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
Level
AnyWarm upCoreHard
Source
AnyReported at a firmStandard
Showing 1–2 of 2 · filtered from 100Clear filters
  1. 055A 9% annual coupon bond has 3 years left and a make-whole call at the government yield plus 50 basis points. The 3-year government yield is 6.5%. What is the make-whole price, and should the issuer call if it can refinance at 7.3%?Issuance and refinancing arithmeticHardSyndicate desksCorporate banking

    Try it first

    At a 7.3% refinancing rate, does calling save the issuer money?

    Show the worked solution

    The make-whole price is about 105.25, and calling to refinance at 7.3% loses the issuer about 0.81 per Rs 100. Discount the remaining 9, 9 and 109 at 6.5% plus 50 basis points, 7.0%, to get 105.25. Valued at the 7.3% refinancing rate, the same payments are worth 104.44, so paying 105.25 to retire them destroys value. Calling only saves money if the issuer can borrow below 7.0%.

    What does a make-whole price actually compute?

    Suppose you repay a relative's loan early and they say: fine, but pay me today everything I would have earned, discounted at a low rate. That is a make-whole callAn issuer option to repay a bond early at the present value of its remaining payments, discounted at the government yield plus a fixed spread set in the documents.. The call price is the present value of every remaining coupon and the principal, discounted at the government yield plus a small fixed spread, here 6.5% plus 0.5%, which is 7.0%. The low discount rate is what pushes the price above par: the lender is compensated for giving up a 9% coupon.

    Make-whole price: discount what is left at the government yield plus 50 bpYear 1 cash flow9/ 1.07^18.41Year 2 cash flow9/ 1.07^27.86Year 3 cash flow109/ 1.07^388.98Make-whole price105.25discounted at 7.0%Per Rs 100 of bonds, axis starts at 100Cost to call today105.25Keep the bond, valued at 7.3%104.44calling loses 0.81 per Rs 100100
    The remaining 9, 9 and 109 discounted at 7.0% are worth 8.41, 7.86 and 88.98, a make-whole price of 105.25; the same payments valued at the issuer's 7.3% refinancing rate are worth 104.44, so calling costs 0.81 per Rs 100 more than keeping the bond.
    The relationship
    PMW=91.07+91.072+1091.073=8.41+7.86+88.98=105.25P_{MW} = \frac{9}{1.07} + \frac{9}{1.07^2} + \frac{109}{1.07^3} = 8.41 + 7.86 + 88.98 = 105.25
    1.07one plus the make-whole discount rate, government 6.5% plus 0.5%
    9the annual coupon per Rs 100
    109the last coupon plus the principal
    What it says in wordsThe make-whole price is the bond's remaining cash flows valued at a rate barely above the government yield.

    Why does refinancing at 7.3% not pay?

    Compare two ways of carrying the same obligation. Keeping the old bond means payments worth 104.44 at the issuer's 7.3% borrowing rate; calling means paying 105.25 in cash today, raised with new 7.3% debt. The issuer would give up 0.81 per Rs 100, about Rs 81 lakh on every Rs 100 crore, to swap into debt that only looks cheaper. The coupon saving from 9% to 7.3% is real, but the make-whole has already charged for it, valued at 7.0%, a lower rate than 7.3% and therefore a higher price.

    That gives a clean rule to say out loud. A make-whole call only saves money if the issuer can refinance below the make-whole discount rate, the government yield plus 50 basis points. Few corporates borrow that tightly, which is why make-wholes are usually exercised for other reasons: to escape a restrictive covenant, to complete a merger, or to tidy the capital structure. The limit: this ignores the fees on the new bond, which make calling worse still.

    Where candidates lose it

    Candidates see a 9% coupon and a 7.3% refinancing rate and say call, because 1.7% a year sounds like free money. They forget the issuer must first pay a premium price that already contains the value of that saving.

    The second loss is discounting at the wrong rate: using 6.5% or 9% instead of the government yield plus the 50 basis point spread named in the documents. Say the rate before you discount.

    What the interviewer asks next

    • At what refinancing rate is the issuer indifferent between calling and keeping the bond?
    • How would a fixed-price call at 102 change the answer?
    • Why do investors prefer a make-whole to a fixed-price call, and what does it do to the bond's price when rates fall?
  2. 082Firm A can borrow fixed at 7.0% or floating at benchmark plus 0.3%. Firm B can borrow fixed at 8.2% or floating at benchmark plus 0.8%. A wants floating rate debt and B wants fixed. How much can they save in total with an interest rate swap, and how could the saving be split?Issuance and refinancing arithmeticHardSyndicate desksCorporate banking

    Try it first

    Firm A is cheaper in both markets. Is there anything to gain from a swap?

    Show the worked solution

    The total saving is 0.7% a year, the difference between the fixed gap of 1.2% and the floating gap of 0.5%. A borrows fixed at 7.0%, B borrows floating at benchmark plus 0.8%, and they swap. Split evenly, B pays A 7.05% fixed and A pays B the benchmark: A ends at benchmark minus 0.05% and B at 7.85% fixed, each 0.35% better than going direct.

    Why is there a gain when one firm is cheaper at everything?

    Picture two flatmates: one cooks and cleans faster than the other, but is much faster at cooking and only slightly faster at cleaning. The household still gets more done if the fast cook cooks and the other one cleans. Borrowing works the same way. What matters is comparative advantage: firm B is 1.2% worse in the fixed market but only 0.5% worse in floating, so B should borrow floating and A fixed, and the gap between those two penalties, 0.7%, is the gain.

    B is worse at both, but much less worse at floatingFixedFloatingFirm A7.0%bench + 0.3%Firm B8.2%bench + 0.8%B pays more by1.20.5Gain to share: 1.2 - 0.5 = 0.7Each borrows where it is relatively cheapA: fixed at 7.0%B: floating at bench + 0.8%then swap to what each wantsFirm AFirm Bbenchmarkfixed 7.05%pays 7.0% fixedto its lenderspays bench + 0.8%to its lendersA's net costbench - 0.05%B's net cost7.85% fixedSaving 0.35 eachagainst going direct
    B pays 1.2% more than A in fixed but only 0.5% more in floating, so A borrows fixed, B borrows floating and they swap at 7.05%, leaving A at benchmark minus 0.05% and B at 7.85% fixed, each 0.35% better than borrowing directly.
    The relationship
    Gain=(8.2−7.0)−(0.8−0.3)=1.2−0.5=0.7%\text{Gain} = (8.2 - 7.0) - (0.8 - 0.3) = 1.2 - 0.5 = 0.7\%
    8.2 - 7.0B's extra cost in the fixed market
    0.8 - 0.3B's extra cost in the floating market
    What it says in wordsThe saving is the difference between the two credit gaps, not either gap on its own.

    How do you check the split adds up?

    Follow each firm's cash. A pays its lenders 7.0% fixed, receives 7.05% fixed from B and pays B the benchmark, so its net cost is the benchmark minus 0.05%, against benchmark plus 0.3% going direct. B pays its lenders benchmark plus 0.8%, receives the benchmark from A and pays A 7.05%, so its net cost is 7.85% fixed, against 8.2% direct. 0.35% plus 0.35% is the full 0.7%, which is the check that nothing was lost or invented. On Rs 1,000 crore that is Rs 7 crore a year between them. In practice a bank sits in the middle and keeps a slice, so each firm gets somewhat less.

    What is the honest limitation?

    The gain is not free money. Part of the gap exists because floating lenders can reprice or refuse to roll a weaker borrower, while fixed lenders are locked in for years; B's floating spread of 0.8% may not hold if its credit slips. Each firm also takes on counterparty risk to the other or to the bank. Say that one sentence and the answer sounds like someone who has watched a swap book.

    Where candidates lose it

    The trap is saying A should simply borrow floating because it is cheaper in both markets. That reasons from absolute advantage and misses the 0.7% entirely.

    The second loss is a split that does not reconcile. Candidates pick a swap rate out of the air and never check that the two firms' savings add back to 0.7%. Walk each firm's net cost out loud; the arithmetic is the proof.

    What the interviewer asks next

    • A bank intermediates and keeps 0.1%. What swap rates give each firm an equal share of the rest?
    • Why might B's floating spread be closer to A's than its fixed spread is?
    • Which firm is exposed if the other defaults halfway through the swap, and to what?