Definition — What the Benefit‑Cost Ratio (BCR) measures
– The Benefit‑Cost Ratio (BCR) is a summary statistic from cost‑benefit analysis that compares the present value of a project’s expected benefits to the present value of its expected costs. It compresses a stream of future cash flows into a single ratio to aid project selection.
Key terms (brief)
– Present Value (PV): The current worth of a future cash flow after discounting by a chosen rate.
– Net Present Value (NPV): PV(benefits) − PV(costs).
– Discount rate: The rate used to convert future cash flows into present value; can be a required return, social discount rate or WACC (weighted average cost of capital).
– Internal Rate of Return (IRR): The discount rate that makes NPV = 0.
– Terminal value / salvage: Value at the end of the project life (sale, disposal, cleanup) included in PV calculations.
Formula (simple)
– BCR = PV of benefits / PV of costs
– If you report undiscounted sums, state that explicitly; best practice is to use discounted (present value) amounts.
How to calculate BCR — step‑by‑step
1. Define the project horizon (years of analysis).
2. List all incremental benefits and costs for each period (revenues, operating costs, taxes, capital expenditures, maintenance, disposal).
3. Choose an appropriate discount rate (e.g., WACC for corporate projects or a social discount rate for public projects).
4. Compute present value of each benefit and cost stream: PV = CashFlow / (1 + r)^t.
5. Sum PVs to get PV(benefits) and PV(costs). Include terminal/salvage values and any remediation costs in the final year.
6. Compute BCR = PV(benefits) / PV(costs).
7. Interpret the result (see next section) and run sensitivity analysis on key assumptions.
Interpreting BCR values
– BCR > 1.0: Present value of expected benefits exceeds present value of costs; generally indicates the project should produce a positive NPV and that the IRR exceeds the chosen discount rate.
– BCR = 1.0: Benefits and costs are equal in present value terms; NPV ≈ 0.
– BCR < 1.0: Costs exceed benefits in present value terms; project likely reduces value relative to the discount rate used.
Checklist before relying on a BCR
– Have you used a justified discount rate for the decision context?
– Are all incremental cash flows included (tax, inflation adjustments, operating changes, decommissioning)?
– Did you convert all future amounts to present value?
– Have you tested sensitivity to key inputs (discount rate, benefit size, timing)?
– Have you compared BCR alongside NPV and IRR?
– Does the analysis capture non‑monetary impacts or are these evaluated separately?
Worked numeric example (renovation leasing case)
Scenario:
– Company plans renovations that raise operating cash profit by $100,000 each year for three years.
– Equipment is leased with an upfront cost of $50,000 (paid at time 0).
– Use a discount rate of 2% (0.02) for present value calculations.
Step calculations:
1. PV of benefits (three annual payments):
– Year 1: 100,000 / (1.02)^1 = 98,039.22
– Year 2: 100,000 / (1.02)^2 = 96,116.18
– Year 3: 100,000 / (1.02)^3 = 94,246.07
– PV(benefits) = 98,039.22 + 96,116.18 + 94,246.07 = 288,401.47
2. PV of costs:
2. PV of costs:
– Upfront cost at time 0: PV(costs) = 50,000 (no discounting needed for a time-0 cash flow).
BCR calculation
– Benefit‑Cost Ratio (BCR) = PV(benefits) / PV(costs)
– Using PV(benefits) = 288,