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ACCA Applied Skills · Financial Management · Specific investment decisions (lease or buy, asset replacement, capital rationing)

Zeta Co has two divisible projects, A and B, and has a capital limit of $100,000 in each of Year 0 and Year 1. Project A needs $40,000 in Year 0 and $20,000 in Year 1 and has an NPV of $12,000. Project B needs $30,000 in Year 0 and $50,000 in Year 1 and has an NPV of $15,000. Let a and b be the proportions of A and B undertaken (each between 0 and 1). Which set of constraints and objective correctly formulates the problem?

Maximise total NPV, 12,000a + 15,000b, with a separate constraint for each period's capital limit: 40,000a + 30,000b ≤ 100,000 for Year 0 and 20,000a + 50,000b ≤ 100,000 for Year 1, with a and b each no more than 1.

  1. AMaximise 12,000a + 15,000b subject to 40,000a + 30,000b ≤ 100,000; 20,000a + 50,000b ≤ 100,000; a ≤ 1; b ≤ 1Correct
  2. BMaximise 12,000a + 15,000b subject to 40,000a + 20,000b ≤ 100,000; 30,000a + 50,000b ≤ 100,000; a ≤ 1; b ≤ 1
  3. CMaximise 40,000a + 30,000b subject to 12,000a + 15,000b ≤ 200,000; a ≤ 1; b ≤ 1
  4. DMaximise 12,000a + 15,000b subject to 60,000a + 80,000b ≤ 100,000; a ≤ 1; b ≤ 1

Explanation

The objective is to maximise total NPV, 12,000a + 15,000b. There is one constraint per period: Year 0 outlays 40,000a + 30,000b ≤ 100,000 and Year 1 outlays 20,000a + 50,000b ≤ 100,000, plus upper limits of 1 for divisible projects. Option B mixes up the coefficients by project and year. Option D wrongly combines both years into one constraint against a single limit.

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