---
title: "Sources of finance; ARR, payback, IRR, PI decision"
subject: "Project Engineering"
chapter: 6
key: "semester_7/project_engineering:project-finance-sources-investment-decision-c75"
source: https://www.bctengineer.com/q/semester_7/project_engineering/project-finance-sources-investment-decision-c75
site: BCT Engineering
---

# Sources of finance; ARR, payback, IRR, PI decision

Project Engineering · Chapter 6: Introduction to Project Financing

- Asked in: 2075 Chaitra, 2+4 marks
- Video: [Project Selection Criteria: NPV, IRR, Payback Period, and Profitability Index](https://www.youtube.com/watch?v=Jx8sFMnuFsw) — Management Tutorials
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/project_engineering/project-finance-sources-investment-decision-c75
- Whole chapter: https://www.bctengineer.com/md/semester_7/project_engineering/chapter-6

## Question

What are the sources of project finance? A project has an initial investment of Rs 3,00,000 which gives an annual return of Rs 50,000 for 8 years. The salvage value after 8 years will be Rs 10,000. Make your investment decision based on ARR, payback period, IRR and Profitability Index (PI) method.

## Short answer

Sources include equity, quasi-equity, debt, government/donor funds, supplier credit, leasing, venture capital, and PPP. For the project: ARR=8.87%, payback=6.0 years, IRR=7.37%, PI=0.905. At a 10% cost of capital, NPV is negative, IRR<10%, and PI<1, so the investment is not recommended.

## Answer

#### Sources of project finance

| Type | Sources |
|---|---|
| Equity | Ordinary shares, sponsors' equity, retained earnings, public issue (IPO) |
| Quasi-equity | Preference shares, convertible debentures |
| Debt (long term) | Bank and financial institution loans, debentures/bonds, syndicated loans, term loans |
| Government / donors | Government grants and budget, soft loans from ADB, World Bank, JICA, Exim banks, bilateral aid |
| Others | Supplier's credit, leasing, venture capital, public-private partnership (PPP), build-operate-transfer (BOT), community and user contribution, remittance/pooled funds |

#### Investment decision

Data: investment = Rs 3,00,000; annual return = Rs 50,000 for 8 years; salvage = Rs 10,000. The required rate is not given, so **10% is assumed** as the cost of capital; the return is treated as annual profit before depreciation (cash inflow), and tax is ignored.

**1. ARR**

$$
\begin{aligned}
\text{Depreciation} &= \frac{300{,}000 - 10{,}000}{8} = 36{,}250\\
\text{Average profit} &= 50{,}000 - 36{,}250 = 13{,}750\\
\text{Average investment} &= \frac{300{,}000 + 10{,}000}{2} = 155{,}000\\
ARR &= \frac{13{,}750}{155{,}000} \times 100 = 8.87\%
\end{aligned}
$$

**2. Payback period**

$$
\text{Payback} = \frac{300{,}000}{50{,}000} = 6.0\ \text{years}
$$

**3. IRR:** find $i$ at which $-300{,}000 + 50{,}000\,(P/A,i,8) + 10{,}000\,(P/F,i,8) = 0$. At 7%, PW = +4,385; at 8%, PW = -7,267. By interpolation, **IRR = 7.37%**.

**4. Profitability index** (at 10%; annuity factor = 5.3349, PV factor = 0.4665)

$$
\begin{aligned}
PV_{inflow} &= 50{,}000 \times 5.3349 + 10{,}000 \times 0.4665 = 271{,}411\\
PI &= \frac{271{,}411}{300{,}000} = 0.905, \quad NPV = -28{,}589
\end{aligned}
$$

| Method | Result | Criterion | Decision |
|---|---|---|---|
| ARR | 8.87% | Accept if ARR > required return (10%) | Reject |
| Payback | 6.0 years | Within the 8-year life, but long (75% of life) | Weak |
| IRR | 7.37% | Accept if IRR > 10% | Reject |
| PI | 0.905 | Accept if PI > 1 | Reject |

**Answer: ARR = 8.87%, payback = 6.0 years, IRR = 7.37%, PI = 0.905. The IRR is below 10% and PI is below 1, so the investment is not recommended** at a 10% cost of capital. It would be acceptable only if the required rate were below about 7.4%.

## Check yourself

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

1. Which is a long-term debt source of project finance?
   A. Ordinary shares
   B. Bank and financial institution term loans
   C. Retained earnings
   D. Sponsors' equity
   Answer: B. Term loans, debentures/bonds and syndicated loans are debt sources. (Key point: Sources of finance)

2. Payback for investment Rs 3,00,000 and annual return Rs 50,000 is:
   A. 8 years
   B. 5 years
   C. 6 years
   D. 7.37 years
   Answer: C. 300,000/50,000 = 6 years. (Key point: Payback)

3. Which gives the ARR (8.87%)?
   A. 50,000 / 300,000
   B. 36,250 / 155,000
   C. 13,750 / 300,000
   D. Average profit 13,750 / average investment 155,000
   Answer: D. Depreciation 36,250; average profit 50,000 - 36,250 = 13,750; average investment = 155,000. (Key point: ARR calculation)

4. Why is the investment not recommended at 10%?
   A. IRR (7.37%) is below 10% and PI is below 1
   B. Payback is 1 year
   C. ARR is above 100%
   D. NPV is positive
   Answer: A. PI = 0.905 and NPV = -28,589; it would be acceptable only if the required rate were below about 7.4%. (Key point: Decision)

## Related in Project Engineering

- [Conventional vs project financing; ARR, NPV, PI, payback](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Aconventional-vs-project-financing-numerical) — Project Engineering, chapter 6
- [EPS and book value; ABC project Rs 6,00,000](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Aeps-bv-abc-project-600000-b79) — Project Engineering, chapter 6
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- [EPS and book value; capital Rs 5,00,000](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Aeps-bv-capital-500000-2000-shares) — Project Engineering, chapter 6
- [Capital budgeting; ARR numerical, Rs 100000](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Acapital-budgeting-arr-numerical-c72) — Project Engineering, chapter 6
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