Fixed-Income Markets for Corporate Issuers: formula sheet

Key formulas

Investment-grade boundary

Investment grade: BBB- or higher (S&P, Fitch); Baa3 or higher (Moody's). High yield: below these

Know where the line falls. BBB- is the lowest investment-grade rating and BB+ is the highest high-yield rating.

Credit quality and yield

Lower credit quality → higher default risk → higher required yield

This is a general relationship, not a calculation. Use it to rank yields.

Public vs private placement

Public: registered, broad buyers, more liquid. Private: limited disclosure, negotiated terms, less liquid

Know the trade-off in each direction.

Market by maturity

Money market: short term (commercial paper). Capital market: long term (bonds, notes, term loans)

Match the funding term to the use of funds.

Floating loan rate

Loan rate = Reference rate + Spread (margin)

The reference rate resets periodically. The spread reflects the borrower's credit risk and stays fixed unless the agreement has a pricing grid.

Commitment fee on a revolver

Fee = Undrawn amount × Commitment fee rate

Charged on the unused part of the committed limit. Interest is charged only on the drawn part.

Total annual cost of a revolver

Cost = Drawn × (Reference rate + Spread) + Undrawn × Commitment fee rate

Ignores upfront fees. Use the average drawn balance if the question gives one.

Maintenance covenant test

Debt ÷ EBITDA ≤ stated maximum; EBITDA ÷ Interest ≥ stated minimum

Tested at set dates, such as each quarter, regardless of any borrower action. A breach can trigger default.

CP price from discount rate (bank discount basis)

Price = Face value × (1 − DR × Days ÷ 360)

US CP quotes use a 360-day year. DR is the annualised discount rate as a decimal.

Add-on yield (money market yield) of CP

Money market yield = (Face − Price) ÷ Price × (360 ÷ Days)

Uses price in the denominator, so it is higher than the discount rate for the same CP.

Holding period yield

HPY = (Face − Price) ÷ Price

Not annualised. Annualise afterwards using the convention asked for.

US CP SEC registration exemption

Maturity ≤ 270 days to qualify for SEC registration exemption

This is not a cap on maturity. Longer paper can be issued but would have to be registered, so US CP is typically 270 days or less. Eurocommercial paper is not tied to this threshold and is more flexible.

Repurchase price of a repo

Repurchase price = Sale price × (1 + repo rate × Days ÷ 360)

Repo rates are commonly quoted on a 360-day basis; follow the question's convention.

Typical ranking of claims in default

Secured senior > Unsecured senior > Subordinated (junior) > Equity

Higher rank usually means higher expected recovery and lower yield, all else equal.

Floating-rate note coupon

Coupon rate = Reference rate + Spread

Reference rate resets each period. The spread is fixed at issue, unless the terms say otherwise.

Bullet bond cash flows

Coupons each period; full principal at maturity

Final payment is the largest cash flow.

Fully amortizing bond

Each payment = interest + principal repayment; balance reaches zero at maturity

Interest falls as the balance falls.

Partially amortizing bond

Periodic payments (interest + some principal) + balloon payment at maturity

The balloon equals the remaining balance.

Underwritten offering risk

Underwriter bears unsold-bond risk; issuer receives the agreed price

Also called a firm commitment. Underwriter's gain = resale price − price paid to issuer.

Best-efforts offering risk

Bank acts as agent; issuer bears unsold-bond risk

No guarantee of proceeds to the issuer.

Shelf registration

Register once, issue in tranches over time

Gives timing flexibility and lower repeat issuance costs.

Private placement

Sold to qualified investors, no public registration

Lower cost and speed, but weaker liquidity and resale limits.

Bid-ask spread

Spread = ask price − bid price

Wider spread means lower liquidity and higher trading cost.

Underwriting proceeds to issuer

Net proceeds = issue size × price paid by underwriter ÷ 100 (price per 100 par)

Use the underwriter's purchase price, not the public offer price.

Quick revision

• Corporate issuers borrow through bank loans, syndicated loans, commercial paper and bonds.
• Short-term funding covers working capital needs; bonds usually fund longer-term needs.
• A syndicated loan is shared among several lenders and arranged by lead banks.
• Commercial paper is short-term funding and is usually available only to issuers with strong credit standing.
• Bank loans are usually more flexible to negotiate than public bonds but are less easily traded.
• Bond features include maturity, coupon structure, security and covenants.
• Covenants protect lenders by restricting or requiring certain issuer actions.
• The primary market is where new securities are sold by the issuer to investors.
• The secondary market is where existing securities trade between investors.
• Public offerings reach many investors; private placements go to a limited group.
• Bond liquidity varies widely, so many bonds trade less often than equities.
• Match instrument to need: size, tenor, credit quality, speed and cost.

Common mistakes

• Treating BB+ or Ba1 as investment grade. Fix: Remember BBB- and Baa3 are the lowest investment-grade ratings. Anything one notch lower is high yield.
• Saying a private placement is cheaper in yield because it is less regulated. Fix: Private placements often carry a yield premium for lower liquidity. Their advantages are speed, flexibility and lighter disclosure.
• Charging the commitment fee on the whole facility. Fix: Split the limit into drawn and undrawn parts. Interest applies to drawn, the commitment fee to undrawn.
• Treating a revolver like a term loan whose repaid amounts are gone. Fix: Remember that a revolver allows repeated draws and repayments up to the committed limit.
• Treating CP as secured or as a bank deposit. Fix: CP is an unsecured corporate promise to pay backed only by credit and usually a back-up line. A CD is a bank deposit.
• Assuming Eurocommercial paper must be in euros. Fix: ECP refers to the market outside the currency's home market. It can be issued in many currencies.
• Saying a floating-rate note has no risk because its price always equals par. Fix: The price stays near par only if the spread still matches the issuer's credit risk. If credit quality worsens, the price can fall below par.
• Treating a bullet bond as one with no coupons. Fix: A bullet pays regular coupons. Only the principal is paid in one lump sum at maturity.
• Saying the issuer bears unsold-bond risk in an underwritten offering. Fix: Remember that underwriters buy the bonds, so they carry the risk. In best-efforts the bank is only an agent.
• Thinking shelf registration is a separate type of bond. Fix: It is a registration method that lets the issuer sell in tranches over time. The bonds themselves are ordinary bonds.

Exam tips

• Memorize the rating line: BBB-/Baa3 is the last investment-grade notch.
• Questions often test trade-offs. Link private placement to flexibility and speed, and public offering to liquidity and breadth.
• Watch for stems that give two facts, such as rating and sale method. Check each fact against each option, because the wrong options usually fit only one.
• Numerical options are listed smallest to largest, but this topic is mostly conceptual, so spend your 90 seconds on reading the stem carefully.
• With no penalty for wrong answers, always answer. Eliminate the option that reverses the risk-yield relationship first.
• Questions are three-option MCQs, so eliminate the two options that reverse typical loan features such as floating rate, seniority and covenants.
• For revolver questions, always check whether the numbers refer to the drawn or the undrawn amount.
• Words like 'typically' and 'usually' matter. Do not choose an option that says loans are always one way.