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Private Wealth Management puzzles, solved step by step

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All topicsCompounding and doubling8Returns arithmetic9Fee and cost drag8Inflation and real return7Tax arithmetic7Probability and risk of loss9Retirement and withdrawal8Fixed income numeracy8Behavioural traps8Estimation and sizing8Options and structured products6Leverage and borrowing6Wealth business economics8
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  1. 059A client spends Rs 1 lakh a month and holds Rs 2.4 crore of investments. How many years of spending is that, and how far is it from the common planning marker of 25 times annual spending?Retirement and withdrawalWarm upIndian wealth management

    Try it first

    Rs 2.4 crore against Rs 1 lakh a month is how many years of spending?

    Show the worked solution

    Twenty years of spending, Rs 60 lakh short of 25 times. Rs 1 lakh a month is Rs 12 lakh a year, and Rs 2.4 crore over Rs 12 lakh is 20. Twenty-five times spending would be Rs 3 crore. Put another way, the client would withdraw 5% of the corpus in year one, against the 4% that the 25 times marker implies.

    Why express a corpus in years of spending?

    A client hears Rs 2.4 crore and feels rich; a client who hears twenty years of your current life hears a question: and after that? Dividing the corpus by annual spending turns an abstract balance into a length of time, which is what a retirement decision is actually about. It also removes the units: the same arithmetic works for a Rs 50 lakh corpus or a Rs 50 crore one.

    Rs 2.4 crore in years of spending: 20 blocks of Rs 12 lakhCorpusRs 240 lakh15101520each block is one year of spending, Rs 12 lakh-6025x spending = Rs 300 lakhThis client20 yearswithdraws 5% a year25x marker25 yearswithdraws 4% a year
    Rs 2.4 crore is 20 blocks of Rs 12 lakh, twenty years of spending, and the 25 times marker sits at Rs 3 crore, so the client is Rs 60 lakh short and would withdraw 5% a year rather than 4%.

    Where does 25 times come from, and how firm is it?

    Twenty-five times spending is the same thing as withdrawing 4% a year, the 4% ruleA planning guideline from US research by William Bengen in the 1990s: withdraw 4% of the starting portfolio, raised each year for inflation, and the money historically lasted about 30 years. from US retirement research. It is a starting point, not a law, because it came from one country's market history and a 30 year retirement. Higher inflation, longer lives and early retirement all argue for a larger multiple, and planners in India often use one. Say the marker, then say its limits.

    Does twenty years of spending mean the money runs out in twenty years?

    Only if the corpus earns exactly inflation. If it earns 2% a year above inflation and the client withdraws Rs 12 lakh in today's money at the start of each year, the money lasts about 25 years. Years of spending is a zero-real-return yardstick, so it is conservative when real returns are positive and optimistic when they are negative. That is why it is the right first number to say, and the wrong last one.

    Where candidates lose it

    The arithmetic trap is dividing by the monthly figure, or mixing lakh and crore, and announcing 240 or 2.4 years. Convert both numbers to lakh a year before dividing.

    The judgement trap is treating 25 times as a pass mark. A good answer gives the gap, Rs 60 lakh, and then says the marker came from one market's history and needs adjusting for this client.

    What the interviewer asks next

    • How much would the client have to cut monthly spending to reach 25 times today?
    • If the corpus earns 1% above inflation, how long does Rs 2.4 crore last?
    • Why might a 45 year old retiring early need more than 25 times?
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