AGECON 211 Practical 03: Discounted Project Appraisal: NPV, BCR, IRR and Discounted Payback
B.Sc. (Hons.) Agriculture | Semester 3 | AGECON 211 | Practical 03
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Learning objectives and assumptions
Calculate and interpret discounted measures using consistent cash flows. The example assumes time-0 investment, year-end receipts, a three-year life, and no additional salvage, tax or working-capital flows.
Net present value
NPV = Σ[Ct/(1+r)t], including negative C0. Positive NPV for an independent project indicates value above the specified required return under the assumptions. It does not guarantee realized returns.
Project A costs ₹1,00,000 now and produces ₹45,000 net cash inflow at each of three year-ends. At 10%:
| Year | Net cash flow | PV |
|---|---|---|
| 0 | −₹1,00,000 | −₹1,00,000.00 |
| 1 | ₹45,000 | ₹40,909.09 |
| 2 | ₹45,000 | ₹37,190.08 |
| 3 | ₹45,000 | ₹33,809.17 |
PV of inflows ≈ ₹1,11,908.34 and NPV ≈ ₹11,908.34.
BCR and profitability index
BCR = PV of specified benefits ÷ PV of specified costs. Define gross benefits and costs consistently. If the ₹45,000 flows are treated as net operating benefits and the initial outlay is the only separate cost, the simplified ratio is 1.1191. This also matches a profitability index of future discounted net inflows divided by initial investment. Do not claim a gross BCR using net flows without explaining this convention.
Internal rate of return
IRR makes NPV zero. For this series it is approximately 16.65%. Use trial rates or a financial function to verify. Interpolation between opposite-sign NPVs is approximate. Nonconventional cash flows can create multiple IRRs; project scale and timing can also cause ranking conflicts. Use NPV at the relevant required return when comparing mutually exclusive alternatives.
Discounted payback
After two years discounted inflows total ₹78,099.17. The remaining ₹21,900.83 divided by the year-3 discounted inflow ₹33,809.17 is about 0.648. Interpolated discounted payback is therefore about 2.65 years. Strictly year-end recovery occurs at year 3.
Sensitivity exercise
If annual inflows fall to ₹40,000 at the same discount rate, NPV becomes approximately −₹525.92. A modest adverse change can reverse the decision. Test input costs, utilization, selling price, delays and residual values separately and in combinations.
Spreadsheet checks
Use consistent nominal cash flows with nominal rates, or real flows with real rates. Many spreadsheet NPV functions discount the first supplied flow as year 1, so enter NPV(rate, future flows)+time-0 flow. IRR normally includes time 0 in the series. Keep loan proceeds and repayments out of a project cash-flow series when using a project-level return framework that already accounts for financing in its discount rate.
Revision and assessment
- State the example NPV at 10%.
- What does IRR represent?
- Why add the time-0 cash flow separately in a standard spreadsheet NPV calculation?
Answer guide
- Approximately ₹11,908.34.
- The discount rate at which NPV of the specified cash-flow series is zero.
- The initial flow is already at present value and should not be discounted one additional period.
Independent English study notes for the topics listed in the AGECON 211 course index. Consult your prescribed university syllabus for official course wording and assessment requirements. Numerical cases are hypothetical learning examples.
