Private Debt: formula sheet

Key formulas

Risk and return ranking (typical)

Direct lending < Mezzanine < Venture debt ≈ Distressed debt (in expected risk and return)

A general guide, not a rule. Venture and distressed risk depend on the specific deal and structure.

Capital structure priority

Senior secured → Senior unsecured → Mezzanine/subordinated → Equity

Claims are paid in this order in liquidation. Mezzanine ranks behind senior debt.

Mezzanine total return sources

Total return ≈ cash interest + PIK interest + fees + equity warrant gains

PIK interest accrues to principal rather than being paid in cash.

Distressed debt return

Return ≈ (Recovery value + any interim cash − Purchase price) ÷ Purchase price

Ignores time value. Annualise it if the holding period matters.

Floating-rate loan yield

All-in rate = Reference rate + Credit spread

Direct loans are usually floating, so income rises and falls with the reference rate.

Floating-rate coupon

Coupon rate = Reference rate (or floor if higher) + Spread

Apply the floor only if the reference rate falls below it. The spread stays fixed.

Blended unitranche rate

Blended rate ≈ (Senior share × Senior rate) + (Junior share × Junior rate)

Use as a weighted average of the implied layers. Actual pricing is negotiated, so treat it as an approximation.

Interest cover

Interest cover = EBITDA ÷ Interest expense

Typical covenant test. Check the definition given in the question.

Leverage ratio

Leverage = Total debt ÷ EBITDA

Maintenance covenants set a maximum; senior-only leverage may be tested separately.

Yield to lender, approximate

All-in yield ≈ Coupon + (Upfront fee ÷ Expected life in years)

Rough approximation for comparing loans. Ignores default losses and compounding.

Mezzanine total return sources

Total return ≈ cash interest + PIK interest + fees + equity kicker value

Use this to list return components. Ignoring the kicker or PIK understates return.

PIK accrual

Ending balance = Principal × (1 + PIK rate)^n

Assumes annual compounding of PIK interest added to principal. Adjust for the compounding stated.

Distressed gain on purchase

Return ≈ (Recovery value + interim cash − Purchase price) ÷ Purchase price

Price is below par. Recovery is the value received in cash or new securities, not par.

Capital structure priority

Senior secured > senior unsecured > subordinated/mezzanine > preferred > common

Absolute priority is the usual rule, but actual restructurings can deviate.

Fulcrum security

Fulcrum = the most senior class of claims that is not paid in full, where value breaks; it typically receives the reorganised equity

Control investors usually target it. Classes above are paid in full; classes below usually get little.

Gross yield decomposition

Loan yield ≈ Base rate + Credit spread (expected loss + credit risk premium) + Illiquidity premium

A framework for explaining return, not an exact pricing formula. Use it to say what the extra yield pays for.

Expected credit loss

Expected loss = Probability of default × Loss given default (× Exposure)

Loss given default = 1 − recovery rate. Compare spread with expected loss to see the compensation left for risk and illiquidity.

Net return after costs

Net return ≈ Gross return − Management fee − Incentive fee − Fund expenses

Fees may be charged on committed or invested capital. State the basis. Check whether a hurdle applies before the incentive fee.

Illiquidity premium (approximation)

Illiquidity premium ≈ Private debt yield − Yield on comparable liquid debt (same seniority, rating, maturity)

The gap also contains credit and structuring differences, so it is only an estimate.

Fair value of a loan (DCF)

Fair value = Σ [CFt ÷ (1 + r)^t], where r = base rate + credit spread + illiquidity premium

CFt includes interest and principal. Use expected cash flows after allowing for default risk, or put the risk in the spread, but not both.

IRR

0 = Σ [CFt ÷ (1 + IRR)^t], with contributions negative, distributions and ending NAV positive

Includes the residual NAV as a final inflow. It is money-weighted, so timing of cash flows matters.

Expected loss rate

Loss rate = Default rate × Loss given default

Loss given default = 1 − recovery rate.

Loss given default

LGD = 1 − Recovery rate

Recovery rate is the share of exposure recovered after default.

Net credit yield (approximate)

Net yield ≈ Gross yield − Expected loss rate

A quick screening tool. Fees come off next to reach the investor's net return.

Floating-rate coupon

Coupon = Reference rate + Spread

Spread is the lender's credit compensation. Price depends mainly on spread, not on the reference rate.

Quick revision

• Private debt is negotiated, illiquid lending outside public bond markets, usually held through funds.
• Direct lending is usually senior, often secured, with covenants and floating rates.
• Floating rates reduce interest rate risk for the lender but raise borrower payment stress when rates rise.
• Unitranche combines senior and subordinated debt into one loan with a blended rate, simplifying documentation.
• Mezzanine is subordinated to senior debt and often adds warrants or equity features for extra return.
• Venture debt lends to growth-stage firms and often comes with warrants because default risk is high.
• Distressed debt investors buy at a discount and earn through recovery, restructuring or control.
• Higher risk strategies should show higher expected return, but also wider outcomes and lower recovery.
• Due diligence covers the manager, underwriting process, documentation, covenants, collateral and conflicts of interest.
• Illiquid loans are often valued by models, so valuation judgement and consistency matter.
• Performance is commonly judged with IRR and multiples, which depend on cash flow timing.
• Always link the recommendation to the client's objectives and constraints.

Common mistakes

• Treating mezzanine as senior debt. Fix: Remember it is subordinated and ranks behind senior lenders. Its higher return pays for that lower priority.
• Saying private debt is always safer than public debt because it is secured. Fix: Safety depends on the strategy and position in the capital structure. Mezzanine, venture and distressed debt carry much higher risk.
• Treating a unitranche loan as lower risk than a senior secured loan. Fix: Remember unitranche includes junior risk. Its blended rate is higher than senior because the lender bears more loss risk.
• Ignoring the floor when the reference rate is below it. Fix: Use the higher of the reference rate and the floor, then add the spread.
• Treating mezzanine as senior-like safe debt because it pays regular interest. Fix: Remember it is subordinated. Recovery in default is low and the equity kicker shows it carries equity-like risk.
• Leaving out PIK interest when assessing mezzanine risk. Fix: PIK adds to principal and raises leverage over time. It boosts stated return but increases default risk and repayment at maturity.
• Treating the full spread over the base rate as the illiquidity premium. Fix: Strip out expected loss first, and compare with a liquid bond of the same quality to estimate the premium.
• Saying floating-rate private loans have no interest rate risk. Fix: State that price risk is low but higher rates can raise borrower interest burden and default risk.
• Using a public bond yield with no liquidity adjustment to discount a private loan. Fix: Add an illiquidity premium and the correct credit spread for the borrower.
• Leaving the ending NAV out of the IRR cash flows. Fix: Treat residual NAV as a final inflow. Without it the IRR is understated for an active fund.

Exam tips

• Expect item sets that describe a borrower and ask you to pick the matching strategy. Practise the borrower-to-strategy match until it is automatic.
• In essays, a command word such as 'justify' needs a reason tied to the client, not just a definition.
• Know the return sources of each strategy separately: coupon, PIK, fees, warrants, discount recovery.
• When comparing with public debt, cover liquidity, transparency, customisation and covenants in your answer.
• Give only the number of points asked for; extra responses are not evaluated, and only the first ones in order count.
• Show every calculation line in essay sets. A correct number alone earns credit, but a clear method protects you if a step is off.
• Always state the rate formula in order: check the floor first, then add the spread, then fees if the question asks for all-in.
• When asked to justify a recommendation, link one point to the client's objective (income, yield) and one to a constraint (liquidity, risk tolerance).