--- title: "Both BCR with FW, gradient revenue" subject: "Engineering Economics" chapter: 3 key: "semester_6/engineering_economics:bcr-fw-gradient-revenue-250000" source: https://www.bctengineer.com/q/semester_6/engineering_economics/bcr-fw-gradient-revenue-250000 site: BCT Engineering --- # Both BCR with FW, gradient revenue Engineering Economics · Chapter 3: Basic Methodologies of Engineering Economic Analysis - Asked in: 2069 Poush - Video: [Scenario analysis |Future formulation |Engineering Economics |Board Exam Solution in NEPALI](https://www.youtube.com/watch?v=csZ0F12UsF8) — OPengineer - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/engineering_economics/bcr-fw-gradient-revenue-250000 - Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-3 ## Question Determine both types of B/C ratio by using FW formulation. | Initial investment (Rs.) | 2,50,000 | |---|---| | Annual revenue (Rs.) | 50,000 at the end of first year and increasing by Rs. 30,000 for each year | | Annual O&M cost (Rs.) | 30,000 | | Salvage value (Rs.) | 50,000 | | Useful life (year) | 5 | | MARR | 15% | ## Short answer Conventional B/C = 1.05; modified B/C = 1.07. Both exceed 1, so the project is marginally acceptable at 15% MARR. ## Answer Revenue is a gradient series: 50,000, 80,000, 1,10,000, 1,40,000, 1,70,000 (base 50,000, G = 30,000). O&M = 30,000 per year, salvage 50,000 at year 5, MARR = 15%. ```text revenue: 50k 80k 110k 140k 170k O&M: 30k each year year : 1 2 3 4 5 yr 5: +50k salvage; yr 0: -2,50,000 ``` Factors at 15%, 5 years: (F/A) = 6.7424, (F/P) = 2.0114, (A/G) = 1.7228 - Equivalent uniform revenue = 50,000 + 30,000 (A/G, 15%, 5) = 50,000 + 30,000 × 1.7228 = 101,684 - FW(B) = 101,684 × 6.7424 = Rs 685,595 - FW(O&M) = 30,000 × 6.7424 = Rs 202,271 - FW(I) = 2,50,000 × 2.0114 = Rs 502,839 - S = Rs 50,000 **Conventional B/C** = FW(B) / [FW(I) + FW(O&M) − S] = 685,595 / (502,839 + 202,271 − 50,000) = 685,595 / 655,111 = **1.047** **Modified B/C** = [FW(B) − FW(O&M)] / [FW(I) − S] = (685,595 − 202,271) / (502,839 − 50,000) = 483,324 / 452,839 = **1.067** **Answer: conventional B/C = 1.05, modified B/C = 1.07. Both are slightly greater than 1, so the project is marginally acceptable at MARR = 15%.** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What type of series is the revenue? A. Arithmetic gradient: 50,000 base plus 30,000 per year B. Geometric growth C. Uniform D. Decreasing gradient Answer: A. Revenue is 50k, 80k, 110k, 140k, 170k. (Key point: Revenue pattern) 2. How is revenue converted to uniform annual form? A. 50,000 + 30,000(P/G) B. 50,000 x 5 C. 50,000 + 30,000(A/G, 15%, 5) = 101,684 D. 30,000 x (A/P) Answer: C. A/G converts a gradient into equivalent equal annual amounts. (Key point: Equivalent annual) 3. What is it? A. 0.95 B. 1.047 C. 1.067 D. 1.50 Answer: B. 685,595 / (502,839 + 202,271 - 50,000). (Key point: Conventional B/C) 4. What is it and what is the verdict? A. 0.95; reject B. 1.047; reject C. 1.50; strongly accept D. 1.067; marginally acceptable Answer: D. (685,595 - 202,271)/(502,839 - 50,000) = 1.067, slightly above 1. 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