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Construction

Construction Engineering · FE Reference Handbook section

Construction Engineering
0 formulas
10 exam-style examples
~45 min
All Construction Engineering lectures

Handbook notes for this section

Definitions and conditions exactly as the handbook states them.

  • Construction project scheduling and analysis questions may be based on either the activity-on-node method or the activity-on-
  • DEPENDS ON THE START OF A DEPENDS ON THE FINISH OF A DEPENDS ON THE FINISH OF A
  • ACTIVITY-ON-ARROW ANNOTATION ACTIVITY-ON-NODE ANNOTATION
  • EARLY START/LATE START EARLY FINISH/LATE FINISH EARLY EARLY

Core formulas for this FE topic

Definitions, applicability, units, assumptions and worked examples for each relation.

This section is conceptual; there are no equations to memorise.

Worked exam-style examples

The four ways this section is written on the real exam — thoughts first, then equations, then substitution.

Example 1
Earned-value analysis: performance indices and forecast at completion — Construction

A $6.0M project reports planned value $3,900,000, earned value $4,320,000 and actual cost $5,356,800 at the reporting date. Compute the cost and schedule variances, both performance indices, and forecast the estimate at completion.

Given

  • BAC = $6,000,000

  • PV = $3,900,000

  • EV = $4,320,000

  • AC = $5,356,800

Find

CV, SV, CPI, SPI and EAC

Start with the thinking

  • Earned-value analysis compares what was accomplished (EV) with what was spent (AC) and what was scheduled (PV).
  • An index below 1.00 signals an overrun; the forecast divides the budget by the cost index.

Step-by-step solution

  1. Formula

    CV=EV−ACCV = EV - AC

  2. Substituting — CV = 4,320,000 − 5,356,800 = $-1,036,800

  3. Formula

    SV=EV−PVSV = EV - PV

  4. Substituting — SV = 4,320,000 − 3,900,000 = $420,000

  5. Indices

    CPI=EV/AC=0.806;SPI=EV/PV=1.108CPI = EV/AC = 0.806; SPI = EV/PV = 1.108

  6. Formula

    EAC=BAC/CPIEAC = BAC / CPI

  7. Substituting — EAC = 6,000,000/0.806 = $7,440,000

Answer:

CPI = 0.81, SPI = 1.11, EAC ≈ $7,440,000

Why the other options are there

  • EAC = $4,838,710 (multiplied by the index)
  • CPI = 1.240 (inverted)

Reference: FE Reference Handbook — Construction Engineering → Construction

Example 2
Earned-value analysis: performance indices and forecast at completion — Construction (2)

A $6.0M project reports planned value $2,100,000, earned value $1,980,000 and actual cost $1,920,600 at the reporting date. Compute the cost and schedule variances, both performance indices, and forecast the estimate at completion.

Given

  • BAC = $6,000,000

  • PV = $2,100,000

  • EV = $1,980,000

  • AC = $1,920,600

Find

CV, SV, CPI, SPI and EAC

Start with the thinking

  • Earned-value analysis compares what was accomplished (EV) with what was spent (AC) and what was scheduled (PV).
  • An index below 1.00 signals an overrun; the forecast divides the budget by the cost index.

Step-by-step solution

  1. Formula

    CV=EV−ACCV = EV - AC

  2. Substituting — CV = 1,980,000 − 1,920,600 = $59,400

  3. Formula

    SV=EV−PVSV = EV - PV

  4. Substituting — SV = 1,980,000 − 2,100,000 = $-120,000

  5. Indices

    CPI=EV/AC=1.031;SPI=EV/PV=0.943CPI = EV/AC = 1.031; SPI = EV/PV = 0.943

  6. Formula

    EAC=BAC/CPIEAC = BAC / CPI

  7. Substituting — EAC = 6,000,000/1.031 = $5,820,000

Answer:

CPI = 1.03, SPI = 0.94, EAC ≈ $5,820,000

Why the other options are there

  • EAC = $6,185,567 (multiplied by the index)
  • CPI = 0.970 (inverted)

Reference: FE Reference Handbook — Construction Engineering → Construction

Example 3
Earned-value analysis: performance indices and forecast at completion — Construction (3)

A $5.0M project reports planned value $1,500,000, earned value $1,650,000 and actual cost $1,815,000 at the reporting date. Compute the cost and schedule variances, both performance indices, and forecast the estimate at completion.

Given

  • BAC = $5,000,000

  • PV = $1,500,000

  • EV = $1,650,000

  • AC = $1,815,000

Find

CV, SV, CPI, SPI and EAC

Start with the thinking

  • Earned-value analysis compares what was accomplished (EV) with what was spent (AC) and what was scheduled (PV).
  • An index below 1.00 signals an overrun; the forecast divides the budget by the cost index.

Step-by-step solution

  1. Formula

    CV=EV−ACCV = EV - AC

  2. Substituting — CV = 1,650,000 − 1,815,000 = $-165,000

  3. Formula

    SV=EV−PVSV = EV - PV

  4. Substituting — SV = 1,650,000 − 1,500,000 = $150,000

  5. Indices

    CPI=EV/AC=0.909;SPI=EV/PV=1.100CPI = EV/AC = 0.909; SPI = EV/PV = 1.100

  6. Formula

    EAC=BAC/CPIEAC = BAC / CPI

  7. Substituting — EAC = 5,000,000/0.909 = $5,500,000

Answer:

CPI = 0.91, SPI = 1.10, EAC ≈ $5,500,000

Why the other options are there

  • EAC = $4,545,455 (multiplied by the index)
  • CPI = 1.100 (inverted)

Reference: FE Reference Handbook — Construction Engineering → Construction

Example 4
Earned-value analysis: performance indices and forecast at completion — Construction (4)

A $12.0M project reports planned value $4,200,000, earned value $4,440,000 and actual cost $4,884,000 at the reporting date. Compute the cost and schedule variances, both performance indices, and forecast the estimate at completion.

Given

  • BAC = $12,000,000

  • PV = $4,200,000

  • EV = $4,440,000

  • AC = $4,884,000

Find

CV, SV, CPI, SPI and EAC

Start with the thinking

  • Earned-value analysis compares what was accomplished (EV) with what was spent (AC) and what was scheduled (PV).
  • An index below 1.00 signals an overrun; the forecast divides the budget by the cost index.

Step-by-step solution

  1. Formula

    CV=EV−ACCV = EV - AC

  2. Substituting — CV = 4,440,000 − 4,884,000 = $-444,000

  3. Formula

    SV=EV−PVSV = EV - PV

  4. Substituting — SV = 4,440,000 − 4,200,000 = $240,000

  5. Indices

    CPI=EV/AC=0.909;SPI=EV/PV=1.057CPI = EV/AC = 0.909; SPI = EV/PV = 1.057

  6. Formula

    EAC=BAC/CPIEAC = BAC / CPI

  7. Substituting — EAC = 12,000,000/0.909 = $13,200,000

Answer:

CPI = 0.91, SPI = 1.06, EAC ≈ $13,200,000

Why the other options are there

  • EAC = $10,909,091 (multiplied by the index)
  • CPI = 1.100 (inverted)

Reference: FE Reference Handbook — Construction Engineering → Construction

Example 5
Earned-value analysis: performance indices and forecast at completion — Construction (5)

A $4.0M project reports planned value $2,400,000, earned value $2,280,000 and actual cost $2,143,200 at the reporting date. Compute the cost and schedule variances, both performance indices, and forecast the estimate at completion.

Given

  • BAC = $4,000,000

  • PV = $2,400,000

  • EV = $2,280,000

  • AC = $2,143,200

Find

CV, SV, CPI, SPI and EAC

Start with the thinking

  • Earned-value analysis compares what was accomplished (EV) with what was spent (AC) and what was scheduled (PV).
  • An index below 1.00 signals an overrun; the forecast divides the budget by the cost index.

Step-by-step solution

  1. Formula

    CV=EV−ACCV = EV - AC

  2. Substituting — CV = 2,280,000 − 2,143,200 = $136,800

  3. Formula

    SV=EV−PVSV = EV - PV

  4. Substituting — SV = 2,280,000 − 2,400,000 = $-120,000

  5. Indices

    CPI=EV/AC=1.064;SPI=EV/PV=0.950CPI = EV/AC = 1.064; SPI = EV/PV = 0.950

  6. Formula

    EAC=BAC/CPIEAC = BAC / CPI

  7. Substituting — EAC = 4,000,000/1.064 = $3,760,000

Answer:

CPI = 1.06, SPI = 0.95, EAC ≈ $3,760,000

Why the other options are there

  • EAC = $4,255,319 (multiplied by the index)
  • CPI = 0.940 (inverted)

Reference: FE Reference Handbook — Construction Engineering → Construction

Example 6
Earned-value analysis: performance indices and forecast at completion — Construction (6)

A $4.0M project reports planned value $1,800,000, earned value $1,320,000 and actual cost $1,372,800 at the reporting date. Compute the cost and schedule variances, both performance indices, and forecast the estimate at completion.

Given

  • BAC = $4,000,000

  • PV = $1,800,000

  • EV = $1,320,000

  • AC = $1,372,800

Find

CV, SV, CPI, SPI and EAC

Start with the thinking

  • Earned-value analysis compares what was accomplished (EV) with what was spent (AC) and what was scheduled (PV).
  • An index below 1.00 signals an overrun; the forecast divides the budget by the cost index.

Step-by-step solution

  1. Formula

    CV=EV−ACCV = EV - AC

  2. Substituting — CV = 1,320,000 − 1,372,800 = $-52,800

  3. Formula

    SV=EV−PVSV = EV - PV

  4. Substituting — SV = 1,320,000 − 1,800,000 = $-480,000

  5. Indices

    CPI=EV/AC=0.962;SPI=EV/PV=0.733CPI = EV/AC = 0.962; SPI = EV/PV = 0.733

  6. Formula

    EAC=BAC/CPIEAC = BAC / CPI

  7. Substituting — EAC = 4,000,000/0.962 = $4,160,000

Answer:

CPI = 0.96, SPI = 0.73, EAC ≈ $4,160,000

Why the other options are there

  • EAC = $3,846,154 (multiplied by the index)
  • CPI = 1.040 (inverted)

Reference: FE Reference Handbook — Construction Engineering → Construction

Example 7
Earned-value analysis: performance indices and forecast at completion — Construction (7)

A $8.0M project reports planned value $4,400,000, earned value $3,600,000 and actual cost $3,276,000 at the reporting date. Compute the cost and schedule variances, both performance indices, and forecast the estimate at completion.

Given

  • BAC = $8,000,000

  • PV = $4,400,000

  • EV = $3,600,000

  • AC = $3,276,000

Find

CV, SV, CPI, SPI and EAC

Start with the thinking

  • Earned-value analysis compares what was accomplished (EV) with what was spent (AC) and what was scheduled (PV).
  • An index below 1.00 signals an overrun; the forecast divides the budget by the cost index.

Step-by-step solution

  1. Formula

    CV=EV−ACCV = EV - AC

  2. Substituting — CV = 3,600,000 − 3,276,000 = $324,000

  3. Formula

    SV=EV−PVSV = EV - PV

  4. Substituting — SV = 3,600,000 − 4,400,000 = $-800,000

  5. Indices

    CPI=EV/AC=1.099;SPI=EV/PV=0.818CPI = EV/AC = 1.099; SPI = EV/PV = 0.818

  6. Formula

    EAC=BAC/CPIEAC = BAC / CPI

  7. Substituting — EAC = 8,000,000/1.099 = $7,280,000

Answer:

CPI = 1.10, SPI = 0.82, EAC ≈ $7,280,000

Why the other options are there

  • EAC = $8,791,209 (multiplied by the index)
  • CPI = 0.910 (inverted)

Reference: FE Reference Handbook — Construction Engineering → Construction

Example 8
Earned-value analysis: performance indices and forecast at completion — Construction (8)

A $12.0M project reports planned value $5,400,000, earned value $6,240,000 and actual cost $7,488,000 at the reporting date. Compute the cost and schedule variances, both performance indices, and forecast the estimate at completion.

Given

  • BAC = $12,000,000

  • PV = $5,400,000

  • EV = $6,240,000

  • AC = $7,488,000

Find

CV, SV, CPI, SPI and EAC

Start with the thinking

  • Earned-value analysis compares what was accomplished (EV) with what was spent (AC) and what was scheduled (PV).
  • An index below 1.00 signals an overrun; the forecast divides the budget by the cost index.

Step-by-step solution

  1. Formula

    CV=EV−ACCV = EV - AC

  2. Substituting — CV = 6,240,000 − 7,488,000 = $-1,248,000

  3. Formula

    SV=EV−PVSV = EV - PV

  4. Substituting — SV = 6,240,000 − 5,400,000 = $840,000

  5. Indices

    CPI=EV/AC=0.833;SPI=EV/PV=1.156CPI = EV/AC = 0.833; SPI = EV/PV = 1.156

  6. Formula

    EAC=BAC/CPIEAC = BAC / CPI

  7. Substituting — EAC = 12,000,000/0.833 = $14,400,000

Answer:

CPI = 0.83, SPI = 1.16, EAC ≈ $14,400,000

Why the other options are there

  • EAC = $10,000,000 (multiplied by the index)
  • CPI = 1.200 (inverted)

Reference: FE Reference Handbook — Construction Engineering → Construction

Example 9
Earned-value analysis: performance indices and forecast at completion — Construction (9)

A $10.0M project reports planned value $3,500,000, earned value $2,300,000 and actual cost $2,208,000 at the reporting date. Compute the cost and schedule variances, both performance indices, and forecast the estimate at completion.

Given

  • BAC = $10,000,000

  • PV = $3,500,000

  • EV = $2,300,000

  • AC = $2,208,000

Find

CV, SV, CPI, SPI and EAC

Start with the thinking

  • Earned-value analysis compares what was accomplished (EV) with what was spent (AC) and what was scheduled (PV).
  • An index below 1.00 signals an overrun; the forecast divides the budget by the cost index.

Step-by-step solution

  1. Formula

    CV=EV−ACCV = EV - AC

  2. Substituting — CV = 2,300,000 − 2,208,000 = $92,000

  3. Formula

    SV=EV−PVSV = EV - PV

  4. Substituting — SV = 2,300,000 − 3,500,000 = $-1,200,000

  5. Indices

    CPI=EV/AC=1.042;SPI=EV/PV=0.657CPI = EV/AC = 1.042; SPI = EV/PV = 0.657

  6. Formula

    EAC=BAC/CPIEAC = BAC / CPI

  7. Substituting — EAC = 10,000,000/1.042 = $9,600,000

Answer:

CPI = 1.04, SPI = 0.66, EAC ≈ $9,600,000

Why the other options are there

  • EAC = $10,416,667 (multiplied by the index)
  • CPI = 0.960 (inverted)

Reference: FE Reference Handbook — Construction Engineering → Construction

Example 10
Earned-value analysis: performance indices and forecast at completion — Construction (10)

A $8.0M project reports planned value $4,400,000, earned value $3,600,000 and actual cost $4,392,000 at the reporting date. Compute the cost and schedule variances, both performance indices, and forecast the estimate at completion.

Given

  • BAC = $8,000,000

  • PV = $4,400,000

  • EV = $3,600,000

  • AC = $4,392,000

Find

CV, SV, CPI, SPI and EAC

Start with the thinking

  • Earned-value analysis compares what was accomplished (EV) with what was spent (AC) and what was scheduled (PV).
  • An index below 1.00 signals an overrun; the forecast divides the budget by the cost index.

Step-by-step solution

  1. Formula

    CV=EV−ACCV = EV - AC

  2. Substituting — CV = 3,600,000 − 4,392,000 = $-792,000

  3. Formula

    SV=EV−PVSV = EV - PV

  4. Substituting — SV = 3,600,000 − 4,400,000 = $-800,000

  5. Indices

    CPI=EV/AC=0.820;SPI=EV/PV=0.818CPI = EV/AC = 0.820; SPI = EV/PV = 0.818

  6. Formula

    EAC=BAC/CPIEAC = BAC / CPI

  7. Substituting — EAC = 8,000,000/0.820 = $9,760,000

Answer:

CPI = 0.82, SPI = 0.82, EAC ≈ $9,760,000

Why the other options are there

  • EAC = $6,557,377 (multiplied by the index)
  • CPI = 1.220 (inverted)

Reference: FE Reference Handbook — Construction Engineering → Construction

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