FE MECHANICAL – Engineering_economics_high_difficulty

#1. A project requires investments of $75,000 at time 0, $25,000 at end of year 2, and $15,000 at end of year 4. It generates revenues of $28,000 per year for years 1-6 and $35,000 per year for years 7-10. Using MARR=11%, what is the NPV?

$32,458

$52,340

$68,750

$45,762

#2. A 25-year mortgage loan of $350,000 has a nominal interest rate of 4.75% compounded monthly. The borrower pays 1.5 points at closing. What is the effective nominal annual interest rate (APR) considering points?

5.15%

4.75%

4.88%

5.02%

#3. A public project costs $3,500,000, has annual user benefits of $480,000, annual non-user benefits of $95,000, annual disbenefits of $45,000, and annual O&M costs of $85,000. Using a 30-year life and i=4%, what is the benefit-cost ratio?

1.42

1.56

1.71

1.28

#4. Option A: Replace equipment costing $75,000, 8-year life, salvage $12,000, AOC $9,500. Option B: Overhaul existing for $35,000, extending life by 5 years, AOC $14,000, salvage $5,000. At MARR=12%, which has lower equivalent annual cost?

A with EAC=$22,876

B with EAC=$22,876

A with EAC=$21,450

B with EAC=$21,450

#5. A project costs $200,000 with revenues of $75,000/year and operating costs of $25,000/year for 6 years. Straight-line depreciation to $20,000 salvage. Tax rate 35%, after-tax MARR 9%. What is after-tax NPV?

$35,250

$8,245

$15,678

$22,456

#6. Construction expenditures: $180,000 at end of year -3, $320,000 at end of year -2, $250,000 at end of year -1, $100,000 at time 0. Interest during construction is 9%. What is total capitalized investment at time 0?

$965,000

$925,873

$850,000

$892,450

#7. Build full capacity now for $2,200,000 or stage: half capacity now for $1,450,000, expand in year 6 for $1,100,000. At i=12%, what is present worth savings from staging?

$245,000

$125,450

$305,000

$192,734

#8. Cash flows: Year 0=-$120,000, Year 1=+$350,000, Year 2=-$250,000. This has multiple IRRs. Using quadratic formula approach, what are the two IRR values?

15% and 35%

8% and 22%

20% and 80%

25% and 100%

#9. The present worth of all costs for Project A is $285,000 over a 15-year life. Project B has present worth costs of $425,000 over a 25-year life. At i=7%, which has lower EUAC?

B with EUAC=$31,285

A with EUAC=$36,465

B with EUAC=$36,465

A with EUAC=$31,285

#10. Machine A: Fixed costs $55,000/year, variable costs $9.50/unit. Machine B: Fixed costs $95,000/year, variable costs $6.25/unit. Machine C: Fixed costs $150,000/year, variable costs $3.75/unit. At 15,000 units, which has lowest total cost?

A with total $197,500

All equal

C with total $206,250

B with total $188,750

#11. $225,000 loan at 6.5% annual interest repaid over 25 years. What is the principal portion of the 8th payment?

$4,258

$6,450

$5,127

$5,843

#12. Company has taxable income of $320,000. Tax rates: 15% on first $50,000, 25% on $50,001-$100,000, 34% on $100,001-$335,000, 39% on amounts above $335,000. What is total tax liability?

$95,050

$108,050

$124,800

$100,450

#13. Capital structure: 30% debt at 5.5% before-tax, 10% preferred stock at 8%, 60% equity at 14%. Tax rate 32%. What is WACC?

11.35%

10.52%

9.72%

10.92%

#14. Project can be continued for 5 more years generating $45,000/year with $25,000 terminal value, or abandoned now for $180,000. At MARR=14%, what is advantage of continuing vs abandoning?

$35,000 (Continue)

$0 (Indifferent)

-$14,250 (Abandon)

$12,750 (Continue)

#15. At MARR=13%. A: First cost $48,000, AOC $8,500, salvage $6,000, life 4 years. B: First cost $72,000, AOC $6,000, salvage $10,000, life 6 years. C: First cost $95,000, AOC $4,500, salvage $15,000, life 8 years. Over 24-year LCM, which has lowest PW of costs?

C with PW=$298,450

A with PW=$298,450

C with PW=$275,892

B with PW=$285,234

#16. Equipment costs $145,000, salvage value $18,000. Expected total production: 250,000 units. Year 1: 45,000 units, Year 2: 52,000 units. What is cumulative depreciation through Year 2?

$43,500

$49,308

$52,750

$58,000

#17. Buy equipment: $120,000, AOC $8,500, salvage $18,000 after 7 years. Maintenance agreement $4,500/year extra. Or lease: $22,500/year with maintenance included. At MARR=10%, which is more economical and what is PW difference?

Lease, saves $8,450

Buy, saves $8,450

Lease, saves $15,250

Buy, saves $15,250

#18. Option 1: $18,000 at 8.5% nominal compounded monthly for 8 years. Option 2: $17,500 at 8.8% nominal compounded quarterly for 8 years. Which has higher future value and by how much?

Option 1 by $525

Option 2 by $1,250

Option 1 by $1,250

Option 2 by $525

#19. Project X: Investment $85,000, returns $28,000/year for 5 years. Project Y: Investment $85,000, returns $22,000/year for 8 years. At what interest rate are NPVs equal?

15.8%

13.2%

10.5%

18.4%

#20. Project: $175,000 investment, $35,000 working capital at time 0, additional $15,000 working capital at year 3. Annual revenue $65,000 for 7 years. All working capital recovered at end. At MARR=11%, what is NPV?

$68,750

$55,340

$42,580

$82,450

#21. Public project: Initial investment $4,200,000, annual benefits $720,000, annual disbenefits $85,000, annual O&M $145,000, major rehabilitation $600,000 at year 15. Life 30 years, i=5%. What is modified B/C ratio?

1.48

1.15

1.65

1.32

#22. Defender: Current market value $32,000, salvage $8,000 in 4 years, AOC $13,500. Challenger: Cost $85,000, salvage $15,000 in 8 years, AOC $7,500, overhaul $12,000 at year 4. At MARR=15%, which has better AW?

Defender with AW=-$23,876

Challenger with AW=-$23,876

Challenger with AW=-$21,450

Defender with AW=-$21,450

#23. Equipment costs $250,000, 5-year MACRS. Year 1 rate=20%, Year 2=32%, Year 3=19.2%. BTCF=$85,000/year. Tax rate 30%. What is sum of ATCF for years 1-3?

$225,750

$212,450

$196,800

$178,500

#24. Project generates real cash flows of $55,000/year for 6 years. Inflation 4%/year, real MARR 6%/year. What is present worth using nominal cash flows and market interest rate?

$245,780

$295,000

$278,450

$262,340

#25. At MARR=12%. A: Investment $150,000, annual benefit $42,000, life 6 years. B: Investment $225,000, annual benefit $58,000, life 6 years. C: Investment $300,000, annual benefit $72,000, life 6 years. Do-nothing available. Select?

B

C

Do Nothing

A

#26. Equipment bought 3 years ago for $95,000. DDB depreciation with 6-year life. Can sell now for $35,000. Tax rate 28%. What are net after-tax proceeds?

$38,250

$28,450

$32,875

$35,000

#27. Retailer offers: $22,000 cash or $3,000 down plus $650/month for 36 months. What is implied nominal annual interest rate?

9.8%

12.4%

17.2%

14.8%

#28. Machine A: Capacity 2,500 units/year, cost $95,000, 6-year life, no salvage, variable cost $18/unit. Machine B: Capacity 4,000 units/year, cost $145,000, 6-year life, $12,000 salvage, variable cost $14/unit. Expected production 2,000 units. At MARR=12%, which has lower total annual cost?

A with TAC=$59,250

B with TAC=$62,450

B with TAC=$55,780

A with TAC=$55,780

#29. Cash flows: Year 1=$6,000, Year 2=$9,000, Year 3=$12,000, Year 4=$8,000, Year 5=$5,000. At i=9%, what is future worth at end of year 5?

$40,000

$44,578

$48,250

$52,000

#30. Fixed costs $280,000, variable costs $32/unit, selling price $52/unit. Current sales 20,000 units. If sales increase 12%, what is percentage increase in operating profit?

12%

36%

48%

24%

#31. Equipment costs $180,000, AOC $48,000, salvage $25,000, life 6 years. Annual production 6,500 units. At MARR=13%, what minimum selling price per unit justifies investment?

$15.75

$21.50

$18.25

$12.50

#32. Annual operating costs: Year 1=$28,000, escalating at 6%/year through year 7. Interest rate 11%/year. What is present worth of these escalating costs?

$165,000

$125,450

$138,275

$152,340

#33. Investment $90,000 at time 0; revenues $25,000/year for years 1-4; additional investment $40,000 at year 4; revenues $35,000/year for years 5-10; salvage $18,000 at year 10. At i=10%, what is NPV?

$68,450

$78,250

$42,580

$55,234

#34. Investment $125,000. Annual cash flows $35,000. Declining salvage: Year 1=$95,000, Year 2=$72,000, Year 3=$52,000, Year 4=$35,000, Year 5=$20,000. At end of which year does cumulative cash flow plus salvage first exceed investment?

Year 3

Year 1

Year 2

Year 4

#35. At what compound interest rate will an investment triple in approximately 12 years?

9%

10%

8%

6%

#36. Current: price $120/unit, sales 8,000 units, fixed costs $220,000, variable costs $75/unit. If price reduced 15% and volume increases 25%, what is change in annual profit?

Decrease of $34,000

Increase of $44,000

Decrease of $18,000

Increase of $26,000

#37. Perpetual endowment pays $12,000/year forever, first payment at end of year 8. At i=6%, what is present worth at time 0?

$118,450

$133,012

$200,000

$148,250

#38. Cash flows: Year 0=-$80,000, Year 1=+$200,000, Year 2=-$125,000. Using the sign changes rule, how many possible IRRs exist?

1

0

2

3

#39. Present worth of all costs is $325,000 over a 14-year life. At i=9%, what is EUAC?

$45,250

$41,678

$36,458

$52,000

#40. Machine A: Fixed $65,000/year, variable $7.50/unit. Machine B: Fixed $110,000/year, variable $4.25/unit. Machine C: Fixed $175,000/year, variable $2.50/unit. Above what volume is Machine C preferred?

30,000 units

26,000 units

22,500 units

18,000 units

#41. Investment $110,000, annual revenues $32,000/year. At MARR=11%, what is unrecovered investment balance at end of year 4?

$42,000

$18,450

$25,678

$33,250

#42. A project’s NPV is $28,000 with investment $95,000 and annual cash flows of $32,000 for 5 years. If the investment increases by 12% and cash flows decrease by 8%, what is the approximate new NPV at MARR=10%?

$15,250

-$5,250

$8,750

$2,450

#43. Equipment costs $115,000, salvage $15,000, life 6 years. Using DDB with switch to straight-line when beneficial, what is book value at end of year 4?

$28,456

$34,250

$23,750

$18,450

#44. A project has present worth of $68,000 at time 0. At i=13%, what is equivalent worth at end of year 5?

$108,250

$145,000

$95,450

$125,345

#45. Investment $145,000, annual revenues $52,000, annual costs $18,000, salvage $22,000 at end of 8-year life. At MARR=12%, what is net annual worth?

$18,000

$4,250

$12,750

$8,456

#46. Public project: Investment $4,500,000, annual user benefits $520,000, annual non-user benefits $125,000, annual disbenefits $65,000, annual O&M $95,000. Life 35 years, i=4%. What is B/C ratio?

1.75

1.18

1.42

1.58

#47. Company has loans: $85,000 at 5.5%, $65,000 at 7.2%, $45,000 at 8.5%. What is weighted average interest rate?

7.07%

6.85%

7.25%

6.58%

#48. Investment $150,000. Cash flows: Year 1=$50,000, Year 2=$55,000, Year 3=$60,000. At MARR=14%, what is project balance at end of year 3?

$0

$8,250

-$5,875

-$12,450

#49. Company uses market MARR of 16%. Expected inflation rate 4.5%/year. What is real MARR?

10.53%

12.00%

11.00%

11.48%

#50. Lessor purchases equipment for $145,000, expects residual value $22,000 at end of 6-year lease. Required return 12%. What annual lease payment (end of year)?

$35,750

$38,250

$28,450

$32,158

#51. Four scenarios: Optimistic (15% probability, NPV=$120,000), Most Likely (45% probability, NPV=$55,000), Conservative (25% probability, NPV=$15,000), Pessimistic (15% probability, NPV=-$35,000). What is expected NPV?

$42,500

$52,000

$46,250

$58,750

#52. Engineer saves for retirement in 25 years. First 10 years: deposit $A/year. Next 15 years: deposit $3A/year. Account earns 8%/year. What value of A results in $1,500,000?

$12,500

$8,450

$11,250

$9,875

#53. Full capacity now: $3,800,000. Or stage: 60% capacity now for $2,650,000, expand to full in year 7 for $1,850,000. At i=11%, what is PW savings from staging?

$315,000

$245,000

$145,250

$198,456

#54. Project NPV is $15,500 at 12% and -$8,200 at 18%. Using linear interpolation, what is approximate IRR?

15.0%

14.2%

15.9%

16.8%

#55. Delivered equipment cost $680,000. Using Lang factor of 5.2 for solid-fluid processing plant, what is estimated total installed cost?

$3,536,000

$2,850,000

$3,256,000

$3,850,000

#56. $75,000 loan at 7% nominal compounded annually for 6 years. How much total interest is saved by making semi-annual payments instead of annual?

$1,578

$2,045

$2,450

$1,125

#57. Defender: Market value $28,000, salvage $6,000 in 4 years, AOC $11,500. Challenger: Cost $72,000, salvage $12,000 in 7 years, AOC $6,500, overhaul $15,000 at year 4. At MARR=14%, better based on AW?

Challenger with AW=-$18,750

Defender with AW=-$21,345

Challenger with AW=-$21,345

Defender with AW=-$18,750

#58. $275,000 loan at 5.5% annual interest, repaid over 25 years. What is principal portion of 7th payment?

$8,250

$6,234

$7,458

$5,125

#59. Current: price $95/unit, sales 12,000 units, variable costs $58/unit, fixed costs $295,000. If price increases to $102 and sales drop to 10,500 units, what is change in profit?

Decrease of $22,500

Increase of $36,500

Increase of $18,000

Decrease of $45,000

#60. Effective annual rate is 13.5%. What is equivalent nominal rate compounded monthly?

12.76%

13.00%

13.50%

12.42%

#61. Investment $185,000, annual revenues $72,000, annual costs $24,000 for 8 years, salvage $28,000. What is NPV at MARR=12% and approximate IRR?

NPV=$65,000, IRR=24%

NPV=$58,750, IRR=22%

NPV=$52,456, IRR=20%

NPV=$45,250, IRR=18%

#62. At MARR=14%, compare three mutually exclusive alternatives over 10-year life. A: First cost $125,000, annual savings $32,000, salvage $15,000. B: First cost $185,000, annual savings $45,000, salvage $25,000. C: First cost $250,000, annual savings $58,000, salvage $35,000. Which should be selected?

C

B

A

None (Do Nothing)

#63. Equipment costs $200,000, 7-year life, $20,000 salvage. Compare SL vs DDB depreciation. Tax rate 30%, MARR 10%. What is the PW of tax savings advantage using DDB?

$6,875

$10,250

$8,450

$4,250

#64. Equipment costs $180,000 in today’s dollars, generates real cash flows of $48,000/year for 6 years. Real salvage value $25,000 at year 6. Inflation 3.5%/year, real MARR 7%. What is present worth?

$102,000

$75,234

$88,750

$62,450

#65. Investment $95,000 at time 0. Cash flows: Year 1=-$15,000, Year 2=$45,000, Year 3=$55,000, Year 4=$65,000. External reinvestment rate 9%. What is ERR?

17.8%

12.5%

15.2%

20.5%

#66. Equipment: Initial cost $165,000, annual O&M $18,500, minor repair $12,000 at year 3, major overhaul $35,000 at year 6, salvage $22,000 at end of 9-year life. At i=11%, what is life cycle cost?

$352,500

$325,000

$298,756

$275,450

#67. Cash flows begin at end of year 3 with $15,000 and increase by $3,000/year through year 8 (6 payments total). At i=10%, what is present worth at time 0?

$65,250

$85,750

$72,458

$98,250

#68. Make option: Fixed $150,000/year, first unit $95 (following 85% learning curve). Buy option: $52/unit flat. At what annual volume (approximately) are alternatives equivalent?

5,750 units

3,500 units

4,250 units

5,000 units

#69. Bond face value $25,000, coupon rate 4.5% paid semi-annually, matures in 12 years. Market yield 6% compounded semi-annually. What is current price?

$20,125

$23,750

$21,875

$22,456

#70. Machine costs $135,000, salvage $18,000 at end of 10 years. Overhaul: $22,000 at year 4, $28,000 at year 7. AOC $14,500/year. At i=12%, what is EUAC?

$42,250

$32,450

$36,785

$48,500

#71. Cash flows start at year 4 with $20,000, then increase 5%/year through year 10 (7 payments). At i=9%, what is present worth at time 0?

$78,456

$65,250

$105,000

$92,750

#72. Investment $225,000 plus working capital $45,000. Annual BTCF $85,000 for 7 years. 7-year SL depreciation to zero. Tax rate 32%. Working capital recovered at end. After-tax MARR 8%. What is NPV?

$52,450

$68,756

$82,350

$95,000

#73. Perpetuity pays $10,000 at end of year 1, then increases every 5 years by $2,000 forever. At i=7%, what is present worth?

$235,000

$185,000

$198,456

$215,750

#74. Challenger: Cost $145,000, AOC $8,500, salvage $18,000 at year 8. Due to technology risk, 25% chance of obsolescence at year 4 (salvage=$55,000 if obsolete). Expected salvage at year 8 is $18,000 if not obsolete. At MARR=13%, what is expected AW?

-$35,250

-$38,500

-$32,756

-$28,450

#75. Plant with capacity 5,000 units costs $2,200,000. Using cost-capacity exponent of 0.65, what is estimated cost for plant with 12,000 units capacity?

$3,850,000

$4,458,000

$4,125,000

$4,850,000

#76. Base case: Investment $140,000, annual benefit $45,000, life 6 years, MARR 11%, NPV=$28,500. Investment increases 15%, benefits decrease 10%, life extends to 7 years. New NPV?

$32,500

$25,250

$18,756

$12,450

#77. Equipment $180,000, MACRS 5-year. Rates: 20%, 32%, 19.2%, 11.52%, 11.52%, 5.76%. Tax rate 28%, MARR 9%. What is present worth of depreciation tax shields?

$52,500

$48,250

$42,756

$38,450

#78. Project costs $400,000 financed with 65% debt at 6% (20-year term) and 35% equity requiring 15% return. Tax rate 30%. What is minimum annual project return to satisfy all providers?

$52,250

$58,500

$42,450

$48,756

#79. Product A: price $45, VC $28, 40% mix. Product B: price $65, VC $42, 35% mix. Product C: price $85, VC $55, 25% mix. Fixed costs $350,000. What is total break-even units?

18,500 units

16,250 units

12,500 units

14,286 units

#80. Cash flows: Year 2=$15,000, Year 3=$18,000, Year 4=$22,000, Year 5=$25,000. At i=12%, what is present worth at end of year 1?

$52,450

$68,500

$62,250

$58,756

#81. Lease equipment: $28,000/year for 6 years with option to purchase at $45,000 at end of year 6. Alternative: Buy now for $145,000, salvage $25,000 at year 6, AOC $8,500. At MARR=11%, which is better?

Buy with PW=$165,756

Lease with PW=$152,450

Buy with PW=$152,450

Lease with PW=$165,756

#82. A company can invest in Project A (PW=$85,000, standard deviation=$22,000) or Project B (PW=$75,000, standard deviation=$12,000). Using coefficient of variation, which project has lower relative risk?

B with CV=0.16

A with CV=0.26

B with CV=0.26

A with CV=0.16

#83. Equipment generates nominal cash flows of $65,000/year. Inflation 3%/year for years 1-3, then 5%/year for years 4-6. Real MARR 7%. What is present worth?

$298,756

$332,500

$285,450

$315,250

#84. Lease payments of $3,500/month for 48 months with $8,000 security deposit (returned at end) and $12,000 buyout option at end. MARR=9% annual. What is PW of lease?

$178,500

$142,450

$152,756

$165,250

#85. Project: Investment phases of $125,000 (Year 0), $85,000 (Year 2), $45,000 (Year 4). Revenues $55,000/year starting Year 3 for 10 years. Salvage $30,000 at Year 12. At MARR=10%, NPV?

$42,450

$55,756

$68,250

$82,500

#86. Capital rationing: Budget $275,000. Projects: A($95,000 invest, $32,000 NPV), B($85,000, $28,000), C($75,000, $24,000), D($65,000, $20,000), E($55,000, $18,000). Maximum NPV combination?

A,B,C with $84,000

A,B,E with $78,000

B,C,D with $72,000

A,B,D with $80,000

#87. Two mutually exclusive projects with uncertain outcomes. Project A: E[NPV]=$45,000, Var=$120,000. Project B: E[NPV]=$52,000, Var=$280,000. If risk-neutral, which to select?

Indifferent

Cannot determine

A because lower variance

B because higher expected NPV

#88. A company’s stock has beta=1.3. Risk-free rate=4%, market return=11%. Using CAPM, what is cost of equity?

9.1%

14.3%

10.4%

13.1%

#89. Project with uncertain life: 40% probability of 5-year life (NPV=$45,000), 60% probability of 8-year life (NPV=$72,000). What is expected NPV?

$64,800

$55,200

$61,200

$58,500

#90. Equipment has 70% probability of lasting 6 years with salvage $15,000 and 30% probability of failing at year 4 with salvage $5,000. Initial cost $80,000, annual benefit $22,000. At MARR=10%, expected NPV?

$18,500

$8,450

$15,250

$12,675

#91. A government project must achieve B/C > 1.25 to be approved. Initial cost $5,000,000, annual benefits $650,000, annual O&M $75,000, life 30 years. At i=5%, is project approved?

Yes, B/C=1.28

Yes, B/C=1.42

No, B/C=1.15

No, B/C=1.22

#92. A company is evaluating three investment alternatives. Using risk-adjusted MARR (base MARR=10% plus risk premium), Project A (low risk, 2% premium) has NPV=$35,000, Project B (medium risk, 5% premium) has NPV=$42,000, Project C (high risk, 8% premium) has NPV=$55,000. Which offers best risk-adjusted return?

A

All equivalent

B

C

#93. Equipment with 80% learning curve. First unit costs $10,000. Cumulative average cost per unit for first 8 units?

$4,096

$5,120

$8,000

$6,400

#94. Project has following cash flows in real dollars: Year 0=-$100,000, Years 1-5=$30,000/year. Inflation 3.5%/year, real MARR 8%. What is real-dollar NPV?

$28,350

$35,000

$12,500

$19,756

#95. Machine A costs $50,000 with reliability 95%. Machine B costs $65,000 with reliability 99%. Expected cost of failure is $200,000 downtime. Which minimizes expected total cost?

B with E[Cost]=$75,000

B with E[Cost]=$67,000

A with E[Cost]=$75,000

A with E[Cost]=$60,000

#96. A company finances a $500,000 project: $200,000 from retained earnings (cost 12%), $150,000 from new equity (cost 15%), $150,000 from bonds (cost 6% after-tax). What is WACC?

11.2%

10.8%

11.7%

12.3%

#97. Project A has IRR=18% and requires $80,000. Project B has IRR=22% and requires $45,000. Projects are independent, budget=$100,000. Which projects should be selected at MARR=12%?

Neither

Both A and B

A only

B only

#98. A bond with $10,000 face value, 5% coupon paid annually, matures in 10 years. Current yield is 6%. If held for 5 years and sold when yield drops to 4%, total return?

$9,125

$7,875

$6,250

$8,456

#99. Manufacturing cell costs $450,000, produces 50,000 units/year. Variable cost $8/unit. After 3 years, upgrade costs $120,000, reduces variable cost to $5.50/unit. At MARR=15%, 8-year horizon, break-even selling price?

$15.85

$14.25

$19.25

$17.50

#100. Project with 5-year life, initial cost $200,000. Net revenues: Y1=$45,000, Y2=$55,000, Y3=$65,000, Y4=$55,000, Y5=$45,000. Salvage $25,000. NPV profile crosses x-axis at what rate?

17.5%

11.2%

8.5%

14.8%

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#1. A project requires investments of $75,000 at time 0, $25,000 at end of year 2, and $15,000 at end of year 4. It generates revenues of $28,000 per year for years 1-6 and $35,000 per year for years 7-10. Using MARR=11%, what is the NPV?

#2. A 25-year mortgage loan of $350,000 has a nominal interest rate of 4.75% compounded monthly. The borrower pays 1.5 points at closing. What is the effective nominal annual interest rate (APR) considering points?

#3. A public project costs $3,500,000, has annual user benefits of $480,000, annual non-user benefits of $95,000, annual disbenefits of $45,000, and annual O&M costs of $85,000. Using a 30-year life and i=4%, what is the benefit-cost ratio?

#4. Option A: Replace equipment costing $75,000, 8-year life, salvage $12,000, AOC $9,500. Option B: Overhaul existing for $35,000, extending life by 5 years, AOC $14,000, salvage $5,000. At MARR=12%, which has lower equivalent annual cost?

#5. A project costs $200,000 with revenues of $75,000/year and operating costs of $25,000/year for 6 years. Straight-line depreciation to $20,000 salvage. Tax rate 35%, after-tax MARR 9%. What is after-tax NPV?

#6. Construction expenditures: $180,000 at end of year -3, $320,000 at end of year -2, $250,000 at end of year -1, $100,000 at time 0. Interest during construction is 9%. What is total capitalized investment at time 0?

#7. Build full capacity now for $2,200,000 or stage: half capacity now for $1,450,000, expand in year 6 for $1,100,000. At i=12%, what is present worth savings from staging?

#8. Cash flows: Year 0=-$120,000, Year 1=+$350,000, Year 2=-$250,000. This has multiple IRRs. Using quadratic formula approach, what are the two IRR values?

#9. The present worth of all costs for Project A is $285,000 over a 15-year life. Project B has present worth costs of $425,000 over a 25-year life. At i=7%, which has lower EUAC?

#10. Machine A: Fixed costs $55,000/year, variable costs $9.50/unit. Machine B: Fixed costs $95,000/year, variable costs $6.25/unit. Machine C: Fixed costs $150,000/year, variable costs $3.75/unit. At 15,000 units, which has lowest total cost?

#11. $225,000 loan at 6.5% annual interest repaid over 25 years. What is the principal portion of the 8th payment?

#12. Company has taxable income of $320,000. Tax rates: 15% on first $50,000, 25% on $50,001-$100,000, 34% on $100,001-$335,000, 39% on amounts above $335,000. What is total tax liability?

#13. Capital structure: 30% debt at 5.5% before-tax, 10% preferred stock at 8%, 60% equity at 14%. Tax rate 32%. What is WACC?

#14. Project can be continued for 5 more years generating $45,000/year with $25,000 terminal value, or abandoned now for $180,000. At MARR=14%, what is advantage of continuing vs abandoning?

#15. At MARR=13%. A: First cost $48,000, AOC $8,500, salvage $6,000, life 4 years. B: First cost $72,000, AOC $6,000, salvage $10,000, life 6 years. C: First cost $95,000, AOC $4,500, salvage $15,000, life 8 years. Over 24-year LCM, which has lowest PW of costs?

#16. Equipment costs $145,000, salvage value $18,000. Expected total production: 250,000 units. Year 1: 45,000 units, Year 2: 52,000 units. What is cumulative depreciation through Year 2?

#17. Buy equipment: $120,000, AOC $8,500, salvage $18,000 after 7 years. Maintenance agreement $4,500/year extra. Or lease: $22,500/year with maintenance included. At MARR=10%, which is more economical and what is PW difference?

#18. Option 1: $18,000 at 8.5% nominal compounded monthly for 8 years. Option 2: $17,500 at 8.8% nominal compounded quarterly for 8 years. Which has higher future value and by how much?

#19. Project X: Investment $85,000, returns $28,000/year for 5 years. Project Y: Investment $85,000, returns $22,000/year for 8 years. At what interest rate are NPVs equal?

#20. Project: $175,000 investment, $35,000 working capital at time 0, additional $15,000 working capital at year 3. Annual revenue $65,000 for 7 years. All working capital recovered at end. At MARR=11%, what is NPV?

#21. Public project: Initial investment $4,200,000, annual benefits $720,000, annual disbenefits $85,000, annual O&M $145,000, major rehabilitation $600,000 at year 15. Life 30 years, i=5%. What is modified B/C ratio?

#22. Defender: Current market value $32,000, salvage $8,000 in 4 years, AOC $13,500. Challenger: Cost $85,000, salvage $15,000 in 8 years, AOC $7,500, overhaul $12,000 at year 4. At MARR=15%, which has better AW?

#23. Equipment costs $250,000, 5-year MACRS. Year 1 rate=20%, Year 2=32%, Year 3=19.2%. BTCF=$85,000/year. Tax rate 30%. What is sum of ATCF for years 1-3?

#24. Project generates real cash flows of $55,000/year for 6 years. Inflation 4%/year, real MARR 6%/year. What is present worth using nominal cash flows and market interest rate?

#25. At MARR=12%. A: Investment $150,000, annual benefit $42,000, life 6 years. B: Investment $225,000, annual benefit $58,000, life 6 years. C: Investment $300,000, annual benefit $72,000, life 6 years. Do-nothing available. Select?

#26. Equipment bought 3 years ago for $95,000. DDB depreciation with 6-year life. Can sell now for $35,000. Tax rate 28%. What are net after-tax proceeds?

#27. Retailer offers: $22,000 cash or $3,000 down plus $650/month for 36 months. What is implied nominal annual interest rate?

#28. Machine A: Capacity 2,500 units/year, cost $95,000, 6-year life, no salvage, variable cost $18/unit. Machine B: Capacity 4,000 units/year, cost $145,000, 6-year life, $12,000 salvage, variable cost $14/unit. Expected production 2,000 units. At MARR=12%, which has lower total annual cost?

#29. Cash flows: Year 1=$6,000, Year 2=$9,000, Year 3=$12,000, Year 4=$8,000, Year 5=$5,000. At i=9%, what is future worth at end of year 5?

#30. Fixed costs $280,000, variable costs $32/unit, selling price $52/unit. Current sales 20,000 units. If sales increase 12%, what is percentage increase in operating profit?

#31. Equipment costs $180,000, AOC $48,000, salvage $25,000, life 6 years. Annual production 6,500 units. At MARR=13%, what minimum selling price per unit justifies investment?

#32. Annual operating costs: Year 1=$28,000, escalating at 6%/year through year 7. Interest rate 11%/year. What is present worth of these escalating costs?

#33. Investment $90,000 at time 0; revenues $25,000/year for years 1-4; additional investment $40,000 at year 4; revenues $35,000/year for years 5-10; salvage $18,000 at year 10. At i=10%, what is NPV?

#34. Investment $125,000. Annual cash flows $35,000. Declining salvage: Year 1=$95,000, Year 2=$72,000, Year 3=$52,000, Year 4=$35,000, Year 5=$20,000. At end of which year does cumulative cash flow plus salvage first exceed investment?

#35. At what compound interest rate will an investment triple in approximately 12 years?

#36. Current: price $120/unit, sales 8,000 units, fixed costs $220,000, variable costs $75/unit. If price reduced 15% and volume increases 25%, what is change in annual profit?

#37. Perpetual endowment pays $12,000/year forever, first payment at end of year 8. At i=6%, what is present worth at time 0?

#38. Cash flows: Year 0=-$80,000, Year 1=+$200,000, Year 2=-$125,000. Using the sign changes rule, how many possible IRRs exist?

#39. Present worth of all costs is $325,000 over a 14-year life. At i=9%, what is EUAC?

#40. Machine A: Fixed $65,000/year, variable $7.50/unit. Machine B: Fixed $110,000/year, variable $4.25/unit. Machine C: Fixed $175,000/year, variable $2.50/unit. Above what volume is Machine C preferred?

#41. Investment $110,000, annual revenues $32,000/year. At MARR=11%, what is unrecovered investment balance at end of year 4?

#42. A project’s NPV is $28,000 with investment $95,000 and annual cash flows of $32,000 for 5 years. If the investment increases by 12% and cash flows decrease by 8%, what is the approximate new NPV at MARR=10%?

#43. Equipment costs $115,000, salvage $15,000, life 6 years. Using DDB with switch to straight-line when beneficial, what is book value at end of year 4?

#44. A project has present worth of $68,000 at time 0. At i=13%, what is equivalent worth at end of year 5?

#45. Investment $145,000, annual revenues $52,000, annual costs $18,000, salvage $22,000 at end of 8-year life. At MARR=12%, what is net annual worth?

#46. Public project: Investment $4,500,000, annual user benefits $520,000, annual non-user benefits $125,000, annual disbenefits $65,000, annual O&M $95,000. Life 35 years, i=4%. What is B/C ratio?

#47. Company has loans: $85,000 at 5.5%, $65,000 at 7.2%, $45,000 at 8.5%. What is weighted average interest rate?

#48. Investment $150,000. Cash flows: Year 1=$50,000, Year 2=$55,000, Year 3=$60,000. At MARR=14%, what is project balance at end of year 3?

#49. Company uses market MARR of 16%. Expected inflation rate 4.5%/year. What is real MARR?

#50. Lessor purchases equipment for $145,000, expects residual value $22,000 at end of 6-year lease. Required return 12%. What annual lease payment (end of year)?

#51. Four scenarios: Optimistic (15% probability, NPV=$120,000), Most Likely (45% probability, NPV=$55,000), Conservative (25% probability, NPV=$15,000), Pessimistic (15% probability, NPV=-$35,000). What is expected NPV?

#52. Engineer saves for retirement in 25 years. First 10 years: deposit $A/year. Next 15 years: deposit $3A/year. Account earns 8%/year. What value of A results in $1,500,000?

#53. Full capacity now: $3,800,000. Or stage: 60% capacity now for $2,650,000, expand to full in year 7 for $1,850,000. At i=11%, what is PW savings from staging?

#54. Project NPV is $15,500 at 12% and -$8,200 at 18%. Using linear interpolation, what is approximate IRR?

#55. Delivered equipment cost $680,000. Using Lang factor of 5.2 for solid-fluid processing plant, what is estimated total installed cost?

#56. $75,000 loan at 7% nominal compounded annually for 6 years. How much total interest is saved by making semi-annual payments instead of annual?

#57. Defender: Market value $28,000, salvage $6,000 in 4 years, AOC $11,500. Challenger: Cost $72,000, salvage $12,000 in 7 years, AOC $6,500, overhaul $15,000 at year 4. At MARR=14%, better based on AW?

#58. $275,000 loan at 5.5% annual interest, repaid over 25 years. What is principal portion of 7th payment?

#59. Current: price $95/unit, sales 12,000 units, variable costs $58/unit, fixed costs $295,000. If price increases to $102 and sales drop to 10,500 units, what is change in profit?

#60. Effective annual rate is 13.5%. What is equivalent nominal rate compounded monthly?

#61. Investment $185,000, annual revenues $72,000, annual costs $24,000 for 8 years, salvage $28,000. What is NPV at MARR=12% and approximate IRR?

#63. Equipment costs $200,000, 7-year life, $20,000 salvage. Compare SL vs DDB depreciation. Tax rate 30%, MARR 10%. What is the PW of tax savings advantage using DDB?

#64. Equipment costs $180,000 in today’s dollars, generates real cash flows of $48,000/year for 6 years. Real salvage value $25,000 at year 6. Inflation 3.5%/year, real MARR 7%. What is present worth?

#65. Investment $95,000 at time 0. Cash flows: Year 1=-$15,000, Year 2=$45,000, Year 3=$55,000, Year 4=$65,000. External reinvestment rate 9%. What is ERR?

#66. Equipment: Initial cost $165,000, annual O&M $18,500, minor repair $12,000 at year 3, major overhaul $35,000 at year 6, salvage $22,000 at end of 9-year life. At i=11%, what is life cycle cost?

#67. Cash flows begin at end of year 3 with $15,000 and increase by $3,000/year through year 8 (6 payments total). At i=10%, what is present worth at time 0?

#68. Make option: Fixed $150,000/year, first unit $95 (following 85% learning curve). Buy option: $52/unit flat. At what annual volume (approximately) are alternatives equivalent?

#69. Bond face value $25,000, coupon rate 4.5% paid semi-annually, matures in 12 years. Market yield 6% compounded semi-annually. What is current price?

#70. Machine costs $135,000, salvage $18,000 at end of 10 years. Overhaul: $22,000 at year 4, $28,000 at year 7. AOC $14,500/year. At i=12%, what is EUAC?

#71. Cash flows start at year 4 with $20,000, then increase 5%/year through year 10 (7 payments). At i=9%, what is present worth at time 0?

#72. Investment $225,000 plus working capital $45,000. Annual BTCF $85,000 for 7 years. 7-year SL depreciation to zero. Tax rate 32%. Working capital recovered at end. After-tax MARR 8%. What is NPV?

#73. Perpetuity pays $10,000 at end of year 1, then increases every 5 years by $2,000 forever. At i=7%, what is present worth?

#74. Challenger: Cost $145,000, AOC $8,500, salvage $18,000 at year 8. Due to technology risk, 25% chance of obsolescence at year 4 (salvage=$55,000 if obsolete). Expected salvage at year 8 is $18,000 if not obsolete. At MARR=13%, what is expected AW?

#75. Plant with capacity 5,000 units costs $2,200,000. Using cost-capacity exponent of 0.65, what is estimated cost for plant with 12,000 units capacity?

#76. Base case: Investment $140,000, annual benefit $45,000, life 6 years, MARR 11%, NPV=$28,500. Investment increases 15%, benefits decrease 10%, life extends to 7 years. New NPV?

#77. Equipment $180,000, MACRS 5-year. Rates: 20%, 32%, 19.2%, 11.52%, 11.52%, 5.76%. Tax rate 28%, MARR 9%. What is present worth of depreciation tax shields?

#78. Project costs $400,000 financed with 65% debt at 6% (20-year term) and 35% equity requiring 15% return. Tax rate 30%. What is minimum annual project return to satisfy all providers?

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