Capital Rationing

Illustrative question

Funds are limited to $200 million. Fractions in the project are listed below:

Required:

Determine the optimum mix of fractions in this project to maximise NPV.

Comment:

PI & ranking:

Production schedule:

Illustrative question

Funds are limited to $200. The project includes the following fractions.

Fraction A and C are mutually exclusive.

Required:

Determine the optimum mix of fractions in this project to maximise NPV if the project is indivisible.

Comment:

Option one:

Option two:

Illustrative question

Funds available:

• Year 0: 65
• Year 1: 60
• Year 2: 100

Required:

Layout steps involved in determining the optimal mix of projects in order to maximise NPV of the business.

1. If projects are indivisible
2. If projects are divisible.

Comment:

Step1: Define objective: Z=50A+70B+80C

Step2: Define constraints:

If projects are indivisible: if projects are divisible:

A, B and C would be 0 or 1. 0<A, B, C<1

30A+40C <=65

20B+50C<=60

40A+50B+60C<=100

Step3: Slot into computer and let it do this.

Exam standard question - Arbore Co (Multi Period Capital Rationing)

Arbore Co is a large listed company with many autonomous departments operating as investment centres. It sets investment limits for each department based on a three-year cycle. Projects selected by departments would have to fall within the investment limits set for each of the three years. All departments would be required to maintain a capital investment monitoring system, and report on their findings annually to Arbore Co’s board of directors.

The Durvo department is considering the following five investment projects with three years of initial investment expenditure, followed by several years of positive cash inflows. The department’s initial investment expenditure limits are $9,000,000, $6,000,000 and $5,000,000 for years one, two and three respectively. None of the projects can be deferred and all projects can be scaled down but not scaled up.

PDur05 project’s annual operating cash flows commence at the end of year four and last for a period of 15 years. The project generates annual sales of 300,000 units at a selling price of $14 per unit and incurs total annual relevant costs of $3,230,000. Although the costs and units sold of the project can be predicted with a fair degree of certainty, there is considerable uncertainty about the unit selling price. The department uses a required rate of return of 11% for its projects, and inflation can be ignored.

The Durvo department’s managing director is of the opinion that all projects which return a positive net present value should be accepted and does not understand the reason(s) why Arbore Co imposes capital rationing on its departments. Furthermore, she is not sure why maintaining a capital investment monitoring system would be beneficial to the company.

Required:
(a) Formulate an appropriate capital rationing model, based on the above investment limits, that maximises the net present value for department Durvo. Finding a solution for the model is not required. (3 marks)

(b)

Provide a brief response to the managing director’s opinions by:

(i) Explaining why Arbore Co may want to impose capital rationing on its departments; (2 marks)

(ii) Explaining the features of a capital investment monitoring system and discussing the benefits of maintaining such a system. (4 marks)

(c)

Category 1: Total Final Value
$1,184,409

Category 2: Adjustable Final Values
Project PDur01: 0.958
Project PDur02: 0.407
Project PDur03: 0.732
Project PDur04: 0.000
Project PDur05: 1.000

Category 3:
Constraints Utilised Slack
Year one: $9,000,000 Year one: $0
Year two: $6,000,000 Year two: $0
Year three: $5,000,000 Year three: $0

Required:

Explain the figures produced in each of the three output categories. (5 marks)

Comment:

(a)

A multi-period capital rationing model would use linear programming and is formulated as follows:

If:
Y1 = investment in project PDur01; Y2 = investment in project PDur02; Y3 = investment in project PDur03; Y4 = investment in project PDur04; and Y5 = investment in project PDur05

Then the objective is to maximise
464Y1 + 244Y2 + 352Y3 + 320Y4 + 383Y5

Given the following constraints
Constraint year 1: 4,000Y1 + 800Y2 + 3,200Y3 + 3,900Y4 + 2,500Y5 ≤ 9,000
Constraint year 2: 1,100Y1 + 2,800Y2 + 3,562Y3 + 0Y4 + 1,200Y5 ≤ 6,000
Constraint year 3: 2,400Y1 + 3,200Y2 + 0Y3 + 200Y4 + 1,400Y5 ≤ 5,000

And where Y1, Y2, Y3, Y4, Y5 ≥ 0

(b)

(i) Normally, positive net present value projects should be accepted as they add to the value of the company by generating returns in excess of the required rate of return (the discount rate). However, in this case, Arbore Co seems to be employing soft capital rationing by setting internal limits on capital available for each department, possibly due to capital budget limits placed by the company on the amounts it wants to borrow or can borrow.

In the latter case, the company faces limited access to capital from external sources, for example, because of restrictions in bank lending, costs related to the issue of new capital and lending to the company being perceived as too risky. This is known as hard capital rationing and can lead to soft capital rationing.

(ii) A capital investment monitoring system (CIMS) monitors how an investment project is progressing once it has been implemented. Initially the CIMS will set a plan and budget of how the project is to proceed.

It sets milestones for what needs to be achieved and by when. It also considers the possible risks, both internal and external, which may affect the project. CIMS then ensures that the project is progressing according to the plan and budget. It also sets up contingency plans for dealing with the identified risks.

The benefits, to Arbore Co, of CIMS are that it tries to ensure, as much as possible, that the project meets what is expected of it in terms of revenues and expenses. Also that the project is completed on time and risk factors that are identified remain valid.

A critical path of linked activities which make up the project will be identified. The departments undertaking the projects will be proactive, rather than reactive, towards the management of risk, and therefore possibly be able to reduce costs by having a better plan.

CIMS can also be used as a communication device between managers charged with managing the project and the monitoring team. Finally CIMS would be able to re-assess and change the assumptions made of the project, if changes in the external environment warrant it.

(c)

Category 1: Total Final Value. This is the maximum net present value that can be earned within the three-year constraints of capital expenditure, by undertaking whole, part or none of the five projects. This amount is less than the total net present value of all five projects if there were no constraints.

Category 2: Adjustable Final Values. These are the proportions of projects undertaken within the constraints to maximise the net present value. In this case, all of project PDur05, 95.8% of project PDur01, 73.2% of project PDur03 and 40.7% of project PDur02 will be undertaken.

Category 3: Constraints utilised, slack. This indicates to what extent the constraint limits are used and whether any investment funds will remain unused. The figures indicate that, in order to achieve maximum net present value, all the funds in all three years are used up and no funds remain unused.

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