Debt Capital Markets puzzles, solved step by step

Puzzles: 100
Traced to a firm: 16
Topics: 13
Hard: 30

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010An inflation-indexed bond pays a 2% real coupon on Rs 100 of principal, and the principal is indexed to inflation. Inflation runs at 5% a year for three years. What is the principal at the end of year 3, and what coupon is paid that year?Compounding, PIK and feesCoreFixed income asset managementIndian debt capital markets
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What is the year 3 coupon?
Show the worked solution
Principal of about Rs 115.76 and a year 3 coupon of about Rs 2.32. The principal is lifted by inflation each year and compounds: 100 times 1.05 cubed is Rs 115.7625. The 2% real coupon is paid on that indexed principal, so the year 3 coupon is Rs 2.315. Both the coupon and the principal keep their buying power, which is what the investor is paying for.
What exactly is being indexed?
Think of a rent agreement where the rent rises with inflation every year and the deposit is topped up by the same percentage. On an indexed bond the principal is scaled up by inflation, and the fixed real coupon rate is then applied to that scaled principal, so both the income and the repayment keep pace with prices. After one year of 5% inflation the principal is Rs 105 and the coupon is 2% of 105, Rs 2.10, not Rs 2.
With 5% inflation the indexed principal steps from 100 to 105, 110.25 and 115.76, and each year's 2% coupon is paid on the indexed amount, rising from 2.10 to 2.315, while an ordinary 2% bond stays at 100 and pays 2.00.
Why does the principal compound instead of adding 5 a year?
Because the index is a price level, and price levels compound: 5% in year 2 is 5% of the already higher year 1 prices. The indexed principal is the original principal times the ratio of today's index to the index at issue, which after three years of 5% is 1.05 cubed. Adding 5 a year gives 115, off by Rs 0.76, small here but large over a 10 or 20 year bond.
The relationship
$P_3 = 100 \times 1.05^3 = 115.7625 \qquad C_3 = 2\% \times P_3 = 2.3153$
P_3 indexed principal at the end of year 3
1.05 one year of 5% inflation
C_3 the coupon paid in year 3
What it says in wordsGrow the principal with the price index, then pay the real coupon rate on the grown amount.
What does that mean for the yield an investor sees?
Bought at Rs 100, the cash flows 2.10, 2.205 and 118.08 give a money return of about 7.1% a year, which is 1.02 times 1.05 minus 1: the real 2% plus inflation plus a small cross term. The investor has locked in a real return of 2% whatever inflation turns out to be, and that certainty is the product. Say the limits: actual indexed bonds use a lagged index, some protect principal from falling below par, and the tax treatment of the uplift varies, so check the specific bond's terms.
Where candidates lose it
The common mistake is paying the coupon on the original Rs 100, giving Rs 2.00 in every year. That treats the bond as if only the principal were protected and misses half of what indexing does.
The second is adding inflation instead of compounding it, giving principal of 115 and a coupon of 2.30. Say 1.05 cubed out loud, and the interviewer hears that you know price levels compound.
What the interviewer asks next
Inflation is 5%, 5% and then minus 2% in year 3. What is the principal, and what does a par floor at maturity do?
An ordinary 3 year bond yields 7.5%. Roughly what inflation rate makes it and the indexed bond equally attractive?
Why might a pension fund prefer indexed bonds even at a lower expected return?
011A 4-year bullet loan pays 10% a year and the borrower pays a 2% upfront fee. Roughly what yield does the lender earn, and how would you estimate it in your head?Compounding, PIK and feesWarm upCorporate bankingLeveraged finance
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Which is closest to the lender's yield?
Show the worked solution
About 10.6%, exactly 10.64%. The lender puts out Rs 98, receives Rs 10 a year and gets Rs 100 back in year 4. In your head: spread the 2 point fee over 4 years, about 0.5 a year, giving 10.5, then divide by the average money at work, about 99, which gives 10.61%. An upfront fee is extra yield spread over the life of the loan.
What does the fee actually change?
Imagine lending a friend Rs 1,000 for four years at 10%, but handing over only Rs 980 because you keep Rs 20 as a processing charge. Your interest is still on Rs 1,000 and you still get Rs 1,000 back. An upfront fee lowers the money the lender actually puts out, so the same coupons and repayment earn a higher yield on it. Look at the top of the figure: Rs 98 out, then 10, 10, 10 and 110 back.
The lender pays out Rs 98 and receives 10 a year plus 100 in year 4; the coupon alone is 10.00%, spreading the fee gives about 10.50%, adjusting for the smaller base gives 10.61%, and the exact yield is 10.64%.
How do you get close to 10.64% without a calculator?
Use the bond trader's approximation: yearly income over the average money at work. Yearly income is the coupon plus the fee spread evenly over the life, 10 plus 2 over 4, which is 10.5; the average money at work is halfway between 98 and 100, which is 99. 10.5 over 99 is 10.61%, within a few basis points of the exact 10.64%. Say the first step, 10.5, as your quick answer and the second as the refinement; interviewers like hearing both.
The relationship
$y \approx \frac{C + F/n}{(100 + P)/2} = \frac{10 + 2/4}{(100 + 98)/2} = \frac{10.5}{99} \approx 10.61\%$
C annual coupon, 10
F upfront fee, 2 points
n years to repayment, 4
P money actually lent after the fee, 98
What it says in wordsYield is roughly the yearly income, with the fee spread over the years, divided by the average money the lender has at work.
What if the loan is repaid early?
Then the fee is spread over fewer years and is worth more a year. If the borrower repays at par after 2 years, the same 2 points lift the yield to about 11.17%, because the fee is earned over half the time. This is why lenders care about expected life, not stated maturity, and why a loan that is likely to be refinanced early is priced partly on its fee. Say that one sentence and you have shown the interviewer you see the fee as yield, not as a one-off receipt.
Where candidates lose it
The two fast wrong answers sit either side. Saying 10% ignores the fee because it is paid once; saying 12% adds the whole fee to one year's coupon. Both miss that the fee belongs to the whole life of the loan.
The quieter loss is stopping at 10.5 when the interviewer asks for more precision. The base is Rs 98, not Rs 100, and that small adjustment is the difference between 10.50% and 10.64%.
What the interviewer asks next
What upfront fee would lift the yield on this loan to 11%?
Why does the same fee matter more on a 2 year loan than on a 7 year loan?
How should a bank book this fee in its income: all at once, or over the life of the loan?
043An issuer raises Rs 1,000 crore at 8.2% twelve months before its old bond matures and parks the cash at 6.9% until then. What does the pre-funding cost, and what risk does it remove?Compounding, PIK and feesCoreSyndicate desksCorporate banking
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What is the cost of carrying the cash for a year?
Show the worked solution
Pre-funding costs about Rs 13 crore of negative carry, before tax. The issuer pays 8.2% on the new bond while earning 6.9% on the parked cash, a 1.3% gap on Rs 1,000 crore for twelve months. In return it removes refinancing risk: it no longer needs the market to be open, spreads to hold and its rating to survive the final year. On a five-year deal, waiting would have to cost more than about 26 basis points a year for pre-funding to lose.
What exactly does pre-funding cost?
A family renting a flat signs a new lease a year before the old one ends because rents are rising and good flats are scarce. For twelve months they pay a little extra holding the new flat, but they are not searching in a panic the week the old lease ends. Pre-funding costs the gap between what the new money costs and what the parked cash earns, for as long as both exist: the negative carryThe cost of holding a position whose income is lower than its funding cost, here cash earning less than the bond that raised it.. Here 8.2% less 6.9% is 1.3%, on Rs 1,000 crore for a year, Rs 13 crore, about Rs 1.08 crore a month.
The relationship
$\text{Carry} = 1{,}000 \times (8.2\% - 6.9\%) \times \tfrac{12}{12} = 13 \text{ crore}$
1,000 amount raised early, Rs crore
8.2% coupon on the new bond
6.9% yield earned on the parked cash
12/12 the fraction of a year the two overlap
What it says in wordsThe cost is the rate gap on the amount raised, for the time both the new bond and the parked cash exist.
Raising Rs 1,000 crore at 8.2% and parking it at 6.9% costs about Rs 1.08 crore a month, Rs 13 crore by the old bond's maturity, in exchange for removing the need to find a market on one fixed day.
What does that Rs 13 crore buy?
Certainty. Without pre-funding, the issuer must refinance in a narrow window before maturity, and if markets are shut, spreads have widened or its rating has slipped in that window, it either pays far more or cannot repay. Pre-funding is insurance with a known premium. A useful breakeven: spread over a five-year replacement bond, Rs 13 crore is about 26 basis points a year before discounting and about 33 after. If waiting risked a rise larger than that, or a missed maturity, the premium was cheap.
Say the refinements. Interest paid is usually tax deductible and interest earned is taxable, so at an assumed 25% rate on both the after-tax carry is about Rs 9.75 crore. The issuer also carries a bigger balance sheet for a year, gross debt rises before the old bond goes, which can briefly worsen reported leverage. And the parked cash must be invested safely and kept liquid; reaching for yield on it defeats the purpose of paying for certainty.
Where candidates lose it
The common miss is quoting the full coupon, Rs 82 crore, as the cost. The cash is not idle; it earns 6.9%, and only the gap is the price of pre-funding.
The second is stopping at Rs 13 crore and calling it a waste. The interviewer wants the other side of the trade named: refinancing risk, which is exactly what issuers with a large maturity and a shaky market fear most.
What the interviewer asks next
The issuer could instead buy back the old bond early. How would you compare the two?
The parked cash earns 7.5% instead. What is the carry, and does the answer change?
Why do rating agencies look favourably on issuers who pre-fund large maturities?
094A borrower can pay 11% in cash or 12% as payment-in-kind on a Rs 500 crore five-year loan. Any cash it does not pay out can be reinvested in the business at a 15% return. Which option leaves the equity better off after five years, and when would the answer flip?Compounding, PIK and feesHardLeveraged financePrivate credit
Try it first
The business earns 15%, more than the 12% PIK rate. Does PIK win?
Show the worked solution
Paying cash leaves the equity about Rs 10 crore better off. PIK debt compounds at 12% to Rs 881 crore. The Rs 55 crore a year that PIK keeps in the business, reinvested at 15%, grows to only Rs 371 crore, so net debt is Rs 510 crore against Rs 500 crore with cash pay. The answer flips if the business earns more than about 16.4% on the cash, or if paying cash would starve it.
What exactly is being compared?
Deferring a credit card bill and investing the money instead only pays if your investment grows faster than the card's balance. PIKPayment in kind: interest is added to the loan balance instead of being paid in cash, so the debt compounds. interest is that deferral, made formal. Under PIK the whole loan compounds at the PIK rate, while only the cash you did not pay compounds at your own return, so the two piles grow on different bases. Line up where each option leaves the company at year 5: debt owed, less any cash built up by reinvesting what was not paid.
Paying 11% in cash leaves Rs 500 crore of debt, while PIK at 12% grows the debt to Rs 881 crore against Rs 371 crore of reinvested cash, so PIK ends Rs 10 crore worse unless the cash earns above 16.4%.
The relationship
$500(1.12)^5 = 881.2 \qquad 55\cdot\frac{1.15^5 - 1}{0.15} = 370.8 \qquad 881.2 - 370.8 = 510.3$
500(1.12)^5 the PIK balance after five years
55 the 11% cash interest that PIK lets the company keep each year
370.8 that cash reinvested at 15% for five years
What it says in wordsNet debt under PIK is the compounded loan less the compounded cash that was kept.
When does the answer flip?
Solve for the return that makes the kept cash worth exactly the extra Rs 381 crore of PIK debt: about 16.4%. PIK is cheap only if the cash it saves earns more than the PIK rate, and here more still, because the PIK rate carries a one point premium over cash pay. At a 12% reinvestment return the kept cash reaches only Rs 349 crore. Two further reasons can flip the answer in practice: a borrower whose cash is scarce may not be able to pay 11% without cutting investment it needs, and a borrower expecting to refinance or be sold early carries the PIK compounding for less time. Tax treatment of PIK interest can also differ; confirm it rather than assuming.
Where candidates lose it
The trap is comparing 15% with 12% and declaring PIK the winner. The PIK rate applies to the whole Rs 500 crore; the 15% applies only to Rs 55 crore a year. Rates on different bases cannot be compared directly.
The second loss is ignoring the one point PIK premium. It is why the break-even is near 16%, not 12%, and it is the number a leveraged finance desk would negotiate hardest.
What the interviewer asks next
If both options were priced at 11%, what reinvestment return would make them equal?
The company is sold at the end of year 3. Does that help or hurt the PIK option?
Why would a lender accept PIK at all, and what does it ask for in return?

P_3	indexed principal at the end of year 3
1.05	one year of 5% inflation
C_3	the coupon paid in year 3

C	annual coupon, 10
F	upfront fee, 2 points
n	years to repayment, 4
P	money actually lent after the fee, 98

1,000	amount raised early, Rs crore
8.2%	coupon on the new bond
6.9%	yield earned on the parked cash
12/12	the fraction of a year the two overlap

500(1.12)^5	the PIK balance after five years
55	the 11% cash interest that PIK lets the company keep each year
370.8	that cash reinvested at 15% for five years

Try it first

What exactly is being indexed?

Why does the principal compound instead of adding 5 a year?

What does that mean for the yield an investor sees?

Where candidates lose it

What the interviewer asks next

Try it first

What does the fee actually change?

How do you get close to 10.64% without a calculator?

What if the loan is repaid early?

Where candidates lose it

What the interviewer asks next

Try it first

What exactly does pre-funding cost?

What does that Rs 13 crore buy?

Where candidates lose it

What the interviewer asks next

Try it first

What exactly is being compared?

When does the answer flip?

Where candidates lose it

What the interviewer asks next