---
title: "EVA; 10 days, 100,000, day 6, spi and cpi"
subject: "Project Engineering"
chapter: 4
key: "semester_7/project_engineering:eva-numerical-day6-spi-cpi-b80"
source: https://www.bctengineer.com/q/semester_7/project_engineering/eva-numerical-day6-spi-cpi-b80
site: BCT Engineering
---

# EVA; 10 days, 100,000, day 6, spi and cpi

Project Engineering · Chapter 4: Project Implementation and Controlling

- Asked in: 2080 Bhadra, 6 marks
- 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-day6-spi-cpi-b80
- Whole chapter: https://www.bctengineer.com/md/semester_7/project_engineering/chapter-4

## Question

Suppose you have a project that is scheduled to be completed in 10 days at a budgeted cost of 100,000. At the end of day 6, you do an analysis and you determine the job is 70% complete and you have spent 55000. (i) Is the project ahead, behind schedule or on time? (ii) Is the project expected to complete on budget, under or over budget? (iii) What is the project's SPI and CPI at day 6?

## Short answer

At day 6, PV=Rs 60,000, EV=Rs 70,000, AC=Rs 55,000; SPI=1.17, CPI=1.27. Thus project is ahead of schedule and under budget.

## Answer

#### Given data

BAC = Rs 1,00,000 (100,000); duration = 10 days; at day 6: work done = 70 %, cost spent = Rs 55,000. Planned work is assumed uniform with time.

#### Calculation

$$
\begin{aligned}
PV &= \frac{6}{10} \times 100{,}000 = 60{,}000 \\
EV &= 0.70 \times 100{,}000 = 70{,}000 \\
AC &= 55{,}000
\end{aligned}
$$

$$
\begin{aligned}
SV &= EV - PV = 70{,}000 - 60{,}000 = 10{,}000 \\
CV &= EV - AC = 70{,}000 - 55{,}000 = 15{,}000 \\
SPI &= \frac{EV}{PV} = \frac{70{,}000}{60{,}000} = 1.17 \\
CPI &= \frac{EV}{AC} = \frac{70{,}000}{55{,}000} = 1.27 \\
EAC &= \frac{BAC}{CPI} = \frac{1{,}00{,}000}{1.2727} = 78{,}571 \\
ETC &= EAC - AC = 78{,}571 - 55{,}000 = 23{,}571 \\
VAC &= BAC - EAC = 1{,}00{,}000 - 78{,}571 = 21{,}429 \\
\text{Forecast duration} &= \frac{10}{SPI} = \frac{10}{1.1667} = 8.6\ \text{days}
\end{aligned}
$$

#### Answers

(i) $SV = +10{,}000$ and $SPI = 1.17 > 1$: the project is **ahead of schedule** (70 % done against 60 % planned). At this rate it can finish in about 8.6 days.

(ii) $CV = +15{,}000$ and $CPI = 1.27 > 1$: the project is expected to complete **under budget**; EAC = Rs 78,571 against Rs 1,00,000, a saving of Rs 21,429.

(iii) **SPI = 1.17** and **CPI = 1.27** at day 6.

- **Action:** continue the same management, keep the quality standard (do not save cost by poor work), and use the saved time/money as contingency or to release resources for other tasks.

## Check yourself

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

1. BAC = 1,00,000, 10 days; at day 6 the job is 70% complete. PV and EV give the status:
   A. PV = 70,000, EV = 60,000: behind schedule
   B. PV = 60,000, EV = 70,000: ahead of schedule
   C. PV = 60,000, EV = 55,000: behind schedule
   D. PV = EV: on time
   Answer: B. PV = 6/10 x 1,00,000 = 60,000 and EV = 70,000, so SV is +10,000: ahead. (Key point: Schedule status)

2. SPI at day 6 is:
   A. 0.86
   B. 0.60
   C. 1.17
   D. 1.27
   Answer: C. SPI = EV/PV = 70,000/60,000 = 1.17. (Key point: SPI)

3. With Rs 55,000 spent, CPI is about 1.27. The project is expected to finish:
   A. Over budget
   B. Under budget
   C. Exactly on budget
   D. Cannot be told from CPI
   Answer: B. CPI = 70,000/55,000 = 1.27 > 1, so it is under budget (EAC about Rs 78,571). (Key point: CPI and budget status)

4. What control action does the answer recommend for this project?
   A. Cut quality to save more cost
   B. Stop all work
   C. Continue the same management, keep quality, and use savings as contingency
   D. Add many more crews to speed up
   Answer: C. Performance is better than plan, so keep going and protect quality rather than cutting it. (Key point: Control action)

## Related in Project Engineering

- [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; 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 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, 50 labour days at Rs 1000](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Aeva-numerical-labour-days-1000) — Project Engineering, chapter 4, asked 2×
- [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
- [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

## Related in other subjects

- [EVA numerical with five activities at day 5](https://www.bctengineer.com/question.md?key=semester_8%2Fconstruction_management%3Aeva-numerical-2070-magh) — Construction Management, chapter 7