Portfolio Management puzzles, solved step by step
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031An office building has gross potential rent of Rs 10 crore a year. Vacancy runs at 8%, and operating costs are 30% of the rent actually collected. At an 8% cap rate, what is the building worth? Walk through it from gross potential rent.InvescoNew York · 2025
Try it first
Which number does the cap rate divide?
Show the worked solution
About Rs 80.5 crore. Vacancy of 8% takes Rs 10 crore of gross potential rent down to Rs 9.2 crore collected. Operating costs of 30% of that are Rs 2.76 crore, leaving net operating income of Rs 6.44 crore. Divide by the 8% cap rate: 6.44 over 0.08 is Rs 80.5 crore, or 12.5 times the income.
Why does the cap rate price net operating income and not the rent?
Think of buying a shop that a friend runs. You would not pay for the sales the shop could make if every shelf sold out; you pay for what is left after empty days and the electricity bill. A cap rate is net operating income divided by value, so the value is only ever as good as the income that actually reaches the owner after vacancy and running costs. Gross potential rent is the ceiling, not the income.
Rs 10 crore of gross potential rent loses Rs 0.8 crore to vacancy and Rs 2.76 crore to operating costs, leaving Rs 6.44 crore of net operating income. At an 8% cap rate that income is worth Rs 80.5 crore. What are the lines between gross rent and value, in order?
Say them as a ladder. Gross potential rent is what a full building earns at the rent roll. Take off vacancy and bad debt to get effective gross incomeThe rent a building actually collects after vacancy and unpaid rent, before any running costs.. Take off operating expenses, such as maintenance, insurance, property tax and management, to get net operating income. Every line above NOI moves the price by 12.5 times its size at an 8% cap rate, so a small leak near the top is a large leak in value. One extra point of vacancy costs Rs 0.1 crore of rent, Rs 0.07 crore of NOI, and Rs 0.875 crore of value.
The relationshipGPR gross potential rent, Rs 10 crore v vacancy rate, 8% o operating costs as a share of collected rent, 30% c the cap rate, 8% What it says in wordsValue is the income that survives vacancy and costs, divided by the yield buyers demand.For an exit value, the same arithmetic runs on the NOI expected in the sale year and an exit cap rate, which analysts often set a little above the entry cap rate to allow for an older building. Say which cap rate you are using and why, and say that capital spending such as a new roof sits below NOI and is not captured by this shortcut.
Where candidates lose it
The costly slip is dividing gross potential rent by the cap rate, which gives Rs 125 crore and overpays by Rs 44.5 crore. The other is applying the 30% cost ratio to gross rent rather than collected rent, which gives NOI of Rs 6.2 crore and a value Rs 3 crore too low.
Walk the ladder aloud, line by line, and name what each deduction is. Interest never appears: it depends on how the buyer finances the building, not on the building.
What the interviewer asks next
- The buyer expects NOI to grow 3% a year and plans to sell in five years at an 8.5% exit cap rate. What is the exit value?
- Why might a buyer's cap rate for this building differ from the seller's?
- What happens to value if operating costs rise to 35% of collected rent?
Asked at Invesco, Real Estate, New York, 2025 (Wall Street Oasis):
Walk me through how to get the exit value of a property from Gross Potential rent, using Cap rate.
054Without a calculator: what IRR turns money into 2.5 times in four years, and what IRR turns it into 3 times in five years?Neuberger BermanLondon · 2026
Try it first
Which pair is closest?
Show the worked solution
About 26% and about 25%. For 2.5 times in four years, take the square root of 2.5 twice: 1.58 and then 1.257, so 25.7% a year. For 3 times in five years, anchor on the fact that 2 times in three years is 26%; 3 times in five sits just below it at 24.6%. The bigger multiple over the longer hold is actually the lower annual return.
Why is the simple average so far off?
A savings account that pays 26% a year does not add 26 rupees every year to your 100. It adds 26 in year one, then 26% of 126 in year two, and so on, so by year four you have about 250. The IRR is the steady annual rate that compounds to the multiple, so it is always well below the total gain divided by the years. The simple average for 2.5 times in four years would be 150% over 4, or 37.5%, which overstates the true 25.7% by more than ten points.
The relationshipM the money multiple, cash back over cash in n the years held, with one cash flow in and one out What it says in wordsThe IRR is the nth root of the multiple, less one.How do you get there in your head?
Use one of two tricks. For four years, take the square root twice: the square root of 2.5 is about 1.58, and the square root of 1.58 is about 1.257. For odd holding periods, use logs: the natural log of 3 is about 1.10, divided by five is 0.22, and adding a little for compounding turns 22% into about 24.6%. Faster still is a small grid of anchors you know by heart, because interviewers ask the same handful of multiples and periods.
A grid of IRRs by multiple and holding period shows 2.5 times in four years at 25.7% and 3 times in five years at 24.6%, and a band of 2 times in three, 2.5 times in four and 3 times in five years all near 25%. Notice the diagonal band. Two times in three years, two and a half in four and three in five all land within a point of 25%. That one pattern lets you place almost any private equity outcome in a second. Say the limitation too: this shortcut assumes a single cash flow in and a single cash flow out. Real funds call and return money in stages, and the IRR then depends on the timing, not just the multiple.
Where candidates lose it
The trap is dividing the gain by the years, 150% over four and 200% over five, and answering 37.5% and 40%. It sounds confident and is wrong by more than ten points, and a private markets interviewer hears it as not understanding compounding.
The quieter miss is thinking 3 times must be the better deal because the multiple is bigger. The extra year costs more than the extra half turn of money earns.
What the interviewer asks next
- What multiple does a 20% IRR give over five years?
- A fund returns 2 times in three years and another 2.5 times in six. Which would you rather have, and what else would you ask?
- Why can two deals with the same multiple and the same holding period show different IRRs?
Asked at Neuberger Berman, Generalist, London, 2026 (Wall Street Oasis):
The associate interview was quite technical, covered 5-7 questions on valuation and understanding of returns in private equity
