Kenney Co is considering a project with the following cash flows:
Year Initial investment Variable costs Cash inflows Net cash flows
$ 000 $ 000 $ 000 $ 000
0 7 000 (7 000)
1 (2 000) 6 500 4 500
2 (2 000) 6 500 4 500
Cash flows arise from selling 650 000 units at $10 per unit. Kenney Co has a cost of capital of 8%.
Required
Measure the sensitivity of the project to changes in variables.
Solution
The PVs of the cash flow are as follows:
Discount PV of initial PV of variable PV of cash PV of net
The project has a positive NPV and would appear to be worthwhile. The sensitivity of each project variable is as follows:
(e) Cost of capital. We need to calculate the IRR of the project. Let us try discount rates of 15% and 20%
Net cash Discount Discount
Year flow factor 15% PV factor 20% PV
The cost of capital can therefore increase from 8% to 18.56% before the NPV becomes negative.
The elements to which the NPV appears to be most sensitive are the selling price followed by the sales volume. Management should thus pay particular attention to these factors so that they can be carefully monitored.
6.3 Weaknesses of this approach to sensitivity analysis
These are as follows:
(a) The method requires that changes in each key variable are isolated. However, management is likely to be more interested in the combination of the effects of changes in two or more key variables.
(b) Looking at factors in isolation is unrealistic since they are often interdependent.
(c) Sensitivity analysis does not examine the probability that any particular variation in costs or revenues might occur.
(d) Critical factors may be those over which managers have no control.
(e) In itself it does not provide a decision rule. Parameters defining acceptability must be laid down by managers.
Question 3: Sensitivity analysis
Nevers Ure Co has a cost of capital of 8% and is considering a project with the following 'most-likely' cash flows:
Year Purchase of plant Running costs Savings
$ $ $
0 (7 000)
1 2 000 6 000
2 2 500 7 000
Required
Measure the sensitivity (in percentages) of the project to changes in the levels of expected costs and savings.
(The answer is at the end of the chapter)
7 Capital rationing
Section overview
• Capital rationing refers to a situation in which a company has a limited amount of capital to invest in potential projects.
• Capital rationing may occur due to internal factors (soft capital rationing) or external factors (hard capital rationing).
• When capital rationing occurs in a single period, projects are ranked in terms of a profitability index, by considering the PV of the future cash flows earned per $ invested in the project. This assumes projects are divisible.
• If the projects are not divisible a decision has to be made by examining the absolute NPVs of all possible combinations of complete projects that can be undertaken within the constraints of the capital available.
• If projects can be postponed until Year 1, the optimal investment plan is determined by reference to the loss of NPV from postponement.
Definitions
Capital rationing: a situation in which a company has a limited amount of capital to invest in potential projects, such that the different possible investments need to be compared with one another in order to allocate the capital available most effectively.
Soft capital rationing is brought about by internal factors; hard capital rationing is brought about by external factors.
If an organisation is in a capital rationing situation it will not be able to enter into all projects with positive NPVs because there is not enough capital for all of the investments.
7.1 Soft and hard capital rationing
Soft capital rationing may arise for one of the following reasons:
(a) Management may be reluctant to issue additional share capital because of concern that this may lead to outsiders gaining control of the business.
(b) Management may be unwilling to issue additional share capital if it will lead to a dilution of earnings per share.
(c) Management may not want to raise additional debt capital because they do not wish to be committed to large fixed interest payments.
(d) Management may wish to limit investment to a level that can be financed solely from retained earnings.
(e) The Board may restrict the capital expenditure budget available to individual business units as a means of management control.
Hard capital rationing may arise for one of the following reasons:
LO 4.1
7.2 Relaxation of capital constraints
If an organisation adopts a policy that restricts funds available for investment (soft capital rationing), the policy may be less than optimal. The organisation may reject projects with a positive net present value and forgo opportunities that would have enhanced the market value of the organisation.
A company may be able to limit the effects of hard capital rationing and exploit new opportunities.
(a) It might seek joint venture partners with which to share projects.
(b) As an alternative to direct investment in a project, the company may be able to consider a licensing or franchising agreement with another enterprise, under which the licensor/franchisor company would receive royalties.
(c) It may be possible to contract out parts of a project to reduce the initial capital outlay required.
(d) The company may seek new alternative sources of capital (subject to any restrictions which apply to it), for example:
• Venture capital.
• Debt finance secured on the assets of the project.
• Sale and leaseback of property or equipment.
• Grant aid.
• More effective capital management.
Sources of finance are considered further in Chapter 4.
7.3 Single period capital rationing
7.3.1 Assumptions
We shall begin our analysis by assuming that capital rationing occurs in a single period, and that capital is freely available at all other times.
The following further assumptions will be made:
(a) If a company does not accept and undertake a project during the period of capital rationing, the opportunity to undertake it is lost. The project cannot be postponed until a subsequent period when no capital rationing exists.
(b) There is complete certainty about the outcome of each project, so that the choice between projects is not affected by considerations of risk.
(c) Projects are divisible, so that it is possible to undertake, say, half of project X in order to earn half of the net present value (NPV) of the whole project.
7.3.2 Ranking of projects
The basic approach is to rank all investment opportunities so that the NPVs can be maximised from the use of the available funds.
Ranking in terms of absolute NPVs will normally give incorrect results. This method leads to the selection of large projects, each of which has a high individual NPV but which have, in total, a lower NPV than a large number of smaller projects with lower individual NPVs.
Ranking is therefore in terms of what is called the profitability index.
This profitability index is a ratio that measures the PV of the future cashflows earned per $ invested in the project, and so indicates which investments make the best use of the limited resources available.
Definition
The profitability index is the ratio of the present value of the project's future cash flows (not including the capital investment) divided by the present value of the total capital investment.
LO 4.1