Capital Rationing

Capital Rationing

Capital Rationing

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Contents:

  • Single period capital rationing
  • Multi period capital rationing

Referenced syllabus: A.2 (g); B.1 (a)

Single period capital rationing

Capital rationing means that a company is unable to invest in all projects with a positive net present value due to its limited funds.

Reasons:

  • Soft capital rationing - unwilling to raise funds due to poor management skills; only focus on limited profitable projects.
  • Hard capital rationing - unable to raise funds due to poor business performance or industry-wide limiting funds.

Ways to deal with capital rationing:

  • Outsource business activities to the third party
  • Seek joint venture with another party
  • Seek new sources of capital finance
  • Operate the business under the franchising agreement

Divisible projects:

These are projects which can be taken under any fraction.

  • When capital rationing occurs in a single period, projects are ranked in terms of Profitability Index (PI) to determine the mix of projects.
  • PI = PV of future cash flows*/Present value of the capital investment.
  • Therefore, this compares the NPV per investment cost of each project, and those with high PI will be ranked first.
  • *PV of future cash flows do not include the initial investment.

Illustrative question

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

Fractions

Initial investment

NPV

A

100

25

B

200

35

C

80

21

D

75

10

Required:

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

Comment:

PI & ranking:

Items

Initial investment

PV

Profitability index (PI) (PV/Initial investment)

Ranking

A

100

25+100=125

1.25

2

B

200

35+200=235

1.175

3

C

80

21+80=101

1.263

1

D

75

10+75=85

1.13

4

Production schedule:

Items

Funds

NPV

200

C

(80)

21

120

A

(100)

25

20

B

(20)

20 x 35 = 3.5

200

0

Total NPV 49.5

Indivisible projects:

  • For non-divisible projects (impossible to undertake a fraction of a project, ie building ship), trial and error method would need to be used to test the NPV available from different project combinations.
  • For example, when there are three projects, A, B, and C, we need to calculate the NPV of A + B, A + C and B + C, the project combinations with the highest NPV will be undertaken.

Illustrative question

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

Items

Initial investment

NPV

A

100

25

B

200

35

C

80

21

D

75

10

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:

Items

Initial investment

NPV

Ranking based on NPV only

A

100

25

2

B

200

35

1

C

80

21

3

D

75

10

4

Option one:

Items

Funds

NPV

200

B

(200)

Total = 35

0

Option two:

Items

Funds

NPV

200

A

(100)

25

100

D

(75)

10

25


Multi period capital rationing

It means funds are limited not just at a time.

Steps: Mnemonics: DD computer

Step 1 - Define objective

  • Maximise NPV by using up the funds available

Step 2 - Define constraints

  • Indivisible projects: either 0 or 1
  • Divisible projects: 0<X<1

Step 3 - Slot into computer and let it do this.


Illustrative question

Projects

A

B

C

Funds required - Year 0

30

-

40

Year 1

-

20

50

Year 2

40

50

60

NPV

50

70

80

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.

Project

Year one
(Immediately)

Year two

Year three

Project net
present value

PDur01

$4,000,000

$1,100,000

$2,400,000

$464,000

PDur02

$800,000

$2,800,000

$3,200,000

$244,000

PDur03

$3,200,000

$3,562,000

$0

$352,000

PDur04

$3,900,000

$0

$200,000

$320,000

PDur05

$2,500,000

$1,200,000

$1,400,000

Not provided

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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Categories: : Advanced Financial Management (AFM)