---
title: "EVA; 10 days, 50 labour days at Rs 1000"
subject: "Project Engineering"
chapter: 4
key: "semester_7/project_engineering:eva-numerical-labour-days-1000"
source: https://www.bctengineer.com/q/semester_7/project_engineering/eva-numerical-labour-days-1000
site: BCT Engineering
---

# EVA; 10 days, 50 labour days at Rs 1000

Project Engineering · Chapter 4: Project Implementation and Controlling

- Asked in: 2072 Chaitra, 1+5 marks; 2079 Baisakh, 6 marks (asked 2 times)
- Video: [Earned value analysis worked example](https://www.youtube.com/watch?v=z7b3SYQuqJM) — Engineer4Free
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/project_engineering/eva-numerical-labour-days-1000
- Whole chapter: https://www.bctengineer.com/md/semester_7/project_engineering/chapter-4

## Question

What is EVA? A construction work had to be completed in 10 days with 50 labour days at Rs 1000 per day, i.e. with a total cost of Rs 50,000. At the end of the third day, only 25% work was completed with the use of 18 labour days at Rs 800 per day. Perform earned value analysis and comment on the performance.

## Short answer

EVA compares planned value, earned value, and actual cost. PV=Rs15,000, EV=Rs12,500, AC=Rs14,400, so SV=-Rs2,500, CV=-Rs1,900, SPI=0.83, CPI=0.87; work is behind schedule and over budget.

## Answer

#### Earned Value Analysis (EVA)

**Earned Value Analysis** is a method of measuring project performance by comparing three quantities: the work planned (PV), the value of the work actually done (EV) and the actual cost (AC). It gives schedule and cost variances and indices in one common unit (money), and forecasts the final cost and time.

| Term | Other name | Meaning |
|---|---|---|
| BAC | Budget at completion | Total approved budget of the project |
| PV | BCWS (planned value) | Budgeted cost of the work scheduled up to the date |
| EV | BCWP (earned value) | Budgeted cost of the work actually completed = % complete x BAC |
| AC | ACWP (actual cost) | Actual money spent on the work done up to the date |

$$
\begin{aligned} SV &= EV - PV, \qquad CV = EV - AC \\ SPI &= \frac{EV}{PV}, \qquad CPI = \frac{EV}{AC} \\ EAC &= \frac{BAC}{CPI}, \qquad ETC = EAC - AC, \qquad VAC = BAC - EAC \end{aligned}
$$

#### Given data

- Budget: 50 labour days x Rs 1,000 = Rs 50,000 for 10 days (assumed uniform, 5 labour days per day).
- At the end of day 3: work done = 25 %; labour used = 18 labour days at Rs 800 per day.

#### Calculation

$$
\begin{aligned}
PV &= \frac{3}{10} \times 50{,}000 = 15{,}000 \\
EV &= 0.25 \times 50{,}000 = 12{,}500 \\
AC &= 18 \times 800 = 14{,}400
\end{aligned}
$$

$$
\begin{aligned}
SV &= EV - PV = 12{,}500 - 15{,}000 = -2{,}500 \\
CV &= EV - AC = 12{,}500 - 14{,}400 = -1{,}900 \\
SPI &= \frac{EV}{PV} = \frac{12{,}500}{15{,}000} = 0.83 \\
CPI &= \frac{EV}{AC} = \frac{12{,}500}{14{,}400} = 0.87 \\
EAC &= \frac{BAC}{CPI} = \frac{50{,}000}{0.8681} = 57{,}600 \\
ETC &= EAC - AC = 57{,}600 - 14{,}400 = 43{,}200 \\
VAC &= BAC - EAC = 50{,}000 - 57{,}600 = -7{,}600 \\
\text{Forecast duration} &= \frac{10}{SPI} = \frac{10}{0.8333} = 12.0\ \text{days}
\end{aligned}
$$

| Parameter | Value |
|---|---|
| PV | Rs 15,000 |
| EV | Rs 12,500 |
| AC | Rs 14,400 |
| SV | Rs -2,500 |
| CV | Rs -1,900 |
| SPI | 0.83 |
| CPI | 0.87 |
| EAC | Rs 57,600 |

#### Comment on performance

- **SV is negative and SPI = 0.83 < 1:** the work is **behind schedule**; only 83 % of the planned work has been done. At this rate the job will take 12 days instead of 10.
- **CV is negative and CPI = 0.87 < 1:** the job is **over budget**. Although the rate per labour day is lower (Rs 800 against Rs 1,000), 18 labour days were used for work that was budgeted at only 12.5 labour days (25 % of 50), so productivity is poor.
- The expected final cost is Rs 57,600, an overrun of Rs 7,600.
- Corrective action: improve productivity (better supervision, tools and work methods), plan materials in advance, and rearrange crews to recover the delay.

**Answer: SV = Rs -2,500, CV = Rs -1,900, SPI = 0.83, CPI = 0.87; the work is behind schedule and over budget.**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. In the problem, what is EV at the end of day 3?
   A. Rs 50,000
   B. Rs 14,400
   C. Rs 15,000
   D. Rs 12,500
   Answer: D. EV = % complete x BAC = 0.25 x 50,000 = Rs 12,500. (Key point: Earned value)

2. How is PV found for day 3 of a 10-day job with BAC Rs 50,000 assumed uniform?
   A. PV = 3/10 x 50,000 = Rs 15,000
   B. PV = 50,000 / 3
   C. PV = 18 x 800
   D. PV = 25% x 50,000
   Answer: A. Planned work to date is 3/10 of the budget, i.e. Rs 15,000. (Key point: Planned value)

3. With AC = 18 x 800 = Rs 14,400, what are CV and CPI?
   A. CV = -2,500, CPI = 0.83
   B. CV = -1,900, CPI = 0.87
   C. CV = 0, CPI = 1
   D. CV = +1,900, CPI = 1.15
   Answer: B. CV = EV - AC = 12,500 - 14,400 = -1,900; CPI = 12,500/14,400 = 0.87. (Key point: Cost performance)

4. SV = -2,500 and SPI = 0.83 mean what?
   A. Under budget
   B. On schedule
   C. Behind schedule; the job would take about 12 days instead of 10
   D. Ahead of schedule
   Answer: C. SPI < 1 means behind schedule; forecast duration = 10/0.8333 = 12 days. (Key point: Schedule performance)

## Related in Project Engineering

- [EVA; 60 days, 25% work, Rs 12,00,000](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Aeva-numerical-60-days-25-percent) — Project Engineering, chapter 4
- [EVA; 60 days, 25% work, 50% budget spent](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Aeva-numerical-60-days-half-budget) — Project Engineering, chapter 4
- [EVA; 10 days, 100,000, day 6, Rs 65,000](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Aeva-numerical-day6-65000-k80) — Project Engineering, chapter 4
- [EVA application; 35 days, Rs 8,00,000 spent](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Aeva-applicable-monitoring-numerical-b82) — Project Engineering, chapter 4
- [EVA; 10 days, 100,000, day 6, spi and cpi](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Aeva-numerical-day6-spi-cpi-b80) — Project Engineering, chapter 4
- [EVA; 125 cu.m concrete in 10 days](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Aeva-concrete-125-cum-s65) — Project Engineering, chapter 4

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