Solutions: Problem Analysis & Recommendations | Môn Engineering Economy - Trường Đại học Quốc tế, Đại học Quốc gia Thành phố Hồ Chí Minh

lOMoAR cPSD| 58583460 Engineering Economy Problem 1: - Given Information: • Initial Cost (P) = $120,000
• Annual electricity savings = 300,000 kWh/year • Cost of electricity = $0.10/kWh • Annual Benefit (A) = 300,000 kWh/year * $0.10/kWh = $30,000/year • Project Life (N) = 6 years • MARR (i) = 15% per year • Salvage Value (S) at end of 6 years = $8,000
• Annual operating and maintenance expenses = negligible Calculate Present Worth of Benefits (PW_B): • PW of annual savings = A * (P/A, i, N) (P/A, 15%, 6) = [(1 + 0.15)^6 - 1] / [0.15 * (1 + 0.15)^6] = [2.31306 - PW of annual savings = $30,000 * 3.7845 = $113,535 • PW of salvage value = S * (P/F, i, N) lOMoAR cPSD| 58583460 PW of salvage value = $8,000 * 0.4323 = $3,458.40 • Total PW_B = $113,535 + $3,458.40 = $116,993.40 - Calculate Present Worth of Costs (PW_C): • Theinitial cost is already a present value. PW_C = $120,000 - Calculate
Benefit-Cost Ratio (B-C Ratio): • B-C Ratio = PW_B / PW_C = $116,993.40 / $120,000 ≈ 0.9749 - Recommendation: Since the B-C Ratio (0.9749) is less than 1.0, the project is not economically justified. ➔ Do not proceed
with installing the retrofitted space-heating system. Problem 2: System PW of Costs PW of B/C Ratio (C) Benefits (B) 1 $1,000 $8,000 8.00 2 $4,000 $8,000 2.00 3 $4,000 $14,000 3.50 4 $10,000 $16,000 1.60 5 $12,000 $24,000 2.00 lOMoAR cPSD| 58583460 a. Which system has the greatest B-C ratio? We have: • System 1: B/C = 8.0 • System 2: B/C = 2.0 • System 3: B/C = 3.5 • System 4: B/C = 1.6 • System 5: B/C = 2.0 System 1 has the greatest B-C ratio (8.0). - Order alternatives by increasing cost. Include a "Do Nothing" (DN) option (C=0, B=0). • DN: C=0, B=0 • System 1: C=1,000, B=8,000 • System 2: C=4,000, B=8,000 • System 3: C=4,000, B=14,000 • System 4: C=10,000, B=16,000 • System 5: C=12,000, B=24,000 - Eliminate
alternatives with equal cost but lower benefits. System 2 and System 3 have the same
cost(4,000).System3hashigherbenefits (4,000). System 3 has higher benefits
(4,000).System3hashigherbenefits (14,000 vs $8,000 for System 2). So, eliminate System 2. - Revised order for incremental analysis: lOMoAR cPSD| 58583460 • DN: C=0, B=0 • System 1: C=1,000, B=8,000 (B/C = 8.0) • System 3: C=4,000, B=14,000 (B/C = 3.5) • System 4: C=10,000, B=16,000 (B/C = 1.6) • System 5: C=12,000, B=24,000 (B/C = 2.0) a All
remaining alternatives have B/C > 1.0, so they are individually acceptable. - Incremental Analysis: • Compare System 1 vs. DN: ΔC = 1,000 - ΔB = 8,000 - ΔB/ΔC = 8,000 / 1,000 = 8.0. Since 8.0 ≥ 1, System 1 is preferred over DN. Current best: System 1. • Compare System 3 vs. System 1: ΔC = 4,000 - 1,000 = 3,000 ΔB = 14,000 - 8,000 = 6,000 ΔB/ΔC = 6,000 / 3,000 = 2.0. Since 2.0 ≥ 1, System 3 is preferred over System 1. Current best: System 3. • Compare System 4 vs. System 3: ΔC = 10,000 - 4,000 = 6,000 ΔB = 16,000 - 14,000 = 2,000 ΔB/ΔC = 2,000 / 6,000 = 1/3 ≈ 0.33. Since 0.33 < 1, the increment to System 4 is lOMoAR cPSD| 58583460 not justified. System 3 remains preferred. • Compare System 5 vs. System 3 (since System 4 was rejected): ΔC = 12,000 - 4,000 = 8,000 ΔB = 24,000 - 14,000 = 10,000 ΔB/ΔC = 10,000 / 8,000 = 1.25. Since 1.25 ≥ 1, System 5 is preferred over System 3. Current best: System 5. b. Which system has the largest incremental B-C ratio (based on differences between alternatives)?
The incremental B-C ratios calculated during the sequential selection process were: • System 1 vs. DN: 8.0 • System 3 vs. System 1: 2.0 • System 4 vs. System 3: 0.33 (This increment was not accepted) • System 5 vs. System 3: 1.25 The largest of
these calculated incremental B-C ratios is
8.0 (for the increment from DN to System 1). c. Which system should be chosen? Based on the incremental B-C analysis, System 5 should be chosen.