---
title: "Sources of risk; best building height"
subject: "Engineering Economics"
chapter: 6
key: "semester_6/engineering_economics:risk-sources-nepal-building-floors"
source: https://www.bctengineer.com/q/semester_6/engineering_economics/risk-sources-nepal-building-floors
site: BCT Engineering
---

# Sources of risk; best building height

Engineering Economics · Chapter 6: Risk Analysis

- Asked in: 2070 Bhadra, 4+8 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/engineering_economics/risk-sources-nepal-building-floors
- Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-6

## Question

What are the sources of risk in engineering projects in Nepal? A real-estate developer seeks to determine the most economical height for a new office building which will be sold after five years. The relevant net annual revenues and net resale values are as given below.
|  | 4 Floors | 5 Floors |
|---|---|---|
| First Cost | 125,000,000 | 200,000,000 |
| Annual Revenues | 19,910,000 | 37,815,000 |
| Net Resale Value | 200,000,000 | 300,000,000 |
The developer is uncertain about the interest rate i to use, but is certain that it is in the range of 5 to 30%. For each building height, find the range of values of i for which that building height is the most economical. Draw sensitivity diagram to support your answer.

## Short answer

Risk sources in Nepal: political/policy, cost/time overruns, natural hazards, market/revenue, financial, technical/supply, social/environmental. For 5%≤i<27.7%, 5-floor building is more economical; for 27.7%<i≤30%, 4-floor is better (curves cross at i*=27.7%). 5-floor IRR=25%, 4-floor IRR=23.5%.

## Answer

#### Sources of risk in engineering projects in Nepal
Risk exists when outcomes are uncertain but their probabilities can be estimated. The main sources in Nepal are:
- **Political and policy risk:** frequent changes of government and policy, bandhs and strikes, delays in decisions, changes in tax and royalty rules.
- **Cost and time overrun:** poor design, delayed land acquisition, right-of-way and compensation disputes, weak contract management, delayed payments to contractors.
- **Natural hazards:** earthquakes, floods, landslides, and hydrological variation (for hydropower), plus difficult terrain and monsoon disruption.
- **Market and revenue risk:** demand uncertainty and a small market, dependence on a single buyer (such as NEA) and changes in tariff.
- **Financial risk:** interest-rate changes, shortage of liquidity or foreign currency, inflation and exchange-rate variation (imported materials and equipment).
- **Technical and supply risk:** unproven technology, dependence on imports through India, transport delays, scarcity of skilled labour.
- **Social and environmental risk:** local opposition, EIA conditions and community demands.

#### Most economical building height
Net resale value is the salvage at year 5. PW(i) = −First cost + Annual revenue (P/A, i, 5) + Resale (P/F, i, 5) (Rs million).

| i | PW (4 floors) | PW (5 floors) | Better |
|---|---|---|---|
| 5% | 117.91 | 198.78 | 5 floors |
| 10% | 74.66 | 129.62 | 5 floors |
| 15% | 41.18 | 75.91 | 5 floors |
| 20% | 14.92 | 33.65 | 5 floors |
| 25% | -5.92 | 0.00 | 5 floors |
| 30% | -22.64 | -27.10 | 4 floors |

Worked example at i = 10%: (P/A,10%,5) = 3.7908, (P/F,10%,5) = 0.6209.
```text
4 floors: −125 + 19.91(3.7908) + 200(0.6209) = 74.66 million
5 floors: −200 + 37.815(3.7908) + 300(0.6209) = 129.62 million
```
#### Break-even interest rate between the two heights
The fifth floor needs an extra investment of Rs 75 million and gives extra annual revenue of 17.905 million and extra resale value of 100 million. Setting PW(5) = PW(4):
```text
−75 + 17.905(P/A,i,5) + 100(P/F,i,5) = 0   →   i* = 27.7%
```
(IRR of 4 floors = 23.5%; IRR of 5 floors = 25.0%.)

#### Sensitivity diagram
```text
   198.8 |    5
         |
   170.5 |
         |
   142.3 |
         |            5
   114.1 |    4
         |
    85.8 |
         |            4       5
    57.6 |
         |                    4
    29.4 |                            5
         |                            4
     1.1 |------------------------------------*-----------
         |
   -27.1 |                                            *
         +------------------------------------------------
             5       10      15      20      25      30   
          interest rate i (%)   (y: PW in Rs million; 4 = 4 floors, 5 = 5 floors)
```
#### Ranges of i
- **5% ≤ i < 23.5%:** both PWs are positive and the **5-floor** building has the larger PW.
- **23.5% < i < 25%:** the 4-floor PW is negative (above its IRR of 23.5%), while the 5-floor PW is still positive, so 5 floors is better.
- **25% < i < 27.7%:** both PWs are negative (the 5-floor PW is zero at 25% and negative above it); 5 floors is the smaller loss.
- **27.7% < i ≤ 30%:** the 4-floor building has the larger (less negative) PW, but both PWs are negative.

**Answer:** Comparing the two heights, the **5-floor building is the more economical for 5% ≤ i < 27.7%** and the **4-floor building for 27.7% < i ≤ 30%** (the curves cross at i* = 27.7%). If not building is also an option, the 5-floor building is worth building only for i ≤ 25%; above 25% neither height earns the required return, and the 4-floor building's advantage above 27.7% is only a smaller loss.

## Check yourself

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

1. Risk differs from uncertainty because in risk:
   A. Outcomes are unknown and no probabilities exist
   B. Outcomes are uncertain but their probabilities can be estimated
   C. Outcomes are certain
   D. There is no cost involved
   Answer: B. Risk exists when outcomes are uncertain but probabilities can be estimated. (Key point: Meaning of risk)

2. How is PW of each building height computed?
   A. PW = -First cost + Annual revenue (P/A,i,5) + Resale (P/F,i,5)
   B. PW = First cost + Annual revenue x 5
   C. PW = Resale - First cost
   D. PW = Annual revenue only
   Answer: A. The net resale value is the year-5 salvage, discounted with (P/F). (Key point: PW comparison method)

3. For 5% <= i <= 25%, which height is most economical?
   A. 4 floors
   B. Neither at any rate
   C. Equal for both
   D. 5 floors
   Answer: D. The 5-floor building has larger PW and positive PW for all i up to 25%. (Key point: Most economical height range)

4. What does the break-even rate of 27.7% between the two heights mean?
   A. Below 27.7% 5 floors has the greater PW; above it 4 floors is the smaller loss, though both have negative PW there
   B. Above 27.7% both are profitable
   C. Below 27.7% 4 floors is better
   D. It is the IRR of 4 floors
   Answer: A. At 27.7% the incremental fifth floor earns exactly zero PW; but beyond 25% neither height earns the required return, so neither should be built. (Key point: Break-even interest rate)

## Related in Engineering Economics

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## Related in other subjects

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- [Most economical conductor, five options (Rs 9)](https://www.bctengineer.com/question.md?key=semester_8%2Ftransmission_and_distribution_system_design%3Aeconomic-conductor-five-options-kwh) — Transmission and Distribution System Design, chapter 4, asked 3×
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- [Preliminary estimate: five-storey office, 2500 m²](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Aprelim-est-five-storey-2500) — Estimating and Costing, chapter 3