Question 7 of 7: Explaining a Large NPV Discrepancy Between Two Bidders

Question 7: Explaining a Large NPV Discrepancy Between Two Bidders (16 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Two error-free analyses that share every listed input can still legitimately diverge by a large margin in maximized NPV, because “same inputs, same constraints, same objective” leaves several modelling choices completely unconstrained. Forestry NPV problems are long-horizon, spatially explicit optimizations with a very large feasible-solution space; the two constraints stated (15% old growth, 1,000 ha early-successional) bound that space but do not uniquely determine a single best schedule, and several other assumptions that are never listed as “inputs” per se can each move the discounted result by a double-digit percentage on their own.

1. Discount rate. Even though “wood prices and costs” matched, the discount rate applied to convert future cash flows to present value is a separate analytical choice, not raw input data — and because forestry cash flows are spread over many decades, even a 0.5–1 percentage-point difference in assumed discount rate compounds into a very large NPV difference. This is very often the single largest source of legitimate NPV divergence between otherwise-identical forestry analyses.
2. Harvest scheduling / spatial sequencing algorithm. “Same treatments, yields and costs” does not mean the same harvest SCHEDULE — which stands are cut in which year, and in what spatial sequence — was chosen. Meeting the same two aggregate constraints (15% old growth, 1,000 ha early-successional) is satisfied by many different sets of specific stands and years; a heuristic solver versus a closer-to-optimal exact solver (or simply a different starting solution) can land on materially different, both-feasible schedules whose cash-flow TIMING differs enough, once discounted, to produce an 18% NPV gap.
3. Planning horizon length and terminal (ending) value treatment. A long-lived forest asset's value is sensitive to how far into the future the analysis is carried and what value (if any) is assigned to the standing forest at the end of that horizon. One bidder using a longer horizon, or a different ending-inventory/bare-land valuation, captures value the other bidder's shorter or zero-terminal-value analysis simply excludes.
4. Real versus nominal price/cost escalation assumptions. “Same wood prices and costs” most naturally describes today's prices; whether each bidder then assumed those prices stay flat in real terms, escalate with inflation, or follow some real growth/decline trend over the multi-decade horizon is a separate assumption that materially changes discounted revenue without technically using a “different” price.
5. Which specific stands satisfy each constraint. The two constraints specify AMOUNTS (at least 15% old growth, at least 1,000 ha early-successional) but not WHICH stands supply them. Designating a high-value, easily-accessible stand as the required old-growth reserve forgoes far more NPV than designating a low-value, hard-to-access stand for the same constraint-satisfying area — so two analyses satisfying the identical constraint LEVEL can have very different opportunity costs depending on which specific hectares were chosen to meet it.

A forensic reviewer would trace the 18% gap by reproducing each bidder's schedule with a common discount rate and terminal-value convention first (the single highest-leverage check), then compare the specific stands assigned to satisfy each constraint and the assumed price/cost escalation path — because none of these choices constitutes an “error” on either bidder's part, the discrepancy can be entirely explained by legitimate, defensible differences in analytical assumptions rather than by any mistake in the underlying calculations.