Capital rationing across investments

With theoretically unlimited capital, an independent project with positive net present value can be accepted after considering risk. Finance leaders usually face a cash ceiling, execution capacity or a financing covenant. Ranking individual projects and taking the first items on the list can then fail. One project may depend on another, two may compete for the same people, and a small project may occupy a team needed for a larger one. Net present value, NPV, is future incremental cash flows discounted for their timing and risk, less the initial investment. In this lesson the NPVs have already been estimated on a consistent basis. We focus on selecting a feasible portfolio, not deriving the discount rate.

Constraints have different meanings. A tradable scarcity, such as a 60 cash spending cap, defines which combinations fit. A nonnegotiable restriction, such as lacking rights to an asset or breaching a binding covenant, cannot be offset by a high benefit score. Exclude or repair the restricted project before ranking eligible choices. Then list each project's cost, value, dependencies and cash dates, with the source and uncertainty of each estimate. Precise arithmetic to two decimal places does not make uncertain forecasts certain. Read the answer beside scenarios and the change in an assumption that would reverse the choice.

A fictional business has 60 million available for investment now. Project A expands an established line, costs 35 and has NPV 14. Project B improves an ordering platform, costs 25 and has NPV 11. Project C launches a new service, costs 30 and has NPV 13, but cannot operate without platform B. Do not spend 30 on C by itself. Assume the values include each project's cash flows when undertaken and that C's 13 is incremental to B without duplicated benefits. Also assume the people can deliver concurrent projects and spending dates fit the 60 ceiling. A real committee must test those assumptions.

Feasible choices are: invest nothing, value zero; A alone, cost 35 and value 14; B alone, cost 25 and value 11; A+B, cost 60 and value 25; or B+C, cost 55 and value 24. C alone fails its dependency. A+C fails that dependency and also costs 65; all three cost 90. A+B has the highest displayed NPV, only 1 above B+C. Ranking projects by stand-alone NPV would put A, then C, then B, inviting the infeasible A+C. NPV per currency unit of cost gives B 11÷25=0.44, C 13÷30≈0.433 and A 14÷35=0.4. That ratio is a useful diagnostic, but it does not solve dependencies or indivisible project choices.

The value margin of 1 is small relative to forecasting uncertainty. Test a decisive input rather than masking the judgment with false precision. If C's NPV is 10 under weaker demand, B+C yields 21 and A+B leads by 4. If C's NPV is 15, B+C yields 26 and leads by 1. The switching point is C NPV 14: B+C and A+B each yield 25, all else equal. That threshold should be connected to evidence about new-service uptake and customer retention, not a generic “risk score.” Ask the market team for evidence that discriminates around the threshold rather than an untestable assurance that the service looks promising.

Holding cash is also an option. A+B consumes the full spending cap; B+C leaves 5. Do not add that 5 to B+C's NPV: NPV already compares incremental cash flows with the relevant spending, while the unused 5 remains available. A reserve can still be a binding liquidity requirement if the business faces a possible operating shock. If the minimum post-investment liquidity is 8 and no other funding exists, A+B may be infeasible and B+C may also fail depending on opening cash and near-term obligations. Do not insert an arbitrary NPV penalty to produce the preferred answer. Build a dated cash schedule and redefine the feasible set.

Dependencies, overlap and delivery

Two projects may claim the same benefit. If part of B's 11 is increased new-service orders already included in C's 13, adding 11 and 13 overstates value. Estimate C's incremental flows conditional on B, not as an independent project and then add them. The reverse can occur when platform savings exist only after launching the service. Use a “with versus without” schedule for each portfolio. If A changes prices or factory capacity, recalculate B and C within the combined case. The numerical answer above holds only under the stated independence of benefits apart from the operational dependency.

Someone may suggest splitting A into a 20 first stage and a 15 second stage. If the first stage has its own output, it is a fourth option with new cash-flow data, not automatically a proportionate slice of the 14 NPV. The first stage might generate demand information and a right to stop, while a delayed purchase might lose an equipment discount. We value timing flexibility in the next lesson. A committee memo should identify the chosen portfolio, runner-up, dependencies, remaining cash and evidence that would change the recommendation. Assigning a time to revisit uncertain assumptions matters: without one, screening numbers quietly turn into a permanent commitment after new information arrives.

Solution: at a cap of 70, X is feasible at value 18 and cost 40; Y at 12 and 30; X+Y at 30 and 70; and Y+Z at 29 and 65, as well as no investment. X+Y wins by 1 over Y+Z. At a cap of 65, X+Y drops out and Y+Z becomes the highest-value feasible combination, unless a newly discovered liquidity or delivery constraint applies. For Y+Z to beat 30, Z must have NPV greater than 18, because Y contributes 12 to both combinations; 18 creates a tie. This shows that ranking is not a permanent property of a stand-alone project. The cash ceiling, dependencies and estimation thresholds change the choice. A strong answer rejects X+Z and Z alone and observes that NPV alone does not show cash obligations due within the year.