Net Present Value (NPV), Internal Rate of Return (IRR), and Payback Period are essential capital budgeting and investment appraisal tools used to evaluate the profitability, risk, and liquidity of projects or investments. This page explains NPV as the difference between the present value of cash inflows and outflows, helping investors determine whether an investment is profitable in dollar terms, while IRR represents the discount rate that makes NPV zero, providing a percentage return to compare against the cost of capital. It also details the Payback Period and Discounted Payback Period, which measure the time required to recover the initial investment, highlighting the difference between simple payback (ignoring time value of money) and discounted payback (accounting for time value of money). Through practical examples, formulas, and step-by-step calculations, this guide demonstrates how investors, financial analysts, and corporate managers can use NPV, IRR, and payback metrics to make informed investment decisions, assess project viability, manage cash flow risk, and optimize capital allocation.
NPV, IRR ও Payback Period সহজ বাংলায় | Banking Diploma, BBA, MBA ও CMA Video Tutorial
Capital Budgeting এবং Investment Appraisal-এর সবচেয়ে গুরুত্বপূর্ণ বিষয়গুলোর মধ্যে রয়েছে Net Present Value (NPV), Internal Rate of Return (IRR), Payback Period (PBP) এবং Discounted Payback Period। এই ভিডিওতে এসব টপিক অত্যন্ত সহজ বাংলা ভাষায় ধাপে ধাপে ব্যাখ্যা করা হয়েছে, যাতে Banking Diploma (IBB), BBA, MBA, CMA, Finance & Banking এবং HSC Finance-এর শিক্ষার্থীরা সহজেই গাণিতিক সমস্যা সমাধান করতে পারে। পাশাপাশি Time Value of Money (TVM), Capital Budgeting Decision Rules, Cash Flow Analysis, Discount Factor, IRR Interpolation Technique, Project Evaluation এবং Investment Decision Making-এর বাস্তব প্রয়োগ উদাহরণসহ বিস্তারিত আলোচনা করা হয়েছে। এছাড়াও বিগত IBB, বিশ্ববিদ্যালয় ও পেশাগত পরীক্ষার গুরুত্বপূর্ণ প্রশ্নের সমাধান ও শর্টকাট কৌশলও তুলে ধরা হয়েছে।
আপনি যদি NPV Calculation, IRR Formula, Payback Period, Discounted Payback Period, Capital Budgeting, Time Value of Money, Project Evaluation, Investment Appraisal, IBB Banking Diploma, BBA, MBA, CMA অথবা Corporate Finance-এর গাণিতিক সমস্যা সহজভাবে আয়ত্ত করতে চান, তাহলে নিচের Play বাটনে ক্লিক করে সম্পূর্ণ ভিডিওটি দেখুন। এই ভিডিওটি শিক্ষার্থী, ব্যাংকার, ফাইন্যান্স পেশাজীবী এবং প্রতিযোগিতামূলক পরীক্ষার্থীদের জন্য সমানভাবে উপযোগী। ভিডিওটি শেষ করার পর নিচের Lecture Notes, Practice Problems এবং Online Quiz সম্পন্ন করে নিজের প্রস্তুতিকে আরও শক্তিশালী করুন।
What is Net Present Value (NPV)?
Net Present Value (NPV) is a financial metric used to evaluate the profitability of an investment or project. It represents the difference between the present value of cash inflows and the present value of cash outflows over a period of time. A positive NPV indicates that the projected earnings (in present value terms) exceed the anticipated costs, making the investment potentially profitable.
📘 Net Present Value (NPV) Formula
CFt = Cash flow at time t
r = Discount rate
n = Number of periods
✅ NPV > 0 → Accept
❌ NPV < 0 → Reject
↔️ NPV = 0 → Indifferent
Example:
Suppose you are considering an investment that requires an initial outlay of 10,000 and is expected to generate cash inflows of 3,000, 4,000, 5,000, and 6,000 over the next four years. The discount rate is 10%.
NPV=3,000/(1+0.10)1+4,000/(1+0.10)2+5,000/(1+0.10)3+6,000/(1+0.10)4−10,000
Calculating each term:
NPV=3,000/1.10 + 4,000/1.21+ 5,000/1.331+ 6,000/1.4641 −10,000
NPV=2,727.27+3,305.79+3,756.57+4,098.08−10,000
NPV=13,887.71−10,000=3,887.71
The NPV is $3,887.71, indicating the investment is profitable.
What is Internal Rate of Return (IRR)?
The Internal Rate of Return (IRR) is the discount rate that makes the Net Present Value (NPV) of all cash flows from a particular project or investment equal to zero. In other words, it is the rate of return at which the present value of cash inflows equals the present value of cash outflows. IRR is used to evaluate the attractiveness of an investment.
📘 Internal Rate of Return (IRR) Formula
CFt = Cash flow at time t
IRR = Internal rate of return (unknown)
n = Number of periods
✅ IRR > Cost of Capital → Accept
❌ IRR < Cost of Capital → Reject
↔️ IRR = Cost of Capital → Indifferent
Example:
Using the same example as above, the IRR is the rate rr that satisfies the equation:
0=3,000/(1+IRR)1+4,000/(1+IRR)2+5,000/(1+IRR)3+6,000/(1+IRR)4−10,0000
Solving for IRR requires trial and error or a financial calculator. Let’s assume the IRR is 20% (for illustration purposes).
0=3,000/1.20+4,000/1.44+5,000/1.728+6,000/2.0736−10,0000
0=2,500+2,777.78+2,893.52+2,893.52−10,0000
0=11,064.82−10,0000
≈1,064.820
Since the result is not zero, we adjust the IRR until the equation balances. Suppose the actual IRR is 25%:
0=3,000/1.25+4,000/1.5625+5,000/1.9531+6,000/2.4414−10,0000
0=2,400+2,560+2,560+2,457.83−10,0000
0=9,977.83−10,0000
≈−22.170
The IRR is approximately 25%, meaning the investment yields a 25% return.
Key Differences:
- NPV provides a dollar/Taka value of profitability, while IRR provides a percentage return.
- NPV is better for comparing projects of different sizes, while IRR is useful for understanding the return relative to the cost of capital.
What is Payback Period?
Payback Period and Discounted Payback Period are financial metrics used to evaluate the time it takes for an investment to recover its initial cost. They help assess the risk and liquidity of an investment.
The Payback Period is the time it takes for an investment to generate cash flows that equal the initial investment cost. It does not consider the time value of money.
How can we calculate Payback Period?
Formula:
Payback Period=Initial Investment/Annual Cashflow ⃒ If Cashflow is even.
Example:
- Initial Investment: $10,000
- Annual Cash Inflows: $2,500 per year
Payback Period=10,000/2,500=4 years
The investment will recover its cost in 4 years.
If cash inflows are uneven or the cumulative sum of cash inflow do not exactly match with initial investment, then the payback period is calculated by adding up the cash inflows until the initial investment is recovered by using the following formula.
📘 Payback Period Formula
📌 When Cash Flows are Even (Equal Annual Cash Inflows):
Payback Period = 10,000 / 2,500 = 4 years
📌 When Cash Flows are Uneven (Different Annual Cash Inflows):
Payback Period = A + (B / C)
A = Last year with negative cumulative cash flow
B = Absolute value of cumulative cash flow at year A
C = Cash flow in the year after A
Initial Investment = Tk. 10,000
| Year | Cash Flow | Cumulative Cash Inflow | Status |
|---|---|---|---|
| 1 | 3,000 | 3,000 | Negative |
| 2 | 3,000 | 6,000 | Negative |
| 3 ⬅️ | 3,000 | 9,000 | Negative (Last) |
| 4 | 3,000 | 12,000 | Positive ✅ |
Shorter payback period is preferred
📊 Useful for liquidity & risk assessment
Ignores time value of money
Ignores cash flows after payback period
Payback Period= Year (where CCF-Cumulative Cash Flow just become 0 or negative but after that become positive) + (Initial Investment- CCF)/ CF of after that year where cumulative sum exceeded the initial investment.
| Year | Cash Flow | Cumulative Discounted Cash Flow |
| 1 | $3,000 | $3,000 |
| 2 | $3,000 | $6,000 |
| 3 | $3,000 | $9,000 |
| 4 | $3,000 | $12,000 |
| 5 | $3,000 | $15,000 |
Payback Period= 3 + (10,000-9000)/3000 Years = 3.33 Years
What is Discounted Payback Period?
The Discounted Payback Period is similar to the payback period but accounts for the time value of money by discounting the cash flows. It measures how long it takes for the discounted cash flows to equal the initial investment.
📘 Discounted Payback Period Formula
📌 Discounted Payback Period accounts for the time value of money:
📝 Step-by-Step Calculation:
Calculate the Discount Factor for each period:
Where: r = discount rate, t = time period
Calculate the Discounted Cash Flow (DCF) for each period:
Then find the cumulative DCF for each year.
Identify the last year where the cumulative DCF is negative, then apply the formula:
A = Last year with negative cumulative DCF
B = Absolute value of cumulative DCF at year A
C = DCF in the year after A
📊 Example Calculation (Discount Rate = 10%):
| Year | Cash Flow | Discount Factor 1 / (1 + 0.10)t | DCF (10%) | Cumulative DCF | Status |
|---|---|---|---|---|---|
| 1 | 3,000 | 0.9091 | 2,727 | 2,727 | Negative |
| 2 | 3,000 | 0.8264 | 2,479 | 5,206 | Negative |
| 3 | 3,000 | 0.7513 | 2,254 | 7,460 | Negative |
| 4 ⬅️ | 3,000 | 0.6830 | 2,049 | 9,509 | Negative (Last) |
| 5 | 3,000 | 0.6209 | 1,863 | 11,372 | Positive ✅ |
✓ Accounts for time value of money
✓ Considers risk of future cash flows
✓ Better for long-term projects
✗ Ignores cash flows after payback period
✗ More complex than simple payback
✗ Requires estimating a discount rate
Key Differences between Payback Period and Discounted Payback Period
📋 Comparison: Payback Period vs Discounted Payback Period
| Feature | Payback Period | Discounted Payback Period |
|---|---|---|
| Time Value of Money | ❌ Ignored | ✅ Considered |
| Complexity | Simple | More Complex |
| Accuracy | Less Accurate | More Accurate |
| Risk Assessment | Moderate | Better |
| Preferred For | Short-term / Liquid projects | Long-term projects |
Written By-Md Kollol Hossain, CEO, CapitalinsightBD
To know more about financial terms, visit here.
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This article is for educational purposes only and does not constitute financial or investment advice.
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