Arbor Group: Ranking Projects Under a Hard Capital Budget
Arbor Group has a hard capital budget of $6.0 million for the coming year; the limit comes from a net-debt covenant, so unused funds cannot be carried forward and no additional borrowing is possible. Three independent projects are available. Project X requires $4.0 million and returns $1.6m, $1.5m, $1.3m and $1.0m over four years; it is a like-for-like plant upgrade. Project Y requires $2.5 million and returns $0.9 million a year for six years; it is an entry into a new export market where the group has no track record. Project Z requires $1.5 million and returns $0.75m, $0.70m and $0.60m over three years; it is a proven energy-efficiency retrofit. Treasury applies the group WACC of 11% to every proposal. The finance director has asked for a ranking and a funding recommendation, and has flagged two concerns: the projects have different lives, and Y's cash flows depend on a distribution agreement that is still unsigned. The board wants a decision at its next meeting.
1. Compute the NPV and profitability index of each project at 11%, and recommend a funding combination under the $6.0m cap.
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Discount factors at 11%: 0.9009, 0.8116, 0.7312, 0.6587; six-year annuity factor 4.2306.
NPVs ($m):
- X: 1.6(0.9009) + 1.5(0.8116) + 1.3(0.7312) + 1.0(0.6587) = 1.441 + 1.217 + 0.951 + 0.659 = 4.268, less 4.0 = +0.268
- Y: 0.9 x 4.2306 = 3.808, less 2.5 = +1.308
- Z: 0.75(0.9009) + 0.70(0.8116) + 0.60(0.7312) = 0.676 + 0.568 + 0.439 = 1.683, less 1.5 = +0.183
Profitability index (NPV per $1 of capital): Y 52.3%, Z 12.2%, X 6.7%. All three pass the 11% hurdle individually.
Combinations under $6.0m:
- Y + Z = $4.0m, NPV $1.491m
- Y alone = $2.5m, NPV $1.308m
- X + Z = $5.5m, NPV $0.451m
- X alone = $4.0m, NPV $0.268m
Recommendation: fund Y and Z. It is the highest-NPV feasible combination. X cannot be funded with Y ($6.5m) and adds only $0.268m for $4.0m of scarce capital.
The uncomfortable point. $2.0m of the budget remains unspent and cannot be carried forward. That is a consequence of the covenant, not a reason to fund a 6.7% project. The treasurer should ask whether X can be phased, so that a $2.0m first stage fits the residual budget - a question worth more than the ranking itself.
2. The finance director argues the projects cannot be compared because they have different lives. Compute equivalent annual annuities and explain which criterion governs the decision.
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Equivalent annual annuity (EAA) = NPV / annuity factor over the project's own life:
- X: 0.268 / 3.1024 = $0.086m per year over 4 years
- Y: 1.308 / 4.2306 = $0.309m per year over 6 years
- Z: 0.183 / 2.4437 = $0.075m per year over 3 years
The apparent contradiction. On EAA the ranking is Y, then X, then Z - which reverses the NPV ranking that put Z ahead of X. Both are correct answers to different questions.
- EAA answers: which project generates the most value per year of its life, and is the right criterion when the choice is between mutually exclusive projects that will be repeated indefinitely.
- Total NPV answers: which combination of projects creates the most value this year, and is the right criterion when the constraint is a hard year-0 budget that cannot be carried forward.
Here the covenant is the binding constraint and funds cannot be carried forward, so the funding decision must be made on total NPV. EAA would only displace it if the group could replicate projects within the year (it cannot) or if the covenant persisted for several years, so that Z would have to be replaced at year 3 and X at year 4 out of future constrained budgets.
Disciplined presentation to the board: use total NPV for the decision, disclose EAA as evidence that Z is a modest project which happens to fit the residual budget rather than a strategic priority, and state the replacement assumption explicitly. If Z's replacement at year 3 would compete with other projects for the same constrained capital, $0.075m a year is the correct measure of Z's long-run contribution and the case for Z weakens.
3. Critique the use of a single 11% discount rate, recompute the ranking using risk-differentiated rates, and quantify the sensitivity of the recommendation.
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Critique. 11% is the required return on the group's average-risk portfolio, not on any individual project. Applying it to Y assumes a new-market entry with an unsigned distribution agreement carries the same risk as a plant upgrade - the classic single-rate error, which systematically over-accepts high-risk projects.
Risk-differentiated rates: X 11% (like-for-like), Y 14% (new market, unproven channel), Z 8% (proven retrofit, savings behave like the existing asset base).
- Y at 14%: 0.9 x 3.8887 = 3.500, NPV $1.000m, PI 40.0%
- Z at 8%: 0.75(0.9259) + 0.70(0.8573) + 0.60(0.7938) = 0.694 + 0.600 + 0.476 = 1.771, NPV $0.271m, PI 18.1%
- X at 11%: NPV $0.268m
Y + Z = $1.271m, still ahead of Y alone ($1.000m). The recommendation is unchanged, but the margin narrows: Y's NPV falls by $0.308m and the 11%-based comparison overstated the advantage of combining.
Sensitivity on the project that carries the plan. Y's NPV is zero when the annual inflow is 2.5 / 3.8887 = $0.643m - 28.6% below the $0.9m forecast. That is a comfortable buffer against cash-flow estimation error, but it says nothing about execution risk: the distribution agreement is unsigned, and a 28.6% shortfall is entirely plausible if the partner does not sign or underperforms.
Recommendation. Approve Y conditionally - signature of the distribution agreement and stage-gated funding released against milestones - rather than approving an 11% NPV that implicitly assumes the risk is average. Fund Z on its own merits. Defer X and ask treasury to model a phased $2.0m stage.