Debt Capital Markets puzzles, solved step by step

Puzzles
100
Traced to a firm
16
Topics
13
Hard
30
Topic
All topicsLeverage, coverage and cash flow9Mental maths and numeracy8Estimation and market sizing7Logic and brainteasers8Cost of capital and valuation riddles7Bond pricing and yield7Compounding, PIK and fees6Issuance and refinancing arithmetic8Credit spreads and default probability8Duration and convexity8Capital structure and recovery8Probability and expected value10Yield curve and forward rates6
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  1. 001A project generates cash flow available for debt service of Rs 60 crore a year for 10 years. The loan costs 9% and the lender wants a minimum debt service cover of 1.3x, with level annual payments. How much can it lend?Leverage, coverage and cash flowCoreCorporate bankingPrivate credit

    Try it first

    Before any maths: which figure is closest to the loan the project can carry?

    Show the worked solution

    About Rs 296 crore. A 1.3x cover means only 60 divided by 1.3, Rs 46.15 crore a year, can go to interest and principal. A level payment of that size for 10 years at 9% repays a loan equal to its present value: 46.15 times the annuity factor of 6.418, about Rs 296.2 crore. Debt capacity is the present value of the cash the lender lets you spend on debt.

    What does the cover ratio actually limit?

    Think of a family with Rs 60,000 a month to spare applying for a home loan. The bank will not let the whole Rs 60,000 go to the EMI; it wants a cushion in case a month goes wrong. A debt service cover of 1.3x means every rupee of loan payment must be backed by 1.3 rupees of cash, so the most the project can pay each year is 60 divided by 1.3, Rs 46.15 crore. The remaining Rs 13.85 crore is the lender's buffer against a bad year. It is not money you can borrow against.

    Cover first, then present value: Rs 60 crore a year supports a Rs 296 crore loanCash for debt serviceRs 60.0 cr a yearforecast, years 1 to 10Allowed debt serviceRs 46.15 cr a year60 / 1.3 coverDebt capacityRs 296.2 cr46.15 x 6.418 annuity factorEach year's payment (outline) and its value today at 9% (green)green bars sum to 296.242.3Yr 138.8Yr 235.6Yr 332.7Yr 430.0Yr 527.5Yr 625.2Yr 723.2Yr 821.3Yr 919.5Yr 1046.15
    Rs 60 crore of yearly cash divided by the 1.3x cover allows Rs 46.15 crore of debt service; ten such payments are worth Rs 42.3 crore down to Rs 19.5 crore each in today's money, and together they support a loan of about Rs 296.2 crore.

    How do you turn an allowed payment into a loan amount?

    The loan is whatever amount those payments exactly repay with interest. A loan is the present value of the payments that service it, discounted at the loan's own rate. Ten level payments of Rs 46.15 crore at 9% are worth 46.15 times the ten year annuity factorThe present value of receiving 1 a year for a set number of years at a given rate. For 10 years at 9% it is about 6.42.. Look at the green bars: year 1's payment is worth Rs 42.3 crore today, year 10's only Rs 19.5 crore, because money further away is worth less now.

    The relationship
    D=CFADSDSCR×1−(1+r)−nr=601.3×6.418≈296.2D = \frac{\text{CFADS}}{\text{DSCR}} \times \frac{1-(1+r)^{-n}}{r} = \frac{60}{1.3} \times 6.418 \approx 296.2
    CFADScash flow available for debt service, Rs 60 crore a year
    DSCRthe minimum debt service cover, 1.3x
    rthe loan rate, 9%
    nthe number of level payments, 10
    Dthe loan the payments can repay, Rs crore
    What it says in wordsDivide the cash by the cover to get the allowed payment, then take the present value of that payment stream at the loan rate.

    Check it out loud. Rs 296 crore at 9% is Rs 26.7 crore of first year interest, so the first payment of Rs 46.15 crore repays only about Rs 19.5 crore of principal. With a level payment, principal is repaid slowly at first and faster later, because interest takes the biggest bite while the balance is largest. If you can say that, the interviewer knows you understand what the annuity factor is doing rather than reciting it.

    What would a lender push back on?

    The Rs 60 crore is a forecast, and a forecast is exactly what a sponsor is paid to be optimistic about. The cover protects the lender only if the cash flow it is applied to is honest, so the real negotiation is over which forecast the 1.3x is applied to. Lenders often size on a downside case, shorten the tenor, or ask for a reserve account that holds some months of debt service in cash. Each of those moves the answer more than a quarter point on the rate would. State the limit too: the sum assumes the project runs all ten years and that nothing needs refinancing.

    Where candidates lose it

    The quick wrong answer is Rs 462 crore: ten payments of Rs 46.15 crore added up. It forgets that each payment carries interest, so the sum of the payments is always more than the loan they repay.

    The other loss is discounting the full Rs 60 crore, which ignores the cover and lends about Rs 385 crore. Say the order out loud before you calculate: cover first, then present value.

    What the interviewer asks next

    • The lender cuts the tenor to 7 years. Roughly how much can it lend now? (About Rs 232 crore.)
    • How would a sculpted repayment, where each year's payment is that year's cash flow divided by 1.3, change the answer if cash flow grows every year?
    • Why might a lender size the loan on a downside cash flow case rather than the base case?
  2. 033EBITDA is Rs 240 crore. The lender requires EBITDA interest cover of at least 2.5x and leverage of at most 4.0x, and debt costs 11%. What is the maximum debt, and which test binds?Leverage, coverage and cash flowCoreLeveraged financeCorporate banking

    Try it first

    Which test sets the limit here?

    Show the worked solution

    Maximum debt is about Rs 872.7 crore, and the interest cover test binds. Cover of 2.5x on EBITDA of 240 allows interest of 96; at 11% that is Rs 872.7 crore of debt. Leverage of 4.0x would allow Rs 960 crore, but the rate is too high for the business to carry it. The two tests meet at a 10% rate; above that, coverage is the tighter limit.

    Why run both tests instead of just the leverage one?

    A household can be told it may borrow up to four years of income, but it also has to afford the monthly instalment. When interest rates are high, the instalment test fails first, long before the four-years rule does. Leverage measures how much debt there is; interest cover measures whether the business can pay for it, and the rate decides which one runs out first. A lender sizing debt computes both and lends the lower.

    The relationship
    Dcover=240/2.511%=960.11≈872.7Dlev=4.0×240=960D_{\text{cover}} = \frac{240 / 2.5}{11\%} = \frac{96}{0.11} \approx 872.7 \qquad D_{\text{lev}} = 4.0 \times 240 = 960
    240EBITDA, Rs crore
    2.5minimum EBITDA over interest
    11%the interest rate on the debt
    4.0maximum debt over EBITDA
    What it says in wordsCover caps the interest bill, and the rate turns that bill into a debt amount; leverage caps the debt directly.
    At 11%, the interest cover test runs out before the leverage testCoverage cap240 / 2.5 = 96 of interest, / 11%872.7Leverage cap4.0 x 240960.0Max debt: Rs 872.7 crore,3.64x EBITDA, not 4.0x6001,0001,4006%8%10%12%14%Interest rate on the debtleverage cap 960coverage cap = 96 / ratecross at 10%at 11%: 873
    At 11% the coverage test allows Rs 872.7 crore of debt against Rs 960 crore under the leverage test, so coverage binds; the two limits cross at a 10% rate, and every point above that belongs to coverage.

    At what rate do the two tests swap?

    Set them equal: 96 divided by the rate equals 960, so the rate is 10%. Above 10%, coverage binds; below it, leverage binds. That is the general rule to leave the interviewer with: the crossover rate is one over the leverage multiple times the cover multiple, 1 over 4.0 times 2.5, which is 10%. When rates rise, the same business can borrow less even though its EBITDA has not changed, and lenders who size on leverage alone find their borrowers failing cover tests a year later.

    Say the limits. EBITDA interest cover ignores capex and tax, so a lender who worries about cash will also run a fixed charge test, which can bind lower still. And the effective leverage here is 3.64x, not the 4.0x the term sheet headline suggests; quoting 4.0x to the borrower would promise debt the second test will not allow.

    Where candidates lose it

    Most candidates run the leverage test, get Rs 960 crore, and stop. The rate was given for a reason, and at 11% that debt would leave cover at 2.27x, a breach on day one.

    The second miss is getting Rs 872.7 crore without saying why the answer changes with rates. The crossover at 10% is the insight that makes this more than arithmetic.

    What the interviewer asks next

    • Rates fall to 9%. What is the maximum debt now, and which test binds?
    • The lender adds a fixed charge cover test of 1.3x with capex of Rs 60 crore and tax of Rs 30 crore. Does that bind?
    • Why might a borrower accept a higher rate for a looser cover covenant?