Case 020Client mandates and IPSCore

A retiree of 60 has Rs 3 crore, spends Rs 15 lakh a year rising with 6% inflation, and expects his portfolio to earn 9%. How many years does the money last, and what starting spending would last 30 years?

The situation

Prakash Hegde has just retired at 60 with Rs 3 crore. He plans to withdraw Rs 15 lakh at the start of each year, rising 6% a year with inflation. His portfolio is expected to earn 9% a year, and he has no pension or other income.

He points out that he is withdrawing only 5% of his money while it earns 9%, and asks why he cannot spend more.

Your task

How long does the money last, what starting withdrawal would last 30 years, and what do you tell him about his 5% against 9% reasoning?

Quick check

Roughly how long do Prakash's savings last?

Worked solution

Try it on paper, then open one step at a time.

30-second answerThe answer to give first

About 28.6 years, so the money runs out at about 89, and a starting withdrawal of about Rs 14.6 lakh would last 30 years. The 9% return is not the number that matters: spending grows 6% a year, so the portfolio effectively earns only about 2.83% more than spending grows. His 5% withdrawal is too high for a gap that thin, though only just.

Step 1Why is 5% against 9% the wrong comparison?

Because the withdrawal is not fixed; it grows with prices. What sustains a rising withdrawal is the gap between the return and inflation, here 1.09 divided by 1.06, about 2.83% a year, not the 9% return. With flat spending, 9% on Rs 3 crore could fund Rs 24.8 lakh a year for ever. A tank with a tap running out and a pipe filling it only stays full if the pipe flows faster than the tap, and here the tap opens a little wider every year.

Step 2How long does the money last?

Treat the withdrawals as a stream that grows 6% a year and is discounted at 9%. Each year's withdrawal, in today's money, is 1.06 over 1.09 times the previous one. Setting the value of that stream equal to Rs 3 crore and solving for the number of years gives about 28.6: 28 full years of spending and part of the 29th, so the money runs out at about age 89.

The relationship
300=15∑t=0n−1(1.061.09)t  ⇒  n=ln⁡(1−20 (1−q))ln⁡q≈28.6,q=1.061.09300 = 15 \sum_{t=0}^{n-1} \left(\frac{1.06}{1.09}\right)^t \;\Rightarrow\; n = \frac{\ln\left(1 - 20\,(1 - q)\right)}{\ln q} \approx 28.6, \quad q = \frac{1.06}{1.09}
300the corpus, Rs lakh
15first withdrawal, Rs lakh, taken at the start of the year
qhow much each withdrawal shrinks in today's money: 1.06 / 1.09
20300 / 15, the corpus in years of starting spending
What it says in wordsThe money lasts until the discounted value of the rising withdrawals adds up to the corpus.
Rs 3 crore at 60: how long it lasts depends on where spending starts012345678Rs crore60708090100age 90Rs 12 lakh: 41.7 yearsRs 15 lakh: 28.6 yearsRs 18 lakh: 22.0 yearsAge; each path withdraws at the start of the year, rising 6% a year, and earns 9%
With a 9% return and withdrawals rising 6% a year, Rs 3 crore lasts about 42 years at Rs 12 lakh, 28.6 years at Rs 15 lakh and 22 years at Rs 18 lakh, so a 3 lakh change in starting spending moves the run-out age by six to thirteen years.
Step 3What starting withdrawal lasts 30 years?

Run the same stream backwards with n fixed at 30. A starting withdrawal of about Rs 14.6 lakh, rising 6% a year, lasts exactly 30 years, to age 90. The gap between Rs 15 lakh and Rs 14.6 lakh looks trivial, but it moves the run-out date by well over a year. Put the other way, keeping Rs 15 lakh and lasting 30 years needs a return of about 9.26%, a small change in the average that is a large change in the risk he must take.

Starting withdrawal, Rs lakhShare of Rs 3 croreYears it lastsMoney runs out at about
124.0%41.7102
155.0%28.689
186.0%22.082
14.64.85%30.090
Every lakh of starting spending matters when the real return is only about 2.83%: Rs 12 lakh lasts past 100, Rs 18 lakh runs out at about 82, and Rs 14.6 lakh lasts exactly 30 years.
Step 4What else would you tell him?

Two things. A 9% average is not a 9% every year, and falls early in retirement do lasting damage because he is selling to fund spending while prices are low, so the real run-out date could come years sooner; keep two or three years of spending in low-risk assets. And plan for living past 88: a starting withdrawal a little under Rs 14.6 lakh, reviewed every year, buys both time and a margin.

Where candidates lose it

The classic error is comparing the withdrawal rate with the nominal return, 5% against 9%, and concluding the money lasts for ever. That holds only for flat withdrawals; once spending rises with prices, only the gap over inflation counts.

The second is using end-of-year withdrawals when the client spends at the start of the year. It adds almost a year of apparent life and shifts the answer the interviewer is checking.

What the interviewer asks next

  • Inflation turns out to be 7% instead of 6%. How long does the money last now?
  • How would buying an annuity with Rs 1 crore change the plan?
  • What is sequence risk, and how would you show it to Prakash with two ten-year return paths?

Company names and figures are illustrative.