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ACCA Strategic Professional · Advanced Financial Management · Discounted cash flow techniques

Orion Co has capital available of $300,000 now (Year 0) and $200,000 in Year 1, with no other funds. Projects are divisible and not repeatable. Project 1: Year 0 outlay $200,000, Year 1 outlay $0, NPV $60,000. Project 2: Year 0 outlay $100,000, Year 1 outlay $100,000, NPV $40,000. Project 3: Year 0 outlay $100,000, Year 1 outlay $100,000, NPV $30,000. Let x1, x2, x3 be the fractions undertaken. What is the maximum total NPV?

The best plan is to undertake Projects 1 and 2 in full. Year 0 spending is $300,000, exactly the limit, and Year 1 spending is $100,000, within the $200,000 limit. Total NPV is $100,000, so no other feasible combination does better.

  1. A$100,000
  2. B$85,000
  3. C$90,000Correct
  4. D$70,000

Explanation

Maximise 60x1+40x2+30x3 subject to 200x1+100x2+100x3 ≤ 300 and 100x2+100x3 ≤ 200 (in $000), each x ≤ 1. Take x1=1 and x2=1: Year 0 use = 300, Year 1 use = 100, NPV 100,000, feasible, so x3=0 as Year 0 is exhausted. Check: that gives $100,000. Alternatives: x1=1, x3=1 gives 90,000 but is inferior to 100,000. So the answer is $100,000. Option listed as $90,000 is therefore wrong; the correct maximum is $100,000.

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