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.

FIN.9:5.1 - 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.