Debt Capital Markets puzzles, solved step by step

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

Showing 1–10 of 20 · filtered from 100Clear filters

004What is the angle between the hour hand and the minute hand of a clock at 3:15?Logic and brainteasersWarm upSyndicate desks
Try it first
Answer inside ten seconds.
Show the worked solution
7.5 degrees. The minute hand at 15 minutes points exactly at the 3, which is 90 degrees from 12. The hour hand moves half a degree every minute, so at 3:15 it sits at 3 times 30 plus 15 times 0.5, which is 97.5 degrees. The gap is 97.5 minus 90, or 7.5 degrees.
Why is zero the wrong answer?
Zero comes from picturing a clock as two independent pointers that jump. The hour hand moves continuously: it covers 30 degrees between one number and the next over 60 minutes, so it moves half a degree every minute. At quarter past, it has done a quarter of its journey from 3 to 4. Think of a train between two stations: fifteen minutes into an hour long run, you are not still standing on the first platform.
At 3:15 the minute hand points exactly at the 3, 90 degrees from 12, while the hour hand has moved a quarter of the way to the 4, to 97.5 degrees, leaving a 7.5 degree gap between them.
What is the general method, so any time works?
Measure both hands from 12 in degrees. The minute hand sits at 6 degrees times the minutes; the hour hand sits at 30 degrees times the hours plus half a degree times the minutes. Subtract, and if the result is over 180, take 360 minus it to get the smaller angle. Saying the method before the number is what the interviewer is listening for, because the next question will be a harder time.
The relationship
$\theta = \left|\,30h + 0.5m - 6m\,\right| = \left|\,30h - 5.5m\,\right| = \left|\,90 - 82.5\,\right| = 7.5^\circ$
h the hour, here 3
m the minutes, here 15
5.5 how many degrees a minute the minute hand gains on the hour hand
What it says in wordsThe minute hand gains 5.5 degrees a minute on the hour hand, starting 30 degrees behind for every hour on the clock.
Why does a capital markets desk ask this?
It is a speed and care test, not a clock test. The question checks whether you notice that two things are moving when the obvious reading has only one moving. The same slip in a desk setting is quoting a yield as if the price had not moved since the morning, or pricing accrued interest as if the settlement date were today. After the answer, one sentence on the 5.5 degrees a minute rule shows you can generalise.
Where candidates lose it
Zero is the whole trap. It comes from answering the picture in your head rather than the mechanism, and it is said fast because the question sounds too easy to need thought.
The second loss is the follow up. Candidates who guessed 7.5 without the half degree a minute rule freeze on 9:45 or 2:20. Learn the one line formula and the times take seconds.
What the interviewer asks next
What is the angle at 9:45?
How many times a day do the hands overlap exactly, and why is it not 24?
At what exact time after 3:00 do the hands first overlap?
007A 91-day Treasury bill with a face value of Rs 100 is issued at Rs 98.25. What annualised yield does the buyer earn on a 365-day basis, and why is it not simply 1.75 times four?Bond pricing and yieldWarm upIndian debt capital markets
Try it first
Is the true yield above or below 7.00%, which is 1.75 times four?
Show the worked solution
About 7.14%. The buyer pays Rs 98.25 and gets Rs 100 back 91 days later, a gain of Rs 1.75 on Rs 98.25 invested, which is 1.781% for the period. Scaling by 365 over 91 gives 7.14% a year. It beats 1.75 times four for two reasons: the return is earned on the price paid, not the face value, and a year holds a little more than four 91 day periods.
Why divide by 98.25 and not by 100?
Lend a friend Rs 98 and get Rs 100 back: you made Rs 2 on Rs 98, not on Rs 100. A yield is always the gain divided by the money you actually put in, and on a discounted bill that is the price, not the face value. Dividing by 100 gives the discount rate, a quoting convention that understates what the buyer earns. On a Rs 1.75 gain the difference is small, but interviewers ask this precisely to see whether you know which base is which.
The Rs 1.75 gain on Rs 98.25 paid is 1.781% over 91 days; annualised on the price paid it is 7.14%, above both 1.75 times four at 7.00% and the discount rate on face value at 7.02%, and compounding would lift it further to 7.34%.
Why 365 over 91 instead of 4?
A quarter is not exactly 91 days: 365 divided by 91 is 4.011. On a 365 day basis a 91 day return is scaled by 365 over 91, so the days in the bill's life, not the word quarter, set the multiplier. That adds only about two basis points here, but on bills of 182 or 364 days, or where day counts differ between markets, getting the multiplier right is exactly what a desk checks.
The relationship
$y = \frac{100 - P}{P} \times \frac{365}{d} = \frac{1.75}{98.25} \times \frac{365}{91} \approx 7.14\%$
P the price paid, Rs 98.25
100 the face value repaid at maturity
d days to maturity, 91
y the simple annualised yield
What it says in wordsGain over price paid, scaled up by how many such periods fit in a 365 day year.
Is 7.14% what the buyer really earns over a year?
Only if the gain is not reinvested. If the buyer rolls into a new bill at the same price every 91 days, interest earns interest and the effective annual rate is about 7.34%. Simple and compounded yields answer different questions, so say which one you are quoting. The simple formula here is the convention commonly used to quote Treasury bills; confirm the convention and day count of the market you are pricing in before comparing a bill yield with a bond yield, which may be stated on a different basis.
Where candidates lose it
The fast wrong answer is 7%. It uses the face value as the base and four as the multiplier, two small errors that both push the answer down, and it tells the interviewer the candidate has memorised a shortcut without knowing what a yield is.
The second loss is quoting the compounded figure without saying so, then being unable to compare it with a quoted bill yield. Name the convention with the number.
What the interviewer asks next
What price for the same bill gives a yield of exactly 7.00%? (About Rs 98.28.)
Why does a bond yield quoted with semi-annual compounding not compare directly with this bill yield?
If yields rise 50 basis points the day after you buy, roughly how much does the bill's price fall?
009Quick maths: what is the accrued coupon on Rs 350 crore of a 7.25% bond for 73 days, on an actual/365 basis?Mental maths and numeracyWarm upPrivate credit
Try it first
Before multiplying: what fraction of a year is 73 days on an actual/365 basis?
Show the worked solution
Rs 5.075 crore. The annual coupon is 7.25% of Rs 350 crore, Rs 25.375 crore. On actual/365, 73 days is exactly one fifth of a year, because 73 times 5 is 365. One fifth of Rs 25.375 crore is Rs 5.075 crore, which a buyer settling on day 73 pays the seller on top of the clean price.
What do you look for before you multiply?
A friendly fraction. Mental maths on a desk is mostly spotting which number makes the rest easy. 73 is exactly a fifth of 365, so the whole calculation collapses to one fifth of the annual coupon. It is like splitting a Rs 25,375 bill between five friends: nobody reaches for a calculator once they see it is a clean fifth. Say the fraction out loud first, so the interviewer hears the shortcut rather than watching you grind through 7.25 times 350 times 73.
Seventy three days is exactly one fifth of a 365 day year, so the accrued coupon is one fifth of the Rs 25.375 crore annual coupon on Rs 350 crore at 7.25%, which is Rs 5.075 crore.
How do you get the annual coupon quickly?
Split the rate. 7% of 350 is 24.5 and a quarter per cent of 350 is 0.875, so the annual coupon is Rs 25.375 crore. Breaking an awkward rate into a round rate plus a small piece keeps each multiplication in your head. Then divide by five: 25 divided by 5 is 5, and 0.375 divided by 5 is 0.075, so Rs 5.075 crore. Another route is 350 divided by 5 first, which is 70, and 7.25% of 70 is 5.075. Either way, two steps.
The relationship
$AI = F \times c \times \frac{d}{365} = 350 \times 7.25\% \times \frac{73}{365} = 25.375 \times 0.2 = 5.075$
AI accrued interest, Rs crore
F face value held, Rs 350 crore
c annual coupon rate, 7.25%
d days since the last coupon, 73
What it says in wordsAccrued interest is the annual coupon times the share of the year that has passed since the last payment.
Why does accrued interest matter on a trade?
Because the seller has earned 73 days of coupon but the buyer will receive the whole next coupon. The buyer pays the accrued interest to the seller at settlement, so the cash that changes hands is the clean price plus accrued, the dirty price. On Rs 350 crore, Rs 5.08 crore is real money. Also say the limit: the day count convention varies by market and by instrument, and actual/365, actual/actual and 30/360 give slightly different answers, so check the bond's terms before you settle.
Where candidates lose it
The loss here is speed, not knowledge. Candidates multiply 350 by 7.25% by 73 and divide by 365 the long way, drop a decimal somewhere, and give 50.75 or 0.5075 instead of 5.075.
The second slip is quietly switching to a 360 day year, which gives about 5.145. The question said actual/365; repeat the convention back as you answer so the interviewer knows you heard it.
What the interviewer asks next
What is the accrued interest after 146 days on the same holding?
The bond is quoted at a clean price of 101.20. What does the buyer pay in total per Rs 100 of face?
Why do markets quote bonds on a clean price rather than a dirty price?
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
Try it first
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?
012A Rs 800 crore bond carries an 8% coupon with a step-up of 25 basis points for each notch the issuer's rating falls below AA. It is downgraded two notches. What does that cost the issuer each year?Issuance and refinancing arithmeticWarm upIndian debt capital markets
Try it first
Answer in rupees, not basis points.
Show the worked solution
Rs 4 crore a year. Two notches below AA, from AA to AA- to A+, trigger two steps of 25 basis points, so the coupon rises from 8.00% to 8.50%. Half a per cent of Rs 800 crore is Rs 4 crore, taking annual interest from Rs 64 crore to Rs 68 crore for as long as the rating stays there. A step-up turns a downgrade into a cash cost.
How do you convert basis points into rupees quickly?
Anchor on one basis point. One basis point of Rs 800 crore is Rs 8 lakh, so 50 basis points is 50 times Rs 8 lakh, Rs 4 crore. It works like a fuel surcharge on a bus ticket: a small percentage, but on a large base and paid every trip. Say the conversion out loud; desks talk in basis points and issuers pay in rupees, and the interviewer wants to hear that you can move between the two instantly.
Each notch below AA adds 25 basis points to the 8% coupon, so annual interest on Rs 800 crore climbs from Rs 64 crore at AA to Rs 66 crore at AA- and Rs 68 crore at A+, an extra Rs 4 crore a year after a two notch downgrade.
Why would an issuer agree to a step-up at all?
To get a lower coupon today. Investors worried about a downgrade will accept a tighter starting coupon if they are compensated when that fear comes true. A step-up couponA coupon that rises by a set amount if a trigger is hit, most often a downgrade of the issuer rating below a stated level. shifts rating risk back to the issuer: cheap while the credit holds, costlier exactly when the credit weakens. That timing is the catch, and it is what a good answer names next.
The relationship
$\Delta \text{Interest} = F \times n \times s = 800 \times 2 \times 0.25\% = 4 \text{ Rs crore a year}$
F face value outstanding, Rs 800 crore
n notches below the trigger, 2
s step-up per notch, 25 basis points
What it says in wordsThe extra interest is the face value times the number of notches times the step per notch.
What is the hidden danger in the structure?
It adds cost at the worst moment. A downgrade usually follows weaker cash flow, and the step-up then raises interest, which weakens coverage further and can invite another downgrade. On this bond, Rs 4 crore is small against Rs 64 crore of interest, but many issues carrying the same clause, or a larger step, can turn one downgrade into a spiral. Close with that, and add the limit: the terms of real step-ups vary, some step back down on an upgrade and some cap the total, so read the clause.
Where candidates lose it
The easy slip is counting the wrong number of notches. AA to AA- is one and AA- to A+ is two, so the step is 50 basis points, not 25 and not 75.
The second loss is answering Rs 68 crore, the new interest bill, when the question asked for the cost of the downgrade. Give the difference first and the new total second.
What the interviewer asks next
What does the step-up cost in present value terms if 5 years remain and the discount rate is 8.5%?
Why might investors prefer a step-up bond to a higher fixed coupon?
How does a step-up clause change the way a rating agency looks at a downgrade?
034What is 1 basis point worth on Rs 2,500 crore for a year, for a quarter and for one day?Mental maths and numeracyWarm upSyndicate desks
Try it first
One basis point on Rs 2,500 crore for a year is:
Show the worked solution
Rs 25 lakh a year, Rs 6.25 lakh a quarter and about Rs 6,850 a day. A basis point is 0.0001, so Rs 2,500 crore times 0.0001 is Rs 0.25 crore, Rs 25 lakh a year. Divide by four for a quarter. Divide by 365 for a day, which gives Rs 6,849 on an actual/365 basis, or Rs 6,944 on a 360-day basis.
Why would a desk ask something this simple?
A shopkeeper who knows that one rupee off a product's price costs her Rs 3,000 a month in margin negotiates very differently from one who has to work it out after the customer leaves. Every pricing conversation in debt markets is in basis points, and the listener has to turn them into rupees on the deal in front of them instantly. An issuer who hears that 5 basis points is on the table wants to know that means Rs 1.25 crore a year, not to wait for a spreadsheet.
The relationship
$2{,}500 \text{ crore} \times 0.0001 = 0.25 \text{ crore} = 25 \text{ lakh a year}$
0.0001 one basis point, a hundredth of one per cent
0.25 crore a quarter of Rs 1 crore, which is Rs 25 lakh
What it says in wordsMultiply the deal size by one ten-thousandth, then convert crore to lakh by multiplying by 100.
One basis point on Rs 2,500 crore is Rs 25 lakh a year, Rs 6.25 lakh a quarter and Rs 6,849 a day on an actual/365 basis, and five years of it discounted at 8% is worth about Rs 99.8 lakh today.
What changes when the basis point is on price instead of coupon?
The numbers above are one basis point of coupon or spread, paid each year. A basis point of yield on a bond's price is a different quantity. A one basis point move in yield changes a bond's value by roughly its duration times the notional times 0.0001, so on a five-year bond with duration near 4 it is about Rs 1 crore, not Rs 25 lakh. The two agree once you see why: five years of Rs 25 lakh, discounted at 8%, is worth about Rs 99.8 lakh today. Duration is roughly the present value of a stream of basis points.
Day counts are the last detail worth a sentence. Many rupee bonds count actual days over 365, while money market instruments and many floating rate loans elsewhere use 360; confirm the convention in the term sheet rather than assume it. The difference on one day is about Rs 95 here, trivial on a day and material over a large book, which is why the convention is always named in the documents.
Where candidates lose it
The common slip is a zero: Rs 2.5 lakh or Rs 2.5 crore, because crore, lakh and 0.0001 are three unit changes in one line. Say the steps aloud: 0.0001 of 2,500 crore is 0.25 crore, which is 25 lakh.
The second loss is treating a basis point of yield and a basis point of coupon as the same thing. On a five-year deal they differ by a factor of about four, and a syndicate desk will ask which one you mean.
What the interviewer asks next
An issuer saves 7 basis points on a Rs 2,500 crore, 5-year deal. What is that worth today at 8%?
What is the price value of a basis point on Rs 2,500 crore of a bond with modified duration 6.5?
Why do money market instruments often use a 360-day year?
037You have a 3-litre and a 4-litre bottle and unlimited water. How do you measure exactly 2 litres and exactly 5 litres, and which whole-litre amounts up to 7 can you make?Logic and brainteasersWarm upNomuraNew York · 2026
Try it first
How many of the amounts 1 to 7 litres can you measure, counting water held across both bottles?
Show the worked solution
For 2 litres: fill the 3, pour it into the 4, fill the 3 again and top up the 4; exactly 2 litres stay in the 3-litre bottle. For 5: fill the 4, pour into the 3 to leave 1, empty the 3, move the 1 into it, then fill the 4, for 1 plus 4. Every whole amount from 1 to 7 is possible, because 3 and 4 differ by 1.
What moves are you actually allowed?
Three: fill a bottle to the top, empty it, or pour from one into the other until the first is empty or the second is full. The only amounts you can know for certain are full bottles and what is left after a pour stops at a full bottle, so every measurement is built from 3s and 4s. Think of it as making change with only Rs 3 and Rs 4 coins, where you are also allowed to hand coins back.
Four moves leave 2 litres in the 3-litre bottle after the 4-litre bottle is topped up, and five moves put 1 litre in the 3-litre bottle beside a full 4-litre bottle, which together hold exactly 5 litres.
Why can you reach every amount from 1 to 7?
Because 4 minus 3 is 1, and once you can make 1 you can make anything by adding bottles. The amounts you can measure are exactly the combinations of 3 and 4 that fit in the bottles, and since the two sizes share no common factor, every whole litre up to their total of 7 is reachable. One litre: fill the 4 and pour into the 3. Three and four: fill one bottle. Five: 1 plus a full 4. Six: 3 in each. Seven: both full.
The relationship
$\gcd(3, 4) = 1 \;\Rightarrow\; 3a + 4b \text{ can equal any whole number}$
gcd the greatest common divisor, the largest number dividing both sizes
a, b how many times you add or remove each bottle's volume, positive or negative
What it says in wordsWhen the bottle sizes share no factor, their combinations reach every whole number.
The same rule tells you when a puzzle has no answer. With a 4-litre and a 6-litre bottle, every amount you can make is even, so 5 litres is impossible, and you can say so without trying a single pour. Interviewers like that sentence more than the pouring itself, because it shows you found the structure rather than a lucky sequence.
Where candidates lose it
Candidates start pouring at random and lose track of the state, which in a phone interview is fatal because the interviewer cannot see your paper. Say each state as a pair, litres in the 3 then litres in the 4, after every move.
The second miss is solving 2 litres and freezing on 5, which cannot fit in either bottle. The question is asking for water held across both bottles, and saying that out loud is half the answer.
What the interviewer asks next
With a 5-litre and a 7-litre bottle, what is the fewest number of moves to measure 1 litre?
Can you measure 5 litres with a 4-litre and a 6-litre bottle? Prove it either way.
How does this relate to what bond sizes you can build from fixed lot sizes?
Asked at Nomura, Equity Capital Markets, New York, 2026 (Wall Street Oasis): How much water can you fill using 1 3liter and 1 4liter bottle using each other?
046A company has 50 of debt and 50 of equity at market value, trades at 10x earnings and pays 6% on its debt. What is its WACC before and after a 25% tax rate on interest?Cost of capital and valuation riddlesWarm upCitiNew York · 2026
Try it first
What cost of equity does a P/E of 10 suggest, as a quick proxy?
Show the worked solution
WACC is 8.0% before tax and 7.25% after. Read the cost of equity as the earnings yield, 1 over a P/E of 10, which is 10%. Half the capital costs 10% and half costs 6%, so the blend is 8.0%. The tax shield cuts debt to 6% x 0.75 = 4.5%, and the blend falls to 7.25%. The P/E shortcut assumes no growth; with growth the true cost of equity is higher.
Where does the cost of equity come from when you are not given a beta?
If a shop earns Rs 10,000 a year and sells for Rs 1 lakh, a buyer earns 10% on the price. Nobody would pay more unless they expected growth, so 10% is roughly what buyers of such a shop demand. A P/E of 10 means earnings are a tenth of the price, an earnings yield of 10%, and with no growth that is a quick proxy for the cost of equity. Say out loud that it is a proxy: it is the fastest honest route when the interviewer gives you only a multiple.
The relationship
$WACC = \tfrac{E}{V}k_e + \tfrac{D}{V}k_d(1-t) = 0.5 \times 10\% + 0.5 \times 6\% \times 0.75 = 7.25\%$
E/V, D/V equity and debt as shares of total capital at market value, 0.5 each
k_e cost of equity, here the earnings yield 1 / 10 = 10%
k_d cost of debt, 6%
t tax rate on interest, 25%
What it says in wordsWeight each funder's required return by its share of the capital, and cut the debt cost by the tax it saves.
Equity of 50 costing 10% and debt of 50 costing 6% blend to 8.0% before tax, and to 7.25% once interest is deducted at 25%, because the debt's after-tax cost falls to 4.5%.
Why does tax only touch the debt half?
Interest is paid before tax and dividends after it. Every rupee of interest reduces taxable profit, so the government in effect pays a quarter of the interest bill at a 25% tax rate, and debt that costs 6% on paper costs 4.5% to the company. Equity gets no such relief. That is why the after-tax WACC is 0.75 points lower: half the capital times the 1.5 point shield. The difference compounds into valuation, since a lower discount rate raises the value of every future cash flow.
State the limit of the shortcut before the interviewer does. The earnings yield equals the cost of equity only for a company that does not grow and pays out all its earnings. If earnings grow at 3% a year, investors paying 10x are expecting roughly 10% plus 3%, about 13%, and the WACC rises with it. For a real company you would build the cost of equity from a risk-free rate, a beta and a market premium instead.
Where candidates lose it
The common error is using 10 as a percentage or treating the P/E itself as a cost. Invert it: a multiple becomes a yield only when you flip it.
The second loss is giving one WACC and not saying whether it is before or after tax. The question asked for both on purpose; give 8.0% and 7.25% and say where the 0.75 points went.
What the interviewer asks next
The company re-levers to 70% debt at a 7% cost. What happens to WACC, and what should happen to the cost of equity?
If earnings grow at 4% a year, what cost of equity does a P/E of 10 imply?
Why do you use market values rather than book values for the weights?
Asked at Citi, Capital Markets, New York, 2026 (Wall Street Oasis): $50 debt, $50 equity, P/E 10x, Cost of Debt 6%, what is WACC
047EBITDA is Rs 150 crore, capex Rs 40 crore, cash taxes Rs 20 crore, interest Rs 30 crore and scheduled principal Rs 20 crore. Compute the fixed charge cover and the interest cover, and say which one a lender trusts more.Leverage, coverage and cash flowWarm upCorporate bankingLeveraged finance
Try it first
What is the fixed charge cover?
Show the worked solution
Interest cover is 5.0x and fixed charge cover is 1.8x; a lender trusts the fixed charge cover more. Interest cover is EBITDA of 150 over interest of 30. Fixed charge cover takes off capex of 40 and tax of 20, leaving 90, and sets it against interest plus the principal that must be repaid this year, 50. It counts the cash that really has to go out, so it shows how thin the cushion is.
Why can a company look five times covered and still be tight?
A salaried person earning Rs 1.5 lakh a month with a Rs 30,000 loan interest bill looks comfortable. But rent and school fees of Rs 60,000 come out first, and the loan also needs Rs 20,000 of principal each month. What is left, Rs 90,000, against Rs 50,000 owed, is the true cushion. Interest cover ignores the cash a business must spend before lenders are paid and ignores the principal it owes, so it flatters the picture. Fixed charge coverCash flow after capex and tax, divided by all the debt payments due in the period, interest and scheduled principal together. fixes both.
The relationship
$\text{ICR} = \frac{150}{30} = 5.0\times \qquad \text{FCCR} = \frac{150 - 40 - 20}{30 + 20} = \frac{90}{50} = 1.8\times$
150 EBITDA, Rs crore
40, 20 capex and cash taxes, which must be paid before lenders
30, 20 interest and scheduled principal due this year
What it says in wordsInterest cover divides earnings by interest; fixed charge cover divides cash left after essential spending by everything owed to lenders this year.
The same company covers its Rs 30 crore of interest 5.0 times from EBITDA of Rs 150 crore, but after Rs 40 crore of capex and Rs 20 crore of tax it covers its Rs 50 crore of interest and principal only 1.8 times.
Which ratio would you put in a covenant?
The fixed charge ratio, for a lender who cares about being repaid on schedule. At 1.8x the company has Rs 40 crore of spare cash a year after paying lenders, and a 44% fall in that cash would leave it unable to meet its schedule; at 5.0x interest cover the same fall would still look safe. Interest cover is still useful: it is quick, comparable across companies, and a lender pricing a bullet bond with no amortisation cares less about principal. But for an amortising term loan, fixed charge cover is the test that fails first.
Say the limits. Definitions vary by document: some deduct only maintenance capex, some add lease payments to the fixed charges, some take tax paid rather than tax charged. Always read the covenant's own definition before comparing a borrower's ratio with a peer's; two companies at 1.8x on different definitions are not equally safe.
Where candidates lose it
The common slip is stopping at 5.0x and calling the credit comfortable. The question gave capex, tax and principal because they are the numbers interest cover leaves out.
The second is putting principal on the wrong side, subtracting it from EBITDA rather than adding it to the charges. Principal is owed to lenders, so it belongs in the denominator with interest.
What the interviewer asks next
Capex rises to Rs 60 crore. What is the fixed charge cover now?
Why might a lender deduct only maintenance capex rather than total capex?
The company adds a Rs 15 crore lease payment. Where does it go in each ratio?
049You buy a 6% annual coupon bond at 100. A year later, just after the coupon is paid, it trades at 95. What total return did you earn over the year, and why is the answer not minus 5%?Bond pricing and yieldWarm upFixed income asset management
Try it first
Your total return for the year is:
Show the worked solution
A total return of +1%. You paid 100. During the year you received a coupon of 6, and the bond is now worth 95, so you hold 101 of value against 100 paid. Total return is income plus price change, 6 minus 5, divided by the price you paid. Quoting minus 5% counts only the price and forgets the coupon, which for a bond is most of the return.
What counts as return on a bond?
If you buy a flat for Rs 1 crore, collect Rs 6 lakh of rent over the year and the flat's market value slips to Rs 95 lakh, you are not down 5%. You have Rs 95 lakh of flat and Rs 6 lakh of cash: Rs 1.01 crore. Total return is everything the investment paid you plus the change in what it is worth, divided by what you paid. For a bond, the coupon is the rent.
The relationship
$TR = \frac{C + (P_1 - P_0)}{P_0} = \frac{6 + (95 - 100)}{100} = +1\%$
C coupon received during the year, 6
P_0 price paid, 100
P_1 price a year later, just after the coupon, 95
What it says in wordsAdd the income received to the change in price, then divide by what you paid.
The investor paid 100, received a 6 coupon and saw the price fall 5 to 95, so ends the year with 101 of value, a total return of +1% rather than the -5% the price alone suggests.
Why would the price have fallen, and what does it mean for next year?
A fixed coupon bond falls in price when market yields rise. If the bond had four years left after the coupon, a price of 95 means new buyers earn about 7.49% a year to maturity, so the loss this year is partly paid back as extra yield in later years if the bond is held. That is the other reason not to fixate on the minus 5: a holder to maturity still gets 100 at the end, and the price fall is a mark-to-market loss, not money gone for good.
Two limits worth saying. This assumes the coupon is simply held as cash; reinvesting it would add a little more. And it assumes the issuer is still sound: if the price fell because default risk rose, the loss may not come back. A desk reports both numbers, the price change and the total return, because they answer different questions.
Where candidates lose it
The instant wrong answer is minus 5%, because the price is the only number on the screen. For a bond, the coupon is usually the larger part of the return, and ignoring it gets the sign wrong here.
The other slip is adding the coupon to the new price and dividing by the new price: 101 over 95. Returns are measured on what you paid, so divide by 100.
What the interviewer asks next
What price a year later would have given a total return of zero?
If the coupon were reinvested at 7% for half a year before you measure, what changes?
Why do index providers publish total return rather than price return for bond indices?

h	the hour, here 3
m	the minutes, here 15
5.5	how many degrees a minute the minute hand gains on the hour hand

P	the price paid, Rs 98.25
100	the face value repaid at maturity
d	days to maturity, 91
y	the simple annualised yield

AI	accrued interest, Rs crore
F	face value held, Rs 350 crore
c	annual coupon rate, 7.25%
d	days since the last coupon, 73

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

Try it first

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What the interviewer asks next

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