Calculate the capital value of a building whose rent is ₹10,000 per annum, inclusive of all taxes. Outgoings are 18% of the gross rent, and the expected rate of return is 9% with a 60-year life of the building.
- A₹81,000
- B₹91,111Correct
- C₹1,01,000
- D₹75,000
Solution
Concept
Capital value = Net annual income × Years' Purchase (YP)
Formula
Net income = Gross rent − Outgoings; YP = 100/r (perpetuity); Capital value = Net income × YP
Step-by-step solution
1. Gross rent = ₹10,000 per year. 2. Outgoings = 18% × 10,000 = ₹1,800. 3. Net income = 10,000 − 1,800 = ₹8,200. 4. YP = 100/9 = 11.111. 5. Capital value = 8,200 × 11.111 = ₹91,111.
Explanation
First remove the outgoings from the gross rent to get the net income. Then multiply the net income by the Years' Purchase at 9%. This gives about ₹91,111. If a sinking fund for the 60-year life is added at 9%, the value is about ₹90,600, which is still closest to option B.
Why the other options are wrong
A: ₹81,000 does not match any correct YP calculation. C: ₹1,01,000 is too high. It is close to the result of using a rate below 9% or ignoring outgoings. D: ₹75,000 is too low and does not come from 8,200 × YP at 9%.
Shortcut
Capital value ≈ Net income / rate = 8,200 / 0.09 = ₹91,111
Common mistake
Using the gross rent ₹10,000 instead of the net rent ₹8,200.
Correct answer: B) ₹91,111