AFMP4
Syllabus B. Advanced Investment Appraisal B1. Discounted cash flow techniques

# B1aiii. Capital rationing - Multi-period 5 / 14

### Syllabus B1aiii)

Evaluate the potential value added to an organisation arising from a specified capital investment project or portfolio using the net present value (NPV) model.

Project modelling should include explicit treatment and discussion of:

iii) Single period and multi-period capital rationing. Multi-period capital rationing to include the formulation of programming methods and the interpretation of their output

### You have limited cash in Year 0 AND other years..

#### Projects may be:

1. Divisible

So here, there's a little scary cheeky monkey to deal with, called linear programming!

But relax - it's easy :)

Basically the idea is we program a computer to tell us which different projects we should take on - when we don't have enough cash to do them all (capital rationing)

The problem is we don't have enough cash in year 0 or in another year (often year 1)

2. Indivisible

Here, integer programming would be required to determine the optimal combination of investments.

Good news!

In the exam you will not be expected to produce the solution to the linear programming problem. Yay!

You will have to formulate a linear programming model and understand its outputs. Booo!

So, to recap..

When capital is rationed for MORE than a single period - profitability index won't help.. we have to use linear programming

Check these projects - all look good but you only have \$150 to spend in Year 0 and \$10 to spend in Year 1 :(
Project Yr 0 Yr 1 Yr 2 Yr 3 NPV
A (100) (30) 90 60 20
B (90) (10) 50 60 10
C (80) 20 80 10 30

#### The steps to answer these questions are:

1. Do the Objective Function

(Posh way of saying write down all the projects NPVs and their names next to them)

2. Do the Constraints Function

(Posh way of saying write down all the costs of each project and say they should be less than the cash available)

3. Do the non-negativitity Function

(Posh way of saying you can only do a project up to once and never less than none (the computer's a bit silly that way))

So here goes with the objective function

NPV maximised = 20a + 10b + 30c

Next the Constraints Functions

Year 0 100a + 90b + 80c < 150
Year 1 30a + 10b - 20c < 10

Finally the silly non-negative function

1 > a,b,c > 0