Page 48 - AFM Integrated Workbook STUDENT S18-J19

Chapter 2

Illustration 3

Kane Co is considering expenditure on three projects over the next two years,
with investment expenditure spread over this period, followed by several years
of positive cash inflows.

Investment needed ($000) T 0 T 1 T 2 Project NPV

P1 6,000 6,000 3,500 4,555

P2 3,700 4,500 2,500 3,214

P3 3,200 3,500 2,200 2,698

Expenditure limits are $12 million for T 0, $10 million for T 1, and $9 million for
T 2. None of the projects can be deferred and all of the projects can be scaled
down but not scaled up.

Required:

Formulate an appropriate capital rationing model, based on the above
investment limits and including the constraints for each year, which
maximises the net present value for Kane Co. Finding a solution for the
model is not required.

Solution

1 Define unknowns.

Let P1 = proportion of Project P1 undertaken, P2 = proportion of Project
P2 undertaken, P3 = proportion of Project P3 undertaken

(Where 1 ≥ P1, P2, P3 ≥ 0)

2 Formulate the objective function (i.e. maximise NPV):

Maximise 4,555 P1 + 3,214 P2 + 2,698 P3

3 Express the given constraints as inequalities

T 0: 6,000 P1 + 3,700 P2 + 3,200 P3 ≤ 12,000
T 1: 6,000 P1 + 4,500 P2 + 3,500 P3 ≤ 10,000
T 2: No constraint, as the maximum funds required are less than the limit

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