--- title: "Value of property and fair value numerical" subject: "Construction Management" chapter: 13 key: "semester_8/construction_management:value-property-numerical-2073" source: https://www.bctengineer.com/q/semester_8/construction_management/value-property-numerical-2073 site: BCT Engineering --- # Value of property and fair value numerical Construction Management · Chapter 13: Valuation - Asked in: 2073 Bhadra, 1+6 marks - Video: [Fair Value of Property Numericals || Valuation Numericals|| Rent Fixation Numericals || valuation](https://www.youtube.com/watch?v=WxtsmI4QrZs) — Mukesh Kumar - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_8/construction_management/value-property-numerical-2073 - Whole chapter: https://www.bctengineer.com/md/semester_8/construction_management/chapter-13 ## Question Define value of any property and what is to be satisfied by any property to have its value. A person desire to sale his property having details as: Gross rent = Rs 5000 per month, total outgoings = 25% of gross rent, estimated future life = 35 yrs, area of land = 200 $m^2$, estimated value of Land = Rs 2000 per square meter. Determine the fare value of property. Take rate of interest on capital as 10% and rate of redemption of capital as 5%. Assume suitable data, if required. ## Short answer A property has value if it has utility, scarcity, demand and transferability. Using the income method: annual net income Rs45,000 after 25% outgoings; land interest Rs40,000 leaves Rs5,000 for building; dual-rate YP 9.003 gives building Rs45,016, land Rs4,00,000; total fair value Rs4,45,016. ## Answer #### Value The **value** of a property is its present worth in money, i.e. the price a willing buyer would pay and a willing seller would accept. To have value a property must satisfy: **utility** (it must be useful), **scarcity** (limited supply), **demand** (people want it, backed by purchasing power) and **transferability** (clear legal title that can be sold or transferred). #### Numerical (income method with land and building separated) Gross rent per year = 5000 × 12 = Rs 60,000 Outgoings = 25% × 60,000 = Rs 15,000 Net income = 60,000 − 15,000 = Rs 45,000 Value of land = 200 × 2000 = Rs 4,00,000 Interest on land at 10% = Rs 40,000 (land does not depreciate, so no redemption) Net income from building = 45,000 − 40,000 = Rs 5,000 **Year's purchase (dual rate)**, i = 10%, sinking fund rate r = 5%, n = 35 years: $$ YP = \frac{1}{i + \dfrac{r}{(1+r)^n - 1}} = \frac{1}{0.10 + \dfrac{0.05}{(1.05)^{35}-1}} = 9.003 $$ Value of building = 5,000 × 9.003 = Rs 45,016 Fair value of property = value of land + value of building = 4,00,000 + 45,016 = Rs 4,45,016 **Answer: Fair value of the property is about Rs 4,45,000.** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Which set of attributes must a property satisfy to have value? A. Colour, shape, size B. Age and name C. Tax only D. Utility, scarcity, demand and transferability Answer: D. A property needs utility, scarcity, demand and transferability. (Key point: Requirements of value) 2. What is the net income in the problem? A. Rs 60,000 B. Rs 45,000 (60,000 less 25% outgoings) C. Rs 5,000 D. Rs 15,000 Answer: B. Gross 5000 x 12 = 60,000, outgoings 15,000, net 45,000. (Key point: Net income) 3. How is the building income found? A. Net income x 10 B. Land value x 5% C. 60,000 - 5,000 D. Net income 45,000 - interest on land 40,000 = Rs 5,000 Answer: D. Land value 4,00,000 at 10% gives 40,000; remaining 5,000 is from the building. (Key point: Land treatment) 4. What is the fair value? A. About Rs 5,000 B. About Rs 4,45,000 (land 4,00,000 + building 45,016) C. About Rs 4,00,000 D. About Rs 45,000 Answer: B. Building = 5,000 x 9.003 = 45,016; plus land 4,00,000 gives about Rs 4,45,000. 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