Mineral Economics, Mine Planning, Systems Engineering · Mineral Economics · 2 marks · Numerical answer
Two project NPVs are $NPV_A=-0.01i^2-0.02i+4.44$ and $NPV_B=-0.03i^2-0.01i+6.55$. Find the positive crossover discount rate i at which both proposals are equally preferred, to two decimals.
Equating the two NPVs and collecting terms gives 0.02i²−0.01i−2.11=0. By the quadratic formula the positive root is [0.01+√(0.0001+4×0.02×2.11)]/0.04=10.52436. Thus the positive crossover rate is 10.52 in the rate units used by the equations. It makes the proposals equally preferred; it is not the internal return of either proposal individually.
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