Debt design: matching debt to the assets it finances

The optimal debt ratio answers how much to borrow. This skill answers what to borrow.

The principle is matching. Debt cash flows should move with the cash flows of the assets being financed. When they match, a downturn that cuts asset value also cuts the value of the debt, and the firm never becomes technically insolvent for structural reasons. When they do not match, the firm carries default risk that has nothing to do with its business. A cyclical firm with flat payments defaults in a recession it would otherwise survive. A firm earning euros and paying dollars defaults on a currency move.

That makes design a value question, not a paperwork question. Better matching lowers default risk at any given debt level, which raises debt capacity, which raises the optimal debt ratio and firm value.

What you produce

A debt_design block inside capital-structure.json, plus its prose section in capital-structure.md. Both artifacts belong to the capital-structure-analyst (SPEC §3, §6). Do not write into another agent's artifact.

"debt_design": {
  "target_duration": 4.3,
  "currency_mix": [{"currency": "USD", "share": 0.82}, {"currency": "EUR", "share": 0.12}],
  "fixed_floating_split": {"fixed": 0.6, "floating": 0.4},
  "special_features": ["payments linked to park attendance"],
  "convertible_yes_no": false,
  "regression_table": [],
  "existing_profile": {},
  "gap_table": [],
  "closure_instruments": ["swap fixed USD into floating EUR"]
}

regression_table carries coefficients and t-statistics, firm-level and bottom-up. A coefficient reported without its t-statistic is not usable evidence.

The script

Every number in that block comes from one engine:

python3 <skills>/debt-design/resources/macrosensitivity.py <subcommand> --in payload.json

Subcommand	Takes	Gives
regress	one macro series against the firm's own history	slope, standard error, t-statistic, R-squared, observation count, and the duration the rate slope implies
duration	project cash flows and a discount rate	the present-value-weighted average time the cash arrives, and the maturity of a par bond that matches it
debt-profile	the four regression results	maturity, currency mix, fixed against floating, straight against convertible
selftest	nothing	runs the bundled worked examples and reports pass or fail

Each reads JSON from stdin or --in FILE and prints JSON. Run any of them with --example to see the payload shape.

The engine grades its own evidence and will not let a weak slope pose as a strong one. Every slope comes back marked finding, hint or noise. A finding clears |t| > 2 on at least ten observations and may carry a financing decision. Anything estimated on fewer than ten annual periods is capped at a hint however large its t-statistic looks, because the sampling distribution behind it is too wide to trust. Carry that grade into regression_table beside the coefficient.

Preconditions

• G3_financials passed. Debt is defined economically, leases capitalized.
• G4_discount_rate passed when you intend to compute project duration, because duration needs a discount rate in the mandate currency.
• The optimal-ratio work (S7) has run, or you are told explicitly that only the design question is in scope.
• The firm is not a financial-service firm. For banks and insurers, debt is raw material rather than financing, and the no-optimal-debt-ratio constraint applies. Deposit and funding structure is a regulatory-capital question, not this one.

The pipeline

Debt design progress:
- [ ] 1. Profile the asset cash flows (intuitive, project duration, or macro regressions)
- [ ] 2. Translate the profile into debt characteristics
- [ ] 3. Overlay tax deductibility
- [ ] 4. Overlay ratings agencies, analysts and regulators
- [ ] 5. Overlay bondholder fears and information asymmetry
- [ ] 6. Tabulate existing debt on the same dimensions and close the gap
- [ ] 7. Feed improved matching back into the optimal debt ratio, once

1. Profile the asset cash flows

Six characteristics decide everything downstream: duration, currency, inflation sensitivity, cyclicality, uncertainty about future cash flows, and any specific driver such as a commodity price or a visitor count.

There are three routes to that profile. They are not ranked. Pick by what the firm looks like, and say which one you used.

Route	Use it when	Weakness
Intuitive — reason business by business about project length, currency and drivers	Multi-business firms, and always as a sanity check on the other two	No numbers; cannot set a floating-rate share
Project duration — PV-weighted life of a typical project	Few, large, independent projects: a mine, a park, a plant	Needs a credible cash flow forecast and terminal value
Historical macro regressions — the firm's own value and income against macro variables	Long-listed firms with a stable business mix	Noisy; often insignificant; assumes the past business persists

The intuitive route is worth doing first even when you plan to regress. Write one line per business naming project length, revenue currency, and the driver of the cash flows. If the regressions later contradict that line, one of the two is wrong, and finding out which is the analysis.

Worked business-by-business profiles: resources/worked-designs.md.

2. Translate the profile into debt characteristics

Asset characteristic	Debt characteristic
Long asset duration	Long debt duration
Revenues earned in several currencies	Debt split across those currencies, by revenue share
Operating income rises with inflation (pricing power)	Larger floating-rate share
Operating income rises with interest rates	Larger floating-rate share
High uncertainty about future cash flows	Shorter maturity
Low current cash flow, high expected growth	Convertible rather than straight debt
Cyclical income	Less debt overall, or payments tied to output
One dominant driver (commodity price, catastrophe, attendance)	A linked feature that ties debt service to that driver

Two of these deserve care.

Floating versus fixed is a pricing-power question. A firm that can pass cost increases to customers has operating income that rises with inflation, so floating-rate payments rise when its cash flows rise. A firm selling to powerful buyers who refuse price increases should hold fixed-rate debt. Giving that firm floating debt stacks interest-rate risk on top of input-cost risk.

Currency follows revenues, not incorporation or listing. A firm expanding into a new market should borrow in the currency it will earn there, not the currency it reports in. Where costs and revenues sit in different currencies, match the debt to the net exposure and say which side you matched.

3. Quantify duration when you have a project

Duration is the present-value-weighted average time at which cash arrives:

duration = Σ t × PV(CF_t) ÷ Σ PV(CF_t)

Include the terminal value. It usually dominates. Omitting it is the single most common error here, and it can halve the answer.

python3 <skills>/debt-design/resources/macrosensitivity.py duration --in project.json

{
  "discount_rate": 0.0846,
  "cash_flows": [-2000, -1000, -859, -267, 340, 466, 516, 555, 615, 681, 715],
  "terminal_value": 11275,
  "coupon_rate": 0.05
}

Cash flows start at year 0. terminal_value is added to the final year; pass it, or fold it into the last cash flow yourself. Leave it out and the output says so in warnings, because that omission is silent and costly. The reply carries the year-by-year present values, the weighted sum, the duration, and the share of the weighted sum the terminal value accounts for — check that last number before you believe the first.

The same arithmetic gives a bond's duration. Pass the coupon stream with the face value added to the final year.

Two facts govern how you use the number. Maturity exceeds duration for any coupon-paying instrument, so setting maturity equal to asset duration overshoots. Pass coupon_rate and the output solves for the maturity of a par bond whose duration hits the target, which is the version you can actually take to a lender. And project-specific financing is right only when projects are few, large and independent. For a portfolio of small, interdependent projects, match at the firm level instead.

Mechanics, the bond-duration comparison, and a worked 19-year theme-park calculation: resources/duration.md.

4. Run the macro sensitivity regressions

Treat the firm as a portfolio of projects and let its own history describe it. Regress annual changes in firm value, and separately in operating income, on four macro variables. These are eight separate univariate regressions, not two multiple regressions. Running one multiple regression produces different numbers and is not the method.

Δfirm value = (market cap + debt)_t ÷ (market cap + debt)_(t−1) − 1
Δoperating income = OI_t ÷ OI_(t−1) − 1

Regressor	Change convention	What the slope tells you
10-year government bond rate	absolute change in the rate	asset duration (firm value); fixed/floating (operating income)
Real GDP	percentage change	cyclicality
Inflation rate	absolute change in the rate	pricing power → floating-rate share
Trade-weighted currency index	percentage change	foreign-currency share of debt

Mixing the change conventions is a silent error. The coefficients still print, and they are wrong by a factor of a hundred.

Run them one at a time:

python3 <skills>/debt-design/resources/macrosensitivity.py regress --in macro.json

{
  "dependent": "firm_value",
  "macro_variable": "interest_rate",
  "history": {"market_cap": [231814, 209728], "total_debt": [54136, 53427]},
  "macro_changes": [0.0027]
}

That is the shape, cut to two periods to fit; a real payload needs at least five. dependent is firm_value or operating_income. macro_variable is one of interest_rate, gdp_growth, inflation, exchange_rate, and the reply echoes the change convention that variable expects so a mismatch is visible rather than silent.

Pass the raw history most recent period first and the engine builds the changes itself: firm value as market cap plus debt, operating income as a percent change, both compared against the period before. Eleven periods give ten change rows, so send ten macro changes covering the same fiscal years. Or skip that and pass dependent_changes directly.

The engine refuses rather than guesses. Operating income at or below zero in any period is rejected by name, because a percent change off that base is meaningless and will dominate the fit. A macro column with no variation, a series with a text placeholder in it, and a sample too short to yield a standard error are all refused with an explanation.

The reply also carries a warnings list. It fires when you read a coefficient off the dependent variable the method does not read it from, and when the sample is short.

Reading a slope as a duration

The interest-rate slope on firm value is an empirical duration. Firm value falls when rates rise, so the slope is negative, and the duration is its magnitude:

asset duration = max(0, −slope of Δfirm value on Δ interest rate)

A slope of −4.34 means debt with a duration of about 4.3 years. The floor at zero matters: a positive slope does not mean negative duration, it means the estimate carries no information about maturity and you should fall back to another route.

The engine makes this reading for you. Any interest_rate regression comes back with implied_duration_years and a duration_note that names it a duration. When the slope is positive the note says the floor has bound and sends you elsewhere, rather than printing a zero you might mistake for a short-duration firm.

When the historical route fails

A slope with |t| below 2 must not drive a financing decision. This is common rather than exceptional. Firm-level macro slopes are noisy, and a graded course team once found exactly one significant coefficient across four firms.

Two other failure conditions:

• Too few observations. Fewer than about ten annual periods leaves standard errors wide enough to swamp any slope. Skip firms listed three years or less entirely.
• A changed business. The regression assumes future projects resemble past ones. After a large acquisition, a divestiture, or a shift in business mix, the history describes a company that no longer exists. Quarterly data buys observations but not relevance.

In all three cases switch to bottom-up: take sector coefficients for each business the firm operates in and value-weight them, exactly as with bottom-up betas.

firm coefficient = Σ (business value weight × sector coefficient)

Sector tables, the Disney reference regressions, the sign conventions that differ between the sector sheet and the bottom-up estimator, and the data sources for each macro series: resources/macro-regressions.md.

Turning the four slopes into a design

Hand the four results back, whether they came from the firm's own history or from value-weighted sector coefficients:

python3 <skills>/debt-design/resources/macrosensitivity.py debt-profile --in slopes.json

{
  "home_currency": "USD",
  "interest_rate": {"slope": -4.34, "t_statistic": 2.20, "observations": 28,
                    "dependent": "firm_value"},
  "gdp_growth": {"slope": 0.55, "t_statistic": 2.03, "observations": 28,
                 "dependent": "firm_value"},
  "inflation": {"slope": 8.1867, "t_statistic": 2.76, "observations": 28,
                "dependent": "operating_income"},
  "exchange_rate": {"slope": -1.67, "t_statistic": 2.13, "observations": 28,
                    "dependent": "operating_income"},
  "operating_income_on_interest_rate": {"slope": -7.9339, "t_statistic": 1.40,
                                        "observations": 28},
  "revenue_by_currency": [{"currency": "USD", "share": 0.82},
                          {"currency": "EUR", "share": 0.18}],
  "expected_revenue_growth": 0.06,
  "current_cash_flow_positive": true,
  "coupon_rate": 0.05
}

A regress reply drops straight into any of those slots. Four blocks are required; the rest refine the answer. Each maps to one debt characteristic:

Slope	Sets
interest_rate on firm value	target duration, and the par-bond maturity that matches it
exchange_rate	whether to borrow abroad; revenue_by_currency then sizes the split
inflation and interest_rate, both on operating income	the floating-rate share
expected_revenue_growth with current_cash_flow_positive	straight against convertible
gdp_growth	cyclicality, which adds output-linked features or argues for less debt

Two behaviours are worth knowing before you read the output.

It reads each slope off the dependent variable the method specifies. Duration and cyclicality come from firm value; inflation and currency come from operating income. Pass operating_income_on_interest_rate so the floating-rate call uses the cash flows that service the debt rather than the market value. Skip it and convention_warnings says so.

Convertible is a growth call, not a cyclicality call. A firm can be sharply cyclical and still belong in straight debt if its current cash flows service it — cyclicality buys output-linked features and a lower debt level instead. Convertible is for the firm whose value sits in what has not been built yet: high expected growth, current cash flows that cannot carry a coupon. Supply both fields or the engine declines the call and says why.

The floating-rate share comes back as a band with a number attached. The source method sets that share by judgment and gives no formula, and the output says as much. Treat it as a starting position to argue with, not an estimate.

5. The overlays

Matching sets the target. Four overlays can move it, and one can stop an issue entirely. Apply them in this order and record any that bind.

Tax deductibility

A perfectly matched instrument that does not deliver a tax deduction has thrown away the main benefit of borrowing. Check deductibility in the relevant jurisdiction before recommending anything structured.

Two limits bind at high debt levels. Interest above EBIT shelters nothing, and statutory caps limit net interest deductions to a share of earnings. Both show up as a reduced tax rate applied to the cost of debt, and the capital-structure schedule already handles them: t_used = MIN(t_EBIT, t_cap). If your design pushes the firm past either limit, the schedule from cost-of-capital-toolkit debt-schedule will show it.

A large enough tax advantage can override matching. Say so explicitly when it does, and quantify it, rather than letting an instrument be chosen for tax reasons in silence.

Ratings agencies, analysts and regulators

Three audiences watch different numbers. Analysts watch earnings per share and comparables, and dislike issues that dilute. Agencies watch ratios and prefer equity. Regulators watch book measures.

The main practical case is a quasi-equity instrument. It benefits one specific firm: an under-levered firm with a rating constraint that moving to its optimum would breach. That firm captures debt-like tax benefits while keeping the rating. Do not generalize the trick. Agencies now grant such instruments only partial equity credit, and a structure designed to fool them will not.

Agencies also penalize speed. A rating-constrained firm should move gradually even when the design is right.

Bondholder fears

Where lenders cannot observe cash flows, or the assets are intangible rather than tangible and liquid, agency costs are high and the firm pays a wide spread. Three features answer that directly: convertible bonds, puttable bonds, and ratings-sensitive notes. Each gives the lender a claim that improves if the borrower behaves badly, which is what lets the coupon come down.

Check the existing covenant load before adding features. A firm already carrying tight investment and financing covenants may be paying twice for the same protection.

Information asymmetry

More uncertainty about future cash flows, or a credibility problem with lenders, argues for shorter-term debt. Short maturities force the firm back to the market often, which is costly, and that cost is what makes the commitment credible.

Do not lock in a market mistake

This one can override the entire design. If the firm is under-rated, issuing long-dated debt locks a rate far above its true default risk for the life of the bond. If the stock is under-priced, issuing equity or equity-linked paper transfers wealth from existing holders to new ones.

When the firm must finance while mispriced, use short-term or delayed structures until the mistake corrects. State the mispricing claim and its evidence. "We think our stock is cheap" is an assertion; a status-quo valuation against the market price is evidence.

Instrument menu, the deductibility checks, and the agency-cost features in detail: resources/overlays.md.

6. Tabulate the gap and close it

Put the recommendation beside the existing debt profile on identical dimensions. The gap table is the deliverable, not the recommendation alone.

Dimension	Recommended	Actual	Gap
Duration / weighted-average maturity	4.3 years	7.92 years	too long
Foreign-currency share	18%	5.49%	too little
Floating-rate share	significant	5.67%	too little
Convertible share	none	none	matched

Compute the actual profile from the debt footnote: face-value weighted average maturity, currency shares, fixed and floating split, convertible share. That side of the table is arithmetic and should be sourced, not estimated.

Close the gap two ways. Swap existing debt into the recommended form, which is usually cheaper and faster than refinancing. And issue new debt in the recommended form. Firm-level matching improves even when a specific new issue does not match a specific new asset, so do not wait for a perfectly matched project to appear.

Write the recommendation as one sentence naming maturity, currency, rate type and features. "Six to eight year duration, in the currency mix where the new stores will earn revenue, with a large floating-rate share given the pricing power" is a recommendation. "Better matched debt" is not.

7. Feed the answer back

Improved matching raises debt capacity. Re-check the optimal debt ratio once with the improved design, then stop. Running the loop repeatedly manufactures precision that the 10% grid and noisy inputs do not support.

Common failures

Symptom	Cause
Duration comes out implausibly short	Terminal value omitted from the cash flow stream
Recommended maturity equals asset duration exactly	Maturity confused with duration; maturity always exceeds it
Macro coefficients look enormous	Percentage changes used where absolute rate changes belong
Firm-level regressions produce a confident design	Slopes with t below 2 were read as if significant
Negative duration	Positive interest-rate slope, which should be floored at zero and routed to bottom-up
Percent change in operating income is meaningless	Operating income near zero or negative in a base period
Design recommends floating debt for a supplier to large retailers	Pricing power assumed rather than tested against the inflation slope
Debt currency matches the listing country	Currency matched to incorporation instead of where revenues arise
Design is elegant and the firm gets no tax deduction	Tax overlay skipped
Long-dated issue at a wide spread just before an upgrade	Market mistake locked in
Design treated as a footnote to the debt ratio	Matching raises debt capacity, so it changes the ratio itself
regress refuses a period by name	Operating income at or below zero there; drop it and re-run
Floating-rate call contradicts the pricing-power story	operating_income_on_interest_rate omitted, so the call fell back to the firm-value slope
debt-profile returns straight debt for an obviously cyclical firm	Correct: convertible is a growth call, and cyclicality buys output-linked features instead