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096

Case 096Retirement, withdrawals and life eventsCore

A 65-year-old has Rs 50 lakh. An annuity at 7% pays Rs 29,167 a month for life with no capital returned. An SWP of the same amount lasts indefinitely if the portfolio earns 7.5% but runs out at about 90 if it earns 5%. How would you split the money?

1The situation

Kurian Mathai has just retired at 65 with Rs 50 lakh of retirement savings, a paid-off house and a small pension that covers about half his living costs. He needs roughly Rs 29,000 a month from the Rs 50 lakh. An insurer offers a life annuity at an assumed rate of 7%: Rs 29,167 a month for as long as he lives, with nothing returned to his family when he dies. A variant that returns the purchase price to his nominee pays an assumed 6%, Rs 25,000 a month.

The alternative is a systematic withdrawal plan from a conservative hybrid fund, drawing the same Rs 29,167 a month. Test it at portfolio returns of 7.5%, 6% and 5% a year. Annuity rates, the tax treatment of annuity income against SWP withdrawals, and the fund's returns are all assumptions; confirm the current figures.

2Your task

What does each option give him and take from him, what does the return assumption do to the SWP, and how would you split the Rs 50 lakh?

Quick check

The SWP portfolio earns 5% a year instead of 7.5%. What happens to a Rs 29,167 monthly withdrawal?

Worked solution

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

30-second answerThe answer to give first

Put about 40% into the annuity and run the SWP on the rest. The annuity sells certainty of income for life and gives up the capital; the SWP keeps the capital but at 5% the money is gone at about 90, while at 7.5% it never is. Rs 20 lakh in the annuity pays Rs 11,667 a month whatever happens, and the Rs 30 lakh SWP supplies the other Rs 17,500 with the capital still his. If returns disappoint, his income falls to the annuity floor rather than to zero.

Step 1What is each option actually selling?

Two different things, which is why the headline rates mislead. Buying a flat and renting one can cost the same each month; one leaves you owning something and exposed to the price, the other leaves you with nothing to sell and nothing to worry about. The annuity converts Rs 50 lakh into an income for life and takes the capital in exchange, so the 7% is not a return, it is the price of the insurer carrying the risk that he lives to 95. The SWP keeps the Rs 50 lakh in his name and lets him draw on it, so he keeps the capital, the flexibility and the whole of the return risk. The systematic withdrawal planA standing instruction to redeem a fixed sum from a mutual fund on a set date each month. The withdrawal is paid from the units, so the corpus shrinks whenever the fund earns less than the amount drawn. is only as reliable as the fund's return.

Step 2What does the return assumption do to the SWP?

Everything. The arithmetic is a race between what the corpus earns and what he takes out. At 7.5% it earns about Rs 31,250 a month against a Rs 29,167 withdrawal, so the corpus grows and the plan lasts indefinitely. At 5% it earns Rs 20,833, the shortfall comes out of capital, and the money is gone after about 25 years, at age 90. At 6% it lasts into his nineties with about Rs 8 lakh left at 95. The sequence matters as much as the average: a bad first five years with full withdrawals does more damage than the same bad years later, because the withdrawals are taken from a smaller base.

The same Rs 29,167 a month: what is left of the Rs 50 lakh at each age20406080Rs lakh65707580859095Agegone at 90earns 7.5%: the corpus growsearns 6%: about Rs 8 lakh left at 95earns 5%: runs out at about 90Rs 50 lakh at 65Annuity at 7%: Rs 29,167 a month for lifecorpus is Rs 0 from day one, income never stops
Drawing Rs 29,167 a month from Rs 50 lakh, the corpus grows at 7.5%, is still about Rs 8 lakh at 95 if it earns 6%, and runs out at about 90 if it earns 5%, while the annuity pays the same income for life with no corpus at all.
The relationship
n=−ln⁡(1−PrW)ln⁡(1+r)=−ln⁡(1−20,83329,167)ln⁡(1.004167)≈301 monthsn = -\frac{\ln\left(1 - \frac{P r}{W}\right)}{\ln(1 + r)} = -\frac{\ln\left(1 - \frac{20{,}833}{29{,}167}\right)}{\ln(1.004167)} \approx 301 \text{ months}
Pthe corpus, Rs 50 lakh
rmonthly return, 5% / 12
Wmonthly withdrawal, Rs 29,167
nmonths until the corpus is exhausted
What it says in wordsThe corpus lasts a number of months set by how far the withdrawal exceeds what the corpus earns; if it earns more than the withdrawal, it lasts forever.
Step 3What does the annuity cost him?

Three things. The capital: if he dies at 72, the insurer keeps most of the Rs 50 lakh; the return-of-purchase-price variant fixes that but pays Rs 25,000 instead of Rs 29,167. Liquidity: an annuity cannot be redeemed for a hospital bill or a daughter's wedding. And inflation: the payment is fixed in rupees, so at 5% inflation its buying power halves in about 14 years, by his late seventies. The SWP can be stepped up each year, at the cost of running out sooner. Tax usually differs too: annuity income is typically taxed as income, while SWP withdrawals are taxed only on the gain inside each redemption; confirm the current treatment, because it can change the comparison by a few thousand rupees a month.

Annuity at 7%SWP at 7.5%SWP at 5%
Income a monthRs 29,167 for lifeRs 29,167Rs 29,167
Corpus after 10 yearsNilRs 53.7 lakhRs 37.1 lakh
Income stopsNeverNeverAbout age 90
Left for the familyNil (unless purchase price returned at 6%)The corpusNil after the money runs out
Can be increased for inflationNoYes, at a costOnly by running out sooner
Can be redeemed in an emergencyNoYesYes
The annuity fixes the income and removes the capital, while the SWP keeps the capital and makes the income depend on a return he cannot control.
Step 4How would you split it?

Cover the floor with the annuity and keep the rest flexible. Rs 20 lakh in the annuity pays Rs 11,667 a month for life; Rs 30 lakh in the SWP supplies the remaining Rs 17,500, keeps Rs 30 lakh liquid and leaves something for his family if returns are reasonable. If the fund earns only 5%, the SWP still runs out around 90, but his income then falls to Rs 11,667 plus his pension rather than to the pension alone, and he has had 25 years to notice and cut the withdrawal. The split can tilt: a man with no family to leave money to and a long-lived family history takes more annuity; one with health problems or dependants takes less. The limits: annuity rates move with interest rates and are set for life on the day he buys, so buying in two tranches a year apart spreads that risk; the SWP returns are assumptions; and the right withdrawal rate from Rs 30 lakh may be lower than Rs 17,500 if he wants it to last past 90 on a 5% return.

Where candidates lose it

Candidates compare 7% with 7.5% and pick the SWP because the number is higher. The annuity's 7% is income from capital he gives up; the SWP's 7.5% is an assumed return on capital he keeps, and at 5% the same withdrawal exhausts it at about 90.

The second miss is treating the two as rivals. The question asks for a split because each covers the other's weakness: the annuity cannot run out, the SWP cannot be lost on death or locked up in an emergency.

What the interviewer asks next

  • He wants his income to rise 4% a year. How does that change the SWP's life at 6%, and what annuity would give it?
  • How would you handle a 25% fall in the SWP fund in his first year of retirement?
  • Why might buying the annuity in two tranches a year apart be sensible?
  • What questions about his health and family would change the split?
← Case 095An equity fund with Rs 1,600 crore of net assets failed to accrue a Rs 3.2 crore dividend on the ex-date. By how much was NAV wrong, which investors were affected, and does the error cross the materiality threshold?Case 097 →An exam-prep subscription company has a customer acquisition cost of Rs 1,800, annual revenue per learner of Rs 3,200 at 65% gross margin, and 55% of learners renew each year. Does it have a competitive advantage and barriers to entry, and can its revenue growth last?

Company names and figures are illustrative.

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