Case 050Products and fund selectionCore

A traditional endowment policy asks Rs 5 lakh a year for 10 years and promises Rs 70 lakh at year 20, sold as a tax-free return. Work out its internal rate of return and compare term cover plus a fund.

The situation

A client of 40 has been offered an invented traditional endowment policy: pay Rs 5 lakh a year at the start of each of the next 10 years, and receive Rs 70 lakh at the end of year 20, with Rs 50 lakh of life cover throughout. The agent calls it a guaranteed tax-free Rs 70 lakh on Rs 50 lakh paid.

The alternative is to buy Rs 50 lakh of term cover for 20 years at an illustrative Rs 12,000 a year and invest the rest of each Rs 5 lakh. Tax rules on the maturity value of high-premium policies and on fund gains have changed in recent years, so confirm both before comparing; the fund returns below are illustrative after-tax figures, not forecasts.

Your task

What is the policy's internal rate of return? What does buying term cover and investing the rest produce at modest assumed returns, and what return does it need to match the policy?

Quick check

Roughly what yearly return does Rs 50 lakh paid over 10 years, growing to Rs 70 lakh at year 20, represent?

Worked solution

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

30-second answerThe answer to give first

The policy's internal rate of return is about 2.2% a year. Term cover plus a fund, with the same Rs 5 lakh a year, reaches about Rs 120 lakh at an illustrative 6% after tax and Rs 163 lakh at 8%, against the policy's Rs 70 lakh. The fund needs only about 2.5% a year to match. The death cover is the same, so the policy's guarantee costs a great deal of return.

Step 1Why is Rs 70 lakh on Rs 50 lakh not a 40% return?

A friend who borrows Rs 5 lakh a year from you for ten years and repays Rs 70 lakh in year 20 has had your money for a long time. A return means nothing without the time the money was tied up, and here the average rupee is locked in for about 15 years. The honest measure is the {term('internal rate of return', 'The single yearly rate at which the present value of all the money paid in equals the present value of all the money received.')}: the yearly rate that makes the payments and the maturity value balance.

The relationship
∑t=095(1+r)t=70(1+r)20⇒r≈2.2%\sum_{t=0}^{9} \frac{5}{(1+r)^t} = \frac{70}{(1+r)^{20}} \quad\Rightarrow\quad r \approx 2.2\%
5yearly premium, Rs lakh, paid at the start of years 1 to 10
70maturity value, Rs lakh, at the end of year 20
rthe policy's internal rate of return
What it says in wordsThe rate at which ten premiums, discounted to today, equal the maturity value discounted to today.
Step 2What does buying term cover and investing the rest produce?

Split the same Rs 5 lakh a year into the two jobs the policy combines. Rs 12,000 buys the same Rs 50 lakh of cover; the remaining Rs 488,000 goes into a fund each year for ten years, and the fund pays the term premium in years 11 to 20. At an illustrative 6% a year after tax the fund reaches about Rs 120 lakh by year 20; at 8% about Rs 163 lakh. And if the client dies early, the family gets the Rs 50 lakh cover plus the fund, rather than the cover alone.

The same Rs 5 lakh a year, two ways, Rs lakhEndowment: IRR 2.2% a yearTerm cover plus a fund+70 in year 20-5 a year, years 0 to 9then nothing for ten yearsPaid 50, received 70over 20 years50100150policy pays 70at 8% a year: 163 by year 20at 6% a year: 120 (dashed)Fund value, after tax, with the term premium paidfrom it in years 10 to 19
The endowment turns ten payments of Rs 5 lakh into Rs 70 lakh at year 20, an IRR of 2.2%, while term cover plus a fund with the same money reaches about Rs 120 lakh at 6% and Rs 163 lakh at 8% after tax, needing only 2.5% to match the policy.
Step 3What is the guarantee worth, and what is the limit of this comparison?

The policy's case rests on certainty: Rs 70 lakh whatever markets do. But the fund only needs about 2.5% a year after tax to match it, a low hurdle for money that stays invested for up to twenty years, so the guarantee is paid for with most of the return. The limits to state: a fund's return is not guaranteed, the tax treatment of both routes must be confirmed, and surrendering such a policy early usually returns far less than was paid in, so the choice is best made before signing, not halfway through.

Where candidates lose it

The common error is dividing 70 by 50 and calling it a 40% return, or dividing 40% by 20 years and calling it 2% simple. The first ignores time completely; the second gets near the right number for the wrong reason.

The second miss is comparing the policy with a fund and forgetting the life cover. Buy the same cover separately, then compare; otherwise the agent will rightly say you left out the insurance.

What the interviewer asks next

  • The client has already paid three premiums. Should he stop, and what would you need to know first?
  • How would a 5% yearly bonus, instead of a fixed maturity value, change the IRR?
  • Why might a client still rationally choose the policy?

Company names and figures are illustrative.