS Management & Legislation syllabus under “Financial Management” includes:

• Capital budgeting
• Payback period
• IRR
• Cost analysis and control
• Break-even chart

🔹 Typical DGMS Questions:

• “Define IRR and its significance.”
• “Explain difference between Payback Period and IRR.”
• “How are these used in mining project decisions?”

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⚡ Quick One-Liners

• IRR = Discount rate where NPV = 0.
• Higher IRR = Better investment.
• Payback = Time to recover investment.
• PBP ignores time value; IRR includes it.
• Shorter PBP preferred in high-risk mines.
• IRR vs Cost of capital → Decision criteria.
• DGMS focuses on both in management papers.

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🧾 Descriptive Model Answer 

  Q: What is the difference between Payback Period and IRR in project evaluation?

  Answer:
Payback Period (PBP) indicates the time required to recover investment through project cash inflows. It’s a simple liquidity measure but ignores time value.
Internal Rate of Return (IRR) considers the time value of money and gives the project’s actual return percentage.
For DGMS exams, both are used in evaluating mine projects under capital budgeting.
In short:

• PBP = Simplicity & Liquidity Focus
• IRR = Profitability & Time Value Focus

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🧩 25 MCQs – IRR & Payback Period in Mining 

  Q1. IRR stands for:
A. Internal Rate of Recovery
B. Internal Rate of Return
C. Incremental Return Ratio
D. Interest Rate Ratio
E. None
Answer: B.
Solution: IRR = Internal Rate of Return.

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Q2. IRR is the rate at which:
A. NPV = 0
B. NPV = Maximum
C. NPV = Minimum
D. Profit = 0
E. None
Answer: A.
Solution: IRR makes NPV zero.

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Q3. Payback Period represents:
A. Time to double investment
B. Time to recover investment
C. ROI percentage
D. Profit margin
E. None
Answer: B.
Solution: Time for initial cost recovery.

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Q4. Which method considers time value of money?
A. PBP
B. IRR
C. Both
D. None
Answer: B.
Solution: IRR includes discounting.

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Q5. Higher IRR implies:
A. Less profitable
B. More profitable
C. No effect
D. None
Answer: B.
Solution: Higher IRR = higher return.

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Q6. Payback period ignores:
A. Investment cost
B. Time value of money
C. Cash inflow
D. Project duration
E. None
Answer: B.
Solution: PBP ignores time value.

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Q7. Formula for PBP (constant inflow):
A. Total inflow / Outflow
B. Investment / Annual inflow
C. Investment × Cash flow
D. Inflow / NPV
E. None
Answer: B.
Solution: PBP = Investment ÷ Annual inflow.

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Q8. If cost of capital = 10%, IRR = 14% →
A. Reject
B. Accept
C. Neutral
D. Delay
E. None
Answer: B.
Solution: IRR > Cost → Accept project.

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Q9. In IRR, cash inflow pattern assumed as:
A. Uniform
B. Random
C. Negative
D. None
Answer: A.
Solution: Assumed uniform over years.

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Q10. IRR is found by:
A. Subtraction
B. Discounting and interpolation
C. Multiplication
D. None
Answer: B.
Solution: Trial and error or interpolation.

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Q11. IRR measures:
A. Project speed
B. Profitability
C. Liquidity
D. Wage cost
E. None
Answer: B.
Solution: Indicates profitability.

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Q12. DGMS syllabus covers IRR under:
A. Financial management
B. Safety
C. Legislation
D. Geology
E. None
Answer: A.
Solution: Part of Management & Legislation.

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Q13. The PBP of a ₹10 Cr project earning ₹2 Cr/year is:
A. 2 years
B. 4 years
C. 5 years
D. 6 years
E. None
Answer: B.
Solution: 10 ÷ 2 = 5 → 5 years.

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Q14. PBP is preferred for:
A. Long-term high-risk projects
B. Short-term risky projects
C. CSR planning
D. None
Answer: B.
Solution: Used for quick decision projects.

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Q15. When NPV = 0, IRR =
A. Cost of capital
B. NPV
C. Profit margin
D. None
Answer: A.
Solution: IRR equates NPV to zero.

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Q16. A project with PBP = 3 years and life = 10 years is:
A. Desirable
B. Undesirable
C. Marginal
D. None
Answer: A.
Solution: Fast recovery = desirable.

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Q17. IRR can have multiple values when:
A. Cash flow signs change
B. Fixed inflows
C. Single period
D. None
Answer: A.
Solution: Non-conventional cash flow pattern.

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Q18. IRR = 10%, Cost of capital = 12% →
A. Accept
B. Reject
C. Postpone
D. None
Answer: B.
Solution: IRR < Cost → Reject project.

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Q19. Advantage of IRR method:
A. Simple
B. Considers time value
C. Easy for unequal cash flow
D. None
Answer: B.
Solution: Considers discounting.

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Q20. IRR is best suited for:
A. Mining projects with long cash flows
B. Short-term trade
C. Only equipment purchases
D. None
Answer: A.
Solution: Used for long-term mining evaluation.

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Q21. NPV stands for:
A. Net Present Value
B. Nominal Project Value
C. Negative Payback Value
D. None
Answer: A.
Solution: Standard financial term.

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Q22. IRR value is determined when:
A. Inflows = Outflows (PV terms)
B. Profit = Cost
C. Time = 0
D. None
Answer: A.
Solution: NPV = 0 condition.

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Q23. PBP suitable for:
A. Preliminary screening
B. Long-term strategy
C. Auditing
D. None
Answer: A.
Solution: Used for early project filtering.

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Q24. IRR does not consider:
A. Reinvestment rate
B. Cash inflow
C. Cost
D. None
Answer: A.
Solution: Assumes same reinvestment rate.

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Q25. In mining, IRR and PBP help in:
A. Project evaluation and budgeting
B. Equipment maintenance
C. Safety inspection
D. None
Answer: A.
Solution: Used for investment decisions.

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