Consider the following projects: A capital constraint of £32m has been imposed on the total initial investment. The projects are divisible and each may be undertaken only once. What is the maximum NPV available from the projects?

Question

Consider the following projects:  A capital constraint of £32m has been imposed on the total initial investment. The projects are divisible and each may be undertaken only once. What is the maximum NPV available from the projects?

Quizplus · Accepted Answer

First, calculate the NPV of each project:
Project A: NPV = £10m + (£4m/1.12) + (£5m/1.12^2) + (£6m/1.12^3) - £15m = £1.113m
Project B: NPV = £8m + (£7m/1.12) + (£6m/1.12^2) - £12m = £7.529m
Project C: NPV = £12m + (£9m/1.12) - £14m = £6.723m
Project D: NPV = £7m + (£11m/1.12) + (£9m/1.12^2) + (£5m/1.12^3) - £13m = £14.161m
Project E: NPV = £6m + (£8m/1.12) + (£7m/1.12^2) + (£6m/1.12^3) - £10m = £7.617m

Then prioritize the projects based on their NPV until the capital constraint is reached. Starting with the highest NPV project, add projects and their NPVs until the total investment reaches £32m. In this case, the best selection would be Project D and Project A, for a total NPV of £15.274m, as this combination has the highest NPV within the capital constraint.

Consider the Following Projects: a Capital Constraint of £32m