NPV, IRR and Payback Period With a Worked Project
One project, three methods, a basic calculator. Here is how each method works and where it misleads.
₹100 received today is worth more than ₹100 received in three years, because today's money can earn a return in between. Capital budgeting puts every year's cash flow on the same footing by discounting it back to today. Payback ignores this. NPV and IRR do not.
In the CCP exam you get a basic calculator only (up to 8 functions, 12 digits; no scientific or financial calculator). Everything below is done with plain division and multiplication.
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The Worked Project
Outlay ₹100 lakh today. Cash inflows over a 5-year life. Cost of capital 12%.
0
Cash flow (₹ lakh)
(100)
Cumulative (₹ lakh)
(100)
1
Cash flow (₹ lakh)
30
Cumulative (₹ lakh)
(70)
2
Cash flow (₹ lakh)
35
Cumulative (₹ lakh)
(35)
3
Cash flow (₹ lakh)
40
Cumulative (₹ lakh)
5
4
Cash flow (₹ lakh)
30
Cumulative (₹ lakh)
35
5
Cash flow (₹ lakh)
20
Cumulative (₹ lakh)
55
| Year | Cash flow (₹ lakh) | Cumulative (₹ lakh) |
|---|---|---|
| 0 | (100) | (100) |
| 1 | 30 | (70) |
| 2 | 35 | (35) |
| 3 | 40 | 5 |
| 4 | 30 | 35 |
| 5 | 20 | 55 |
Method 1: Payback Period
- 1
Find the year the cumulative turns positive
After year 2, ₹35 lakh is still to be recovered. Year 3 brings in ₹40 lakh, so recovery happens during year 3.
- 2
Prorate the last year
Payback = 2 + 35 ÷ 40 = 2.875 years, roughly 2 years 10½ months.
- 3
Know its blind spots
Payback ignores the time value of money and ignores everything after the payback year. Here it ignores ₹50 lakh of inflows in years 4 and 5. A shorter payback is still useful as a quick risk screen: money comes back sooner.
Method 2: NPV at 12%
Discount factor for year n = 1 ÷ 1.12ⁿ. On a basic calculator: 1 ÷ 1.12 = 0.8929, then divide that answer by 1.12 again for each later year.
1
Cash flow
30
Discount factor at 12%
0.8929
Present value
26.787
2
Cash flow
35
Discount factor at 12%
0.7972
Present value
27.902
3
Cash flow
40
Discount factor at 12%
0.7118
Present value
28.472
4
Cash flow
30
Discount factor at 12%
0.6355
Present value
19.065
5
Cash flow
20
Discount factor at 12%
0.5674
Present value
11.348
PV of inflows
Cash flow
Discount factor at 12%
Present value
113.574
Less outlay
Cash flow
Discount factor at 12%
Present value
(100.000)
NPV
Cash flow
Discount factor at 12%
Present value
13.574
| Year | Cash flow | Discount factor at 12% | Present value |
|---|---|---|---|
| 1 | 30 | 0.8929 | 26.787 |
| 2 | 35 | 0.7972 | 27.902 |
| 3 | 40 | 0.7118 | 28.472 |
| 4 | 30 | 0.6355 | 19.065 |
| 5 | 20 | 0.5674 | 11.348 |
| PV of inflows | 113.574 | ||
| Less outlay | (100.000) | ||
| NPV | 13.574 |
Decision Rules
- NPV
- Present value of inflows minus present value of outflows. Accept if NPV is zero or more. Here ₹13.57 lakh, so accept.
- Benefit-cost ratio (profitability index)
- PV of inflows ÷ PV of outflows. Accept if 1 or more. Here 113.574 ÷ 100 = 1.14.
- IRR
- The discount rate at which NPV is exactly zero. Accept if IRR is at least the cost of capital (the hurdle rate).
- Discounted payback
- Payback worked on present values instead of raw cash flows. Here 3 + 16.839 ÷ 19.065 = 3.88 years, longer than simple payback because later rupees count for less.
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Method 3: IRR by Trial and Interpolation
No calculator in the hall finds IRR directly. Try two rates, one giving positive NPV and one negative, as close together as you can.
12%
Year 1 to 5 factors
0.8929, 0.7972, 0.7118, 0.6355, 0.5674
NPV (₹ lakh)
+13.57
16%
Year 1 to 5 factors
0.8621, 0.7432, 0.6407, 0.5523, 0.4761
NPV (₹ lakh)
+3.59
18%
Year 1 to 5 factors
0.8475, 0.7182, 0.6086, 0.5158, 0.4371
NPV (₹ lakh)
-0.88
| Rate | Year 1 to 5 factors | NPV (₹ lakh) |
|---|---|---|
| 12% | 0.8929, 0.7972, 0.7118, 0.6355, 0.5674 | +13.57 |
| 16% | 0.8621, 0.7432, 0.6407, 0.5523, 0.4761 | +3.59 |
| 18% | 0.8475, 0.7182, 0.6086, 0.5158, 0.4371 | -0.88 |
Interpolating Between 16% and 18%
- 1
Formula
IRR = lower rate + (NPV at lower rate ÷ (NPV at lower rate - NPV at higher rate)) × gap between the rates.
- 2
Plug in
IRR = 16 + (3.59 ÷ (3.59 + 0.88)) × 2 = 16 + (3.59 ÷ 4.47) × 2 = 16 + 1.61 = 17.61%.
- 3
Check
The exact IRR of this project is 17.60%, so a 2-point bracket lands within a few hundredths of a percent. Interpolating across a wide bracket, say 12% to 20% (NPV -5.04), gives 17.83%. The wider the bracket, the larger the error.
- 4
Decide
17.6% is above the 12% cost of capital, so IRR agrees with NPV: accept.
Why the Bank Cares
A project whose IRR only just beats the cost of capital has little room for error. Lenders compare project IRR with the weighted average cost of capital, and a riskier project is held to a higher discount rate. That is the same thing as a higher hurdle for IRR.
How the IIBF Exam Tests This
- check_circlePayback with uneven cash flows: cumulate until the sign changes, then prorate the last year.
- check_circleNPV with given discount factors: multiply, add, subtract the outlay. Watch for the outlay being spread over two years.
- check_circleIRR by interpolation between a positive and a negative NPV.
- check_circleConcept checks: IRR is the rate where NPV = 0; payback ignores time value and post-payback flows; a higher discount rate lowers NPV.
FAQs
What is the difference between NPV and IRR?expand_more
NPV gives a rupee figure: how much value the project adds at a chosen discount rate. IRR gives a percentage: the rate at which NPV becomes zero. For a single ordinary project they lead to the same accept or reject decision.
How do I calculate IRR without a financial calculator?expand_more
Find NPV at two rates, one positive and one negative, then interpolate: lower rate + (NPV at lower ÷ difference in NPVs) × gap in rates. Keep the two rates close for accuracy.
What is the main weakness of the payback method?expand_more
It ignores the time value of money and every cash flow after the payback year, so it can reject a project that earns well in its later years.
Can I use a financial calculator in the IIBF CCP exam?expand_more
No. IIBF allows a basic battery-operated calculator with up to 8 functions and 12 digits. Scientific and financial calculators are not allowed.
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