FIN.9 - Compare Capital Investments and Allocations

Type: Method

Status: Stable

FIN.9:0 - Use this when

Several uses of capital compete, interact or displace one another, or the corporation is considering an acquisition or divestment. Compare feasible combinations and their incremental value. Use FIN.6 directly for a sufficient standalone project question.

FIN.9:1 - Problem frame

The object is a capital-use choice or combination for a named corporation. Acquisition and divestment are transaction uses of this comparison: they add a specified interest, consideration and combination or separation effects. Legal closing and operational execution require their applicable professional methods.

FIN.9:2 - Problem

Choosing the largest standalone NPV can exclude a better combination. Adding an attractive business to the corporation can destroy buyer value at the offered price. Divestment proceeds can look beneficial while the remaining business loses shared services or customers.

FIN.9:3 - Forces

Compare value, limited capital, operating dependencies and risk concentration on compatible grounds. Preserve indivisibilities and institutional feasibility without hiding judgments in an unexplained weighted score.

FIN.9:4 - Solution

1. Specify the feasible alternatives and combinations, including continuation or deferral where available. Recover the capital, capacity, time, financing and authority constraints. If alternatives are still missing, develop them before claiming to rank the available set.
2. Obtain matching values from FIN.6–8 and relevant cash requirements from FIN.2. Align valuation date, currency, baseline, tax and risk treatment. Compatible treatment need not mean the same discount rate: price each component on its supported risk grounds and bring its value to the common date. Identify shared costs, mutually exclusive projects and dependencies; do not sum contributions that assume the same scarce resource twice. For a proposed combination, forecast its whole incremental cash against the feasible baseline. An interaction is the difference between those combined flows and the sum of the individual incremental flows; value it on matching grounds. This captures, for example, customer overlap or a shared resource block that the separate forecasts treated differently.
3. Compare whole feasible combinations. For a few indivisible projects, list the empty choice, single projects and possible combinations, removing those that violate a constraint and retaining the best supported whole value. For larger sets, use an appropriate constrained model. A binary variable can mean whether an indivisible project is selected; an exclusion limits two such variables to a total of one, while a dependency permits one project only if its prerequisite is selected. Resource and funding limits apply at the dates they bind, including shared requirements. Use the combination’s dated cash account: later receipts do not pay earlier obligations. Inspect the meaning and completeness of the model before relying on its optimum. Stress shared demand, input-price and funding shocks across the combination. A profitability index can help a suitable divisible-capital question but does not solve arbitrary indivisible combinations.
4. For an acquisition, identify the interest and included claims. Compare its standalone value, incremental buyer-specific benefits, integration and other incremental costs, and total consideration. Include the conditions required to obtain benefits and the effect on the buyer’s remaining business. Reconcile debt, cash and other claims through FIN.7 before comparing equity value with an equity price.
5. For a divestment, compare net disposal proceeds plus the value and obligations of the remaining business with the no-sale alternative. Include taxes, transaction costs, lost contribution, retained liabilities and changes to shared operations. Do not count both sale proceeds and continued ownership of what is sold.
6. Use FIN.10–12 for material financing conditions and FIN.21 for the retain-or-return alternative. Separate a favorable financial comparison from the availability of funds and transaction consents.
7. State the recommendation, robust alternatives, constraints and facts that can reverse it. C.11 supplies the general choice contribution over these available alternatives; this pattern supplies their financial consequences and feasible combinations.

Construct the alternatives that actually compete

Start with the corporation’s choice and the work or service it must accomplish. Include continuation without new investment, and retention or return of capital through FIN.21 where relevant. A mandatory service need can make “spend nothing” infeasible while still leaving several ways to meet it. A financially attractive project can be excluded by a real capacity or permission limit. Preserve the distinction between a required constraint and a sponsor’s preference.

Describe each available whole alternative before ranking it. Projects may be independent, mutually exclusive, complementary or prerequisites for later work. Two projects using the same site can exclude each other; a shared facility can make the combined cost lower than the sum; a first stage can create a later choice whose value FIN.8 must establish. Names such as “strategic” or “synergistic” do not specify those relations.

Recover the baseline used by each valuation. If two projects each count the full benefit of replacing the same old process, adding their NPVs double counts that improvement. If one project presumes that another has already paid for a facility, its apparent standalone value belongs to a different alternative. Rebuild the whole cash account or adjust the contributions explicitly before comparison. FIN.6 owns that cash construction; this Method owns which whole alternatives and combinations are compared.

A resource shortage can be a genuine external limit or a chosen internal budget. If the budget can be changed, compare the obtainable financing or additional resource with the gain it enables and the costs it creates. Do not silently relax a binding limit because the projects have positive NPV, and do not treat a discretionary budget as an immutable physical fact. Use FIN.10–12 to establish obtainable financing that could change the available set.

Compare value under interactions and dated constraints

Bring values to one date, currency, claimant and compatible tax and risk grounds. Different components may properly have different required returns. Value them on their supported bases before combining present values; forcing their cash differences through one convenient rate can change the economics. If selecting the combination changes financing terms or risk treatment, recalculate those affected values through FIN.5.

For a proposed combination, project whole incremental cash against the common baseline. Compare it with the sum of the individual incremental cash accounts. Their difference is the interaction to be valued: shared setup savings, lost customers, capacity congestion, duplicated costs or another actual effect. It can be positive or negative and can arise at several dates. Explain the operating cause so that it can be revised when the combination changes.

Map the resource use and money needed when each constraint binds. Include initial commitments, later investment, collateral, working capital, operating capacity and financing access. A project with a modest initial outlay can absorb the capital needed by another one next year. A positive annual ending balance can conceal an earlier shortage. FIN.2 supplies the dated cash requirement; operating practice supplies the capacity account.

For a small set, enumeration is often enough. Include the empty choice when feasible, singles and combinations; remove only those excluded on established grounds; compare the whole values of those remaining. A useful dominance conclusion requires one alternative to be no worse on every relevant consequence and constraint and better on at least one, under the stated conditions. A higher NPV alone does not dominate a lower-NPV alternative that uses less scarce capital.

A larger problem can use a constrained optimization model. Let a binary selection variable represent an indivisible project. A mutual exclusion restricts two selections to at most one; a prerequisite requires the dependent selection to imply the prerequisite. Resource constraints use the actual dates and amounts. Interaction terms or scenario-dependent choices need their own representation. Inspect what the objective and constraints mean before accepting the computed optimum; a solver cannot find an alternative omitted from the model.

For divisible independent investments with one initial capital limit, linear scalable values and no other constraints, ranking value per unit of capital can construct an allocation. State the chosen profitability-index definition; conventional PV-of-receipts divided by initial outlay and NPV divided by initial outlay differ by one for that simple flow pattern. Indivisibility, minimum scale, interactions or future funding constraints can defeat the ranking. A large ratio is not evidence that the leftover budget can be usefully deployed.

Align service lives and preserve later choices

Different asset lives do not automatically make NPVs incomparable. Ask what is being chosen. Two complete opportunities can be compared at one date even if their cash ends at different times. A choice of equipment to deliver the same continuing service is different: the shorter-lived asset may require replacement, outsourcing or a period without that service. Include the actual continuation instead of comparing only the first purchase.

Construct the service horizon, operating effects, available replacements, residual values and timing through FIN.6. Repeating the shorter investment on unchanged terms is a substantive premise about future availability and cost. If technology, prices, capacity or the service requirement changes, use the changed continuation. Do not assume perpetual identical replacement solely to make a standard calculation convenient.

An equivalent annual amount can compact a comparison under an appropriate common service and repeatability basis. It is obtained by dividing a present value by the matching annuity factor for its life; the transformation does not establish those economic conditions. An explicit common-horizon cash comparison is often clearer when future replacements or residuals differ. The worked case below demonstrates the premise without requiring annualization.

Where a later action remains optional, include the contingent rule supplied by FIN.8. Several options can compete for the same later capacity or finance. Summing their separately optimal values can presume that each may be exercised in a state where the corporation can fund only one. Value the feasible joint policy with the same information dates and shared constraints. An action chosen before a future signal cannot be optimized separately in each final state.

Dependence between outcomes also matters. A sum of compatible expected cash values does not itself require statistically independent outcomes, but common shocks can cause simultaneous funding needs, operating failures or changes in financing cost. Stress the shared drivers across the combination, not a different favorable environment for each component. Return how the recommended combination behaves under those conditions and which feasible response remains.

Build the buyer’s acquisition comparison

Identify what the buyer obtains and pays for: assets, shares or another specified interest. Recover the included debt, cash, ownership rights and remaining obligations through FIN.7 and FDM where needed. A quoted enterprise price, an equity price and the cash required at closing are different amounts. Reconcile them before evaluating the premium.

Start from adequate standalone values of the affected businesses under their attainable no-deal continuations. Then construct what the combination changes. A cost synergy needs the actual reduction in resource commitments and the expenditure or delay needed to achieve it. Additional sales need their contribution after operating cost, investment, working capital and tax. A financing or tax benefit needs the actual available terms and usable deductions. FIN.4 supplies the accounts, FIN.6 the incremental cash and FIN.5 the corresponding financing valuation.

Use a combined with/without forecast when the effects are too interdependent to allocate reliably between businesses. Compare combined value with the sum of the standalone values on matching grounds. That difference can include both gains and losses. Integration disruption, customer departure, lost supplier terms and capacity constraints belong in the same account as hoped-for savings. Do not treat each claimed synergy as certain while assigning all execution uncertainty to a separate generic discount.

Distinguish improved standalone management from benefits requiring the specific combination. If the target could make a supported improvement without this buyer, the change may already belong to its no-deal value or to the price demanded. If only the combined resources make an improvement attainable, explain that dependence. A percentage “control premium” and a percentage “synergy premium” can charge for the same underlying change twice.

For a cash equity purchase on the simple common basis, buyer incremental value is the target interest’s standalone value plus attainable incremental buyer benefits, less integration and other incremental costs, less the equity price. Equivalently, the maximum price at zero buyer gain is standalone interest value plus net buyer benefits. That threshold is conditional on the assumptions; it is not an instruction to offer the seller all of it. Compare the surplus with other available capital uses.

Where consideration includes shares, earn-outs or contingent payments, value the actual claim transferred and its consequences for the buyer’s existing owners. Issuing shares is not costless merely because no cash leaves at closing: the recipients share in the combined business. An earn-out can shift outcome risk while creating a later payment and incentives that alter behavior. Use the relevant claim and option valuation, actual ownership terms and financing account rather than forcing every structure into a fixed cash-price subtraction.

Reconcile funding separately at each date. The target’s included cash may be accessible only after closing or remain restricted; debt may stay in place, require repayment or need refinancing. Acquisition fees, collateral and integration expenditure can precede any synergy. A source of financing with a fee or changed risk must enter the valuation once on matching grounds. A positive buyer value does not establish access to the funds or the ability and authority to realize the operational changes.

Build the seller’s divestment comparison

Compare the whole no-sale continuation with the sale proceeds and the remaining business under the proposed separation. Start with the actual net proceeds: consideration, transaction costs, tax, settlement timing, retained interests, escrows and contingent amounts as applicable. A headline price payable over time is not the same as cash available now.

Rebuild the remaining operation. Which shared services, customers, purchasing terms, intellectual property or capacity remain, change or disappear? Which costs are actually avoided, and which become stranded? Removing an allocated headquarters expense from the sold unit’s account does not eliminate the corporation’s remaining payment. Conversely, a separation plan can make a real resource reduction possible, but it must include the transition cost and timing.

Retain obligations left with the seller, including supported guarantees, tax, closure or service commitments. A transition-services agreement can create temporary revenue and cost as well as continued dependencies. Avoid counting the sold business’s future cash as still owned after also including its sale proceeds. FIN.7 supplies any retained-interest value; FIN.6 supplies separation cash and FIN.22 supplies a wider recovery-route comparison when distress governs the choice.

Ask what happens to the proceeds. Repaying debt, retaining funds for investment and distributing them have different financing and claimant consequences. Include those effects only in the alternatives that actually take the corresponding action. FIN.21 supplies the retain-or-return comparison. The sale itself does not create the investment gains of an unspecified future project.

A divestment can raise cash while reducing total value, or reduce reported profit while improving value through an attainable better use. Explain the receiving criterion through FIN.1. If liquidity is a binding condition, compare the feasible alternatives and their value sacrificed or preserved; do not present gross cash proceeds as evidence that the seller became richer.

Return the allocation with its grounds and reconsideration conditions

Explain why the selected whole alternative is preferable under the stated basis, which constraints bind, and what a plausible change would do. A close result can depend on a price, capacity block, replacement assumption, shared customer effect or funding date. Use the relevant sensitivity or coherent scenario to identify that dependence; an unexplained composite score cannot repair incompatible financial meanings.

Retain a robust alternative or a conditional recommendation where the evidence warrants it. If the gain turns on an attainable missing fact, use C.11.DUA to compare obtaining it with acting, deferring or choosing a smaller commitment. If the uncertainty cannot be resolved in time, make the available choice and its consequences explicit rather than assume the most favorable branch.

The financial recommendation is an input to the corporation’s decision. Existing authority may already cover routine action; other transactions need their actual consents and execution arrangements. FIN.16 combines the warranted financial answer with those conditions, and FIN.17 refreshes the affected value or constraint when the relied-on facts change. A changed constraint reopens the feasible set, while a changed operating assumption reopens the values it affects.

FIN.9:5 - Archetypal Grounding

With a capital limit of 100, indivisible projects A, B and C cost 100, 60 and 40 and have NPVs 25, 18 and 12 on compatible grounds. Assuming no interaction, B+C costs 100 and yields 30, exceeding A’s 25. Ranking standalone NPV would select A and miss five of value. Suppose instead that doing B and C together loses 8.8 of incremental after-tax cash at the end of year 1 because they compete for the same customers. At a matching 10% return for that lost cash, the interaction is −8 today. Combined NPV becomes 18 + 12 − 8 = 22, so A at 25 is preferable. If B and C require the same unavailable capacity, remove their combination as infeasible rather than merely assigning it a lower value.

A separate replacement choice must provide the same service for four years. Assume equal operating effects, a qualified 10% return, no resale proceeds and feasible funding. A short-lived asset costs 70 now and lasts two years; another costs 110 now and lasts four. If the short-lived asset can actually be replaced at year 2 on the same terms, its complete present cost is 70 + 70/1.1² = 127.85. The four-year asset at 110 is preferable despite its larger initial payment. If service is needed for only two years, retaining the no-resale premise makes the 70 asset preferable. If replacement is unavailable or its future terms differ, rebuild that continuation instead of repeating 70 automatically. FIN.6 constructs the dated alternatives; this comparison chooses between them.

In a constructed acquisition at one valuation date and currency, standalone operating enterprise value is 100. Debt with a market value of 30 remains outstanding in the acquired company, and included excess cash of 10 is freely transferable after closing. With no other claim adjustment, standalone equity value is 80. Buyer-specific incremental benefits have present value 30; integration and other incremental costs have present value 15, on compatible after-tax grounds.

Positive combination benefits therefore do not justify the price of 100. A price of 90 changes the financial answer on unchanged grounds. A new financing effect must enter the appropriate valuation once; it cannot be both capitalized in the rate and subtracted again as the same cost. The included 10 is not available to pay the seller before closing. Actual funding, consent and the ability to realize benefits can still block the transaction.

A separate acquisition pays for the target entirely with newly issued shares. Suppose the buyer’s standalone equity value is 200, represented by 100 identical shares, and the target’s equity value is 80. On matching date, claim and tax grounds, the combination adds 20 after all incremental costs. The buyer issues 50 shares with identical rights to the seller in exchange for all the target equity. There are then 150 shares: the seller owns one third and the buyer’s existing owners retain two thirds. Combined equity is 200 + 80 + 20 = 300; the transferred interest is worth 100 and the retained interest 200. The old owners gain zero over their no-deal value, even though the combination creates 20.

If supported net combination gain instead rises to 50 with every other term unchanged, combined equity becomes 330. The seller’s third is now worth 110 and the old owners’ two thirds 220, giving them a gain of 20. Pricing the 50 new shares at the old share value of 200/100 = 2 would charge only 100 and incorrectly report buyer gain 80 + 50 − 100 = 30. The consideration shares participate in the same combined value being assessed. Their issue transfers an ownership claim; cash fees, integration payments and any debt settlement still enter the separate dated funding account.

For a divestment, suppose the whole business is worth 150 before sale. Net sale proceeds are 45 and the remaining business, after all lost synergies and retained obligations, is worth 100. The comparable total is 145, five below retaining the business. A headline offer of 50 would not establish a gain without the net-proceeds and residual-business calculation.

A project, an acquisition and an expansion choice

A corporation has 110 of usable capital today and must choose among a project P, acquisition A and an expansion that can be reserved as right O or committed to now as K. O and K are alternative strategies for the same expansion. The question is incremental value to this buyer, in one currency at date 0, against continuing the existing activities without these additions. All amounts below use consistent after-tax claims and include their relevant costs. The project, acquired business and expansion use different operating resources; absent a stated constraint their cash effects are additive. This is FIN.1’s financial frame.

For P, use one tenth of FIN.6’s constructed project. Equipment 90 and working capital 10 require 100 now. An operating projection prepared through FIN.4 supplies annual sales 110 and cash operating costs 40; FIN.6 then subtracts displaced contribution 6 and feasible rent forgone 4, giving margin 60. With depreciation 45 and same-year usable tax at 25%, operating cash is (60−45)×0.75 + 45 = 56.25. Year 2 adds working-capital recovery 10, asset sale after tax 7.5 and closure after tax −1.5, giving 72.25. A qualified supplied return of 10% fits these operating flows; use FIN.5’s construction if that basis must be obtained. NPV is −100 + 56.25/1.1 + 72.25/1.1² = 10.85.

For A, use FIN.7’s zero-growth operating value 100: 10/1.1 + (10+100)/1.1². Subtract the debt of 30 remaining in the acquired company and add included excess cash 10 to obtain equity value 80. Buyer benefits produce incremental after-tax cash 16.5 and 18.15 in years 1 and 2, with supported return 10%; their present value is 30. Integration costs 15 are paid today. At equity price 90, buyer NPV is 80 + 30 − 15 − 90 = 5. Both price and integration payment fall due before closing; the acquired 10 becomes usable only afterward.

For O, use FIN.8’s fee-8 strategy: pay 8 today, then pay 60 in one year only if the revealed expansion value is 90 rather than 40. Its probability 0.5 and stipulated absence of priced risk before exercise support discounting the 30-or-zero payoff at 5%, giving NPV 6.29. This rate differs from P’s because the risk grounds differ. A pre-existing deposit, unavailable today, releases 60 just before that exercise date; its receipt is in the baseline cash plan for every alternative. Exercising consumes that money, already included as the 60 exercise cost, so the deposit is not added again to O’s value. The available fixed strategy K also pays 60 at that date but must do so in both states. Its NPV is (0.5×30 + 0.5×(−20))/1.05 = 4.76 and it requires no payment today.

Every combination containing both P and A exceeds 110; O and K cannot be selected together. The reservation fee is due before the acquired cash is released, so that cash cannot rescue A+O at the required time. With the stated independent effects and later exercise funding, P+O leads. The full cash plan must also support P’s intervening payments; that feasibility is a supplied condition of this case, not inferred from expected NPV.

Now suppose obtainable rent for P’s resource rises from 4 to 15 per year, leaving the acquisition and both expansion strategies unchanged. P’s flows become −100,+48,+64 and NPV −3.47. P+O remains affordable but falls to 2.81; P+K falls to 1.29. A+K at 9.76 now leads, exceeding O alone at 6.29. The changed recommendation follows the baseline through the cash construction into the whole comparison. If the deposit’s release is delayed, funding for O or the binding K payment must be recovered through FIN.2 and any changed financing effect valued before relying on either recommendation.

FIN.9:6 - Bias-Annotation

Synergies and strategic benefits often receive the sponsor’s most optimistic assumptions. A corporation-level total can hide the burden on particular operations or claimants. Preserve those constraints and the uncertainty that matters to the recommendation.

FIN.9:7 - Conformance Checklist

Are all combinations feasible, and do their values share a comparison basis? Are shared resources and effects counted once? For a transaction, can the reader recover the interest, claim bridge, price, incremental effects and residual business? Are financial preference and closing conditions distinct?

FIN.9:8 - Common Anti-Patterns and How to Avoid Them

Ranking by standalone return can miss dependencies; compare combinations. Treating synergy as permission to pay any premium omits price; calculate buyer value after consideration. Calling disposal proceeds profit can ignore the asset and continuing obligations surrendered; compare the complete alternatives.

FIN.9:9 - Consequences

The corporation obtains a conditional allocation or transaction recommendation that explains why a combination or price changes the result. A useful financial answer may still require operating, financing or authority action before implementation.

FIN.9:10 - Architectural Rationale

Individual values become an allocation answer only after the alternatives can be selected together on their stated grounds. Shared resources, common baselines and future choices can make a sum of correct standalone figures describe no feasible action. Constructing the whole alternative reveals the interaction and locates the binding constraint, while retaining the constituent Methods for the calculations they actually supply.

The horizon follows the required consequence. A four-year service choice can need a replacement after two years; an independently complete two-year opportunity need not be repeated just to match another investment’s life. Likewise, preserving two valuable options does not supply the capacity to exercise both. These differences are reasons to construct the actual continuation, not to reject NPV or choose a universal annualization rule.

A transaction changes more than the cash paid or received. Buying changes claims and operations, and the price determines how much of the combined gain remains with the buyer. Selling can leave costs and obligations with the remaining business. Comparing those whole alternatives prevents standalone target value or headline proceeds from being mistaken for an incremental gain to the corporation. Legal closing and operational delivery remain the actual practices that make the selected financial premises attainable.

FIN.9:11 - SoTA-Echoing

The public CFA capital-allocation and corporate-restructuring readings frame the investment and transaction questions. Damodaran’s historical capital-rationing and unequal-life discussion develops the effects of limited capital and attainable continuations. His acquisition-motive analysis distinguishes mispricing, operating changes and combination gains. FIN.9 uses these financial distinctions with actual incremental cash, consideration and dated constraints, including the buyer’s or seller’s remaining operation. Historical deal outcomes supply no evidence that a particular proposed synergy will occur. Changed scope, shared operating effects or available funding reopens the comparison.

FIN.9:12 - Relations

FIN.6–8 supply values; FIN.2 supplies timed funding needs; FIN.10–12 supply financing conditions; FIN.21 supplies retention or payout alternatives. FIN.16 prepares the receiving advice. C.11 supports the local choice once these financial alternatives exist.

FIN.9:End