At the end of the fourth bridge, a business carries debt and has shown that it can. Its facility was sized to a downside it set itself, its covenants are watched monthly against a trigger of its own, its owner's guarantee is released or on a path to release, and it has serviced its debt through a soft quarter or a refinancing without help. The result is summed up in free cash flow to equity, the cash left for the owners after the lender has been paid: free cash flow to the firm, less interest after tax, less principal repaid, plus net new borrowing.
What the buyer is asked to believe
A levered equity buyer, and the credit committee beside them, are asked to believe that this business's cash carries its own debt through a bad quarter, leaves a residual for the owners that is reported and reconciled every month, and funds growth from that residual without the owners putting in more, with neither the owner's guarantee nor the owner's relationship with the bank holding it up.
As at every anchor, each part of that story is tested against a record, and each test fixes a number. The lender packs, the capital structure file, the coverage history and the holder's return fix the free cash flow to equity being discounted. The covenant record, the seasoning memo, the released guarantees and the finance function, by showing the debt carried under stress and without the owner, fix the probability of a breach in the scenarios. The levered forecast, the debt schedule, the rate policy and the growth record under the debt fix the reinvestment rate and the return on new capital. Any claim without a record behind it comes out of the story.
Whose value
The standard is fair market value, the one a leveraged buyer and its lender price on. Where a buyer would restructure the debt, its investment value is computed alongside, and the difference is attributed to that buyer's structure, not to the business. Where the number goes to a court or a dispute, the jurisdiction's statutory standard applies, and it decides whether any discount for illiquidity is allowed.
The business is valued as a going concern, its facility assumed to stay in place or to be refinanced on the terms the second lender's indication supports. The liquidation alternative is computed too: what the assets would fetch in an orderly sale, less the costs of selling and winding down, less the debt, which ranks ahead of the owners. Because the debt comes off the top, a levered business in decline reaches the point where liquidation beats continuing sooner than an unlevered one would, so the file carries both figures.
The conclusion is at the control level of a levered equity, and it means nothing without the debt it sits behind stated beside it. An equity value of $5.7 million behind $2.8 million of debt is a different claim from the same figure behind none.
Where a shareholder or buy-sell agreement prices an interest in the equity, the file records who selects the appraiser, how many appraisers there are, the date of value and the level of value the agreement fixes. An agreement silent on any one of them leaves co-owners something to dispute on the day it is used.
Two routes, reconciled
This is the first point in the framework where the owners' cash may be valued directly: free cash flow to equity is a cash flow to one claim, so discounting it at the cost of equity gives an equity value without passing through the enterprise. The route is permitted only because the checkpoint has shown two things: leverage held inside a stated band, with covenant headroom, through the latest year, and the debt serviced through a soft quarter or a refinancing. If either is missing, the direct route is not used.
The enterprise route is always computed as well: free cash flow to the firm, discounted at the weighted cost of capital, less the debt and debt-like items, plus excess cash, gives a second equity value. The two are reconciled line by line, with the sources of difference named, chiefly the tax shield, the timing of principal and the treatment of the undrawn growth line. A gap beyond a stated tolerance counts against the direct figure, because the direct route is the one that goes wrong when the cost of equity is not moved as the debt changes. During a recapitalization, or while a facility is being drawn, leverage is moving and the enterprise route governs alone.
Each cash flow is discounted at the rate for its own claim, so equity cash flows never meet the weighted cost of capital and enterprise cash flows never meet the cost of equity. A levered transaction multiple is kept, labelled as pricing with its drivers stated, and never governs.
A cost of equity that moves with the debt
The marginal investor is a diversified equity holder standing behind a lender. Its cost of equity starts from the sector's unlevered beta, relevered for the debt actually in place, and is relevered again for every year of the forecast, because the debt is amortizing.
A cost of equity that falls as the debt is repaid
Illustrative. The sector's unlevered beta is relevered for the debt the business carries, relative to its equity, and turned into a cost of equity. As principal is repaid, the ratio falls and so does the return the owners require. Debt is priced at the risk-free rate. The cost of the business's capital before the tax shield does not move with the debt; only the shield, which shrinks as the debt is repaid, brings the weighted cost below it.
As principal is repaid, the owners' claim becomes less risky and their required return falls. In the illustration, a business carrying debt of 49 percent of its equity value, the $2.8 million behind $5.7 million used below, has a cost of equity of about 13.5 percent. Once the debt has been paid down to 20 percent of equity, the same business's cost of equity is about 12.1 percent. A single rate held across an amortizing forecast overstates the cost of equity in the later years and so understates the equity, which is why the file shows the rate year by year.
The weighted cost of capital, computed from the same components at each year's structure, stays flat apart from the tax shield, and the file shows that it does. In the illustration, with the debt priced at the risk-free rate, the cost of capital before the shield is 11.1 percent whatever the debt. The shield brings the weighted cost down to about 10.2 percent today and 10.6 percent once the debt is down to 20 percent of equity. That flat line is the bridge's central principle in numbers: debt creates no value by itself. No premium is added for size or for the business's particular risks. A breach, a failed refinancing, a rate shock and the owner's death while a guarantee remains are each named and priced in the scenarios, and none is also put in the rate.
Whether growth counts
The first test carries over from the previous anchor: a return on invested capital above the cost of capital in every year of the recent record, on the framework's single definition, with the barrier that explains it read from a current competitor map.
This anchor adds a second. Growth counts only where the reinvestment plan is funded after debt service in the base and downside cases without asking the owners for more, where the loan agreement's baskets permit it, and where the register shows reinvestment at or above plan every year since the facility closed, at returns still above the cost of capital. An equity buyer will not pay for growth that the structure would force the business to cut in a soft quarter, so that growth is valued at zero.
Where growth passes both tests, it is the reinvestment rate multiplied by the register's return on new capital, shrunk toward the base rate the fewer projects stand behind it, held for an advantage period no longer than the base rate allows, and then faded to the cost of capital. The fade is applied to free cash flow to the firm and the debt schedule is laid over it, so that no growth appears in the owners' cash that the business as a whole did not earn first.
Three layers, at the equity level
The three layers of value are the previous anchor's enterprise values, carried forward in time, and each is reduced by the same debt so that all three are compared at the level of the equity. Leverage leaves unchanged what the assets would cost to reproduce and what the business earns on them. It changes only who receives the result.
One new intangible enters reproduction value: the finance function and the lender relationship, costed as what it would take to build a reporting function a lender would accept and to obtain a facility on these terms. Growth value stays on its own line so that the equity buyer can see what it is paying for the franchise and the lender can see that none of it is in the coverage the debt was sized on.
Why the equity is a riskier number
The equity is a residual, so an error in the enterprise value lands on it whole. In the illustration, a business with an enterprise value of $8.5 million and $2.8 million of debt has equity worth $5.7 million. If the enterprise value is wrong by 10 percent, the equity is wrong by about 15 percent, because the debt does not move, and the more debt there is, the larger the magnification.
A residual magnifies error
Illustrative. The equity is what is left of the enterprise value after the debt. An error in the enterprise value falls entirely on the equity, so the same error is a larger share of it, and more so the more debt there is.
So the margin of safety here is wider than at the last anchor. The floors for each layer are unchanged, but the gap between the expected value and the downside, set by the leverage as well as the business, is larger, and that gap governs.
The scenarios that set the downside are those of a levered business: a rate shock on the unhedged debt; a covenant breach, with the cost of curing it charged to the owners; a soft quarter with growth spending held at plan; the owner's death or disability while a guarantee or key-person clause remains; and, where there are co-owners, a co-owner's death, disability, divorce or departure, priced through the buy-sell agreement and tested against whether a purchase under it would breach a covenant or trip a change-of-control clause in the facility.
Illiquidity, reconciliation and the owner's return
The holder is a controlling equity buyer behind a lender, so the discount for illiquidity is the cost and time of a sale and nothing else. Where a guarantee has not been released, that cost includes obtaining the departing owner's consent, which is how a released guarantee narrows the discount. The depth of the pool of leveraged buyers is the other component, and a second lender's indication deepens it. The discount is computed on the business's actual structure, never on debt a hypothetical buyer might add.
The approaches are weighted by their evidence. With reviewed statements, two years of reconciled packs and a seasoned soft quarter, the income approach scores highest and governs. Leveraged comparables at this size are few and rarely disclosed, so the market approach usually scores low. Every price the business meets is reversed into what it implies, one input at a time, and a price that implies leverage above the band the checkpoint allows is treated as the buyer's bet.
The holder's return is measured here, beside the history of distributions: what the business paid its owners each year, and what it could have paid after the reserves the covenants and the growth line require. For each year since the facility closed, distributions plus the change in the reconciled equity value, over the opening value, is set against that year's relevered cost of equity. A cumulative return below the cost of equity is reported as a finding against the bridge.
Who underwrites it
The underwriter is an equity buyer working alongside a senior lender's credit committee. They will not pay for cash flow that cannot carry its own debt, for debt never seen through a bad quarter, or for borrowing that rests on the owner's guarantee or the owner's relationship with the bank. The lender prices its claim at a cost of debt, and the equity holder prices the residual at a cost of equity relevered for that debt, higher than the unlevered cost because the residual is riskier. As the flat weighted cost of capital showed, the split itself creates no value. What the anchor changes is which buyers can bid, and what they will pay.
What the crossing produced
The checkpoint at the end of the fourth bridge is the list the fifth bridge inspects on its first day, and it follows the four spans. The first leaves two years of monthly lender packs and a capital structure file. The second leaves a levered forecast with its record, a rate policy, and a structure that funds growth, with baskets and an undrawn line. The third leaves a debt schedule and maturity ladder from the executed documents, released guarantees, two years of clean covenant certificates and coverage, and quarterly headroom. The fourth leaves a seasoning memo, a second lender's indication, a record of growth continued under the debt, and the file that reconciles the two equity values. The essay on inspecting free cash flow to equity sets each of them out.