Private Wealth Management puzzles, solved step by step

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  1. 031A taxable bond yields 7.5% and a tax-free bond of similar quality and tenor yields 5.4%. For a client paying tax at an illustrative 30% slab, which one pays him more?Tax arithmeticWarm upIndian wealth management

    Try it first

    Pick one before you calculate.

    Show the worked solution

    The tax-free bond pays him more: 5.4% against 5.25%. The taxable bond's 7.5% loses 30% to tax, leaving 7.5 x 0.7 = 5.25%. Put the other way, the tax-free 5.4% is worth 5.4 / 0.7 = 7.71% to a taxable investor at this slab, which is more than 7.5%. On Rs 1 crore the difference is about Rs 15,000 a year.

    What is the fair way to compare the two yields?

    Two job offers: Rs 20 lakh with a company flat thrown in, or Rs 23 lakh with no flat. You do not compare 20 with 23; you compare what each leaves you after rent. Yields are compared on what the client keeps, which means after his own tax, not on the number printed on the term sheet. Either shrink the taxable yield by the tax rate, or gross the tax-free yield up to its taxable equivalent.

    The relationship
    yafter=y (1−t)=7.5×0.7=5.25%yeq=ytf1−t=5.40.7=7.71%y_{\text{after}} = y\,(1-t) = 7.5 \times 0.7 = 5.25\% \qquad y_{\text{eq}} = \frac{y_{tf}}{1-t} = \frac{5.4}{0.7} = 7.71\%
    ythe taxable bond's yield, 7.5%
    tthe client's marginal tax rate, an illustrative 30%
    y_tfthe tax-free bond's yield, 5.4%
    What it says in wordsEither take the tax off the taxable yield or add it back onto the tax-free one; both routes pick the same winner.
    Compare what the client keeps, not what the bond paysTaxable bond, pre-tax7.50%Taxable bond, after 30% tax5.25%Tax-free bond, pre-tax5.40%Tax-free bond, after tax5.40%taxtaxable-equivalent 7.71%0%2%4%6%8%On Rs 1 crore, the tax-free bond leaves the client Rs 15,000 a year more
    At an illustrative 30% slab, the taxable bond's 7.5% leaves the client 5.25% after tax, while the tax-free bond keeps its full 5.4%. The taxable bond would need to yield at least 7.71% to match.

    For which clients does the answer flip?

    Solve for the tax rate at which the two are equal: 1 minus 5.4 / 7.5, which is 28%. Any client whose marginal rate is below 28% keeps more from the taxable bond; any client above it keeps more from the tax-free one. That is why the same product can be right for a senior partner and wrong for his retired mother, and why an adviser asks about the slab before quoting yields.

    Limits worth saying: tax-free bonds are often thinly traded, so the exit price matters; surcharge and cess change the effective rate; and tax treatment depends on current law, so confirm the client's actual rate and the bond's status before you rely on the comparison.

    Where candidates lose it

    The trap is answering 7.5% because it is the bigger number, without asking about tax at all. For a wealth desk that is the one question you must never skip, because nearly every client comparison is an after-tax comparison.

    The second slip is dividing when you should multiply, and grossing 7.5 up instead of 5.4. Name which yield you are converting, and why, before you touch the numbers.

    What the interviewer asks next

    • What is the taxable-equivalent yield for a client at a 20% slab?
    • Why might a tax-free bond trade below its issue price in the secondary market?
    • How would the comparison change if the client expected his slab to fall after retirement?