--- title: "Purchase or hire construction equipment" subject: "Engineering Economics" chapter: 4 key: "semester_6/engineering_economics:purchase-or-hire-equipment-1000000" source: https://www.bctengineer.com/q/semester_6/engineering_economics/purchase-or-hire-equipment-1000000 site: BCT Engineering --- # Purchase or hire construction equipment Engineering Economics · Chapter 4: Comparative Analysis of Alternatives - Asked in: 2065 Chaitra, 6 marks - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/engineering_economics/purchase-or-hire-equipment-1000000 - Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-4 ## Question A construction company needs an equipment which costs Rs 10,00,000 and has salvage value of Rs. 1,00,000 at the end of 10 years. The equipment supplier is also willing to provide the equipment on hire for Rs 1,25,000 per year for 10 years. What will you do? Purchase or Hire. MARR = 12%. ## Short answer Annual equivalent cost of purchase = 10,00,000(A/P,12%,10) − 1,00,000(A/F,12%,10) = Rs 1,71,286. Hire cost is Rs 1,25,000 per year. Hire is cheaper by Rs 46,286 per year; choose hiring. ## Answer Compare the annual equivalent cost of owning the equipment with the yearly hire charge over the same 10 years at MARR = 12%. **Cash-flow diagram (purchase, Rs):** ```text year 0 1 ... 9 10 −10,00,000 0 ... +1,00,000 (salvage) ``` **Hire:** −1,25,000 at the end of each of years 1 to 10. #### Annual cost of purchase ```text AEC(purchase) = P(A/P,12%,10) − S(A/F,12%,10) (A/P,12%,10) = 0.17698 (A/F,12%,10) = 0.05698 = 10,00,000(0.17698) − 1,00,000(0.05698) = 176,984 − 5,698 = Rs 171,286 per year ``` #### Annual cost of hire AEC(hire) = Rs 1,25,000 per year. | Option | Annual equivalent cost (Rs) | |---|---| | Purchase | 171,286 | | Hire | 1,25,000 | PW check: PW(hire) = 1,25,000(P/A,12%,10) = 1,25,000(5.6502) = Rs 706,278; PW(purchase) = 10,00,000 − 1,00,000(P/F,12%,10) = Rs 967,803. **Answer: Hire the equipment.** It costs Rs 1,25,000 per year against Rs 171,286 per year for buying, a saving of about Rs 46,286 per year (assuming no other operating cost differences). ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. How are purchase and hire compared? A. By comparing initial cost with one year of hire B. By comparing annual equivalent cost of owning with the yearly hire charge C. By comparing salvage value with hire charge D. By ignoring MARR Answer: B. Both options are converted to cost per year over the same 10 years at MARR 12%. (Key point: Basis of comparison) 2. How is the salvage value treated in AEC(purchase)? A. Added: + S(A/F,12%,10) B. Multiplied by (A/P,12%,10) C. Ignored D. Subtracted after conversion: - S(A/F,12%,10) Answer: D. AEC = P(A/P) - S(A/F); salvage reduces the annual cost. (Key point: AEC of purchase formula) 3. AEC(purchase) is about Rs 171,286 and hire is Rs 125,000 per year. What is the decision? A. Hire, saving about Rs 46,286 per year B. Purchase, because it is owned C. Purchase, because salvage value is positive D. Indifferent Answer: A. Hire has the lower annual cost, so hire the equipment. 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