Education Course Note [Session 1 & 2]
ACCA P4
Advanced Financial Management
Education Class 1
Session 1 & 2
Chapter 1
Patrick Lui
Chapter 1 Discounted Cash Flow Techniques
1. Evaluate the potential valued added to an organization arising from a specified capital investment project or portfolio using the NPV model. Project modeling should include explicit treatment of:
a. Inflation and specific price variation
b. Taxation including capital allowances and tax exhaustion
c. Single period capital rationing and multi-period capital rationing. Multi-period capital rationing to include the formulation of programming methods and the interpretation of their output.
d. Probability analysis and sensitivity analysis when adjusting fro risk and uncertainty in investment appraisal
e. Risk adjusted discount rates
2. Outline the application of Monte Carlo simulation to investment appraisal.
3. Establish the potential economic return (using IRR and MIRR) and advise on a project’s return margin.
1. Net Present Value with Inflation and Taxation
1.1 NPV and shareholder wealth maximization
1.1.1 All acceptable investment project should have positive NPV.
1.1.2 The market value of the company, theoretically at least, increases by the amount of the NPV.
1.1.3 The share price of the company should theoretically increase as well.
1.1.4 Objective of maximizing the wealth of shareholders is usually substituted by the objective of maximizing the share price of a company.
1.2 The effect of inflation
1.2.1 It is important to adapt investment appraisal methods to cope with the phenomenon of price movement. Future rates of inflation are unlikely to be precisely forecasted; nevertheless, we will assume in the analysis that follows that we can anticipate inflation with reasonable accuracy.
1.2.2 Two types of inflation can be distinguished.
(a) Specific inflation refers to the price changes of an individual good or service.
(b) General inflation is the reduced purchasing power of money and is measured by an overall price index which follows the price changes of a ‘basket’ of goods and services through time.
Even if there was no general inflation, specific items and sectors might experience price rises.
1.2.3 Inflation creates two problems for project appraisal.
(a) The estimation of future cash flows is made more troublesome. The project appraiser will have to estimate the degree to which future cash flows will be inflated.
(b) The rate of return required by the firm’s security holders, such as shareholders, will rise if inflation rises. Thus, inflation has an impact on the discount rate used in investment evaluation.
1.3 Real and money interest rate
1.3.1 The money (nominal or market) interest rate incorporates inflation. When the nominal rate of interest is higher than the rate of inflation, there is a positive real rate. When the rate of inflation is higher than the nominal rate of interest, the real rate of interest will be negative.
1.3.2 / Fisher’s (1930) Equation (Dec 08)The generalized relationship between real rates of interest and nominal rate of interest is expressed as follow under Fisher’s equation:
(1 + i) = (1 + r) (1 + h)
Where h = inflation rate
r = real interest rate
i = nominal interest rate
Example 1
$1,000 is invested in an account that pays 10% interest pa. Inflation is currently 7% pa. Find the real return on the investment.
Solution:
Real return = $1,000 × 1.1/1.07 = $1.028. A return of 2.8%.
1.3.3 Real rate or nominal rate? The rule is as follows:
(a) We use the nominal rate if cash flows are expressed in actual numbers of dollars that will be received or paid at various future rates.
(b) We use the real rate if cash flows are expressed in constant price terms.
1.4 Allowing for taxation
1.4.1 In investment appraisal, tax is often assumed to be payable one year in arrears, but you should read the question details carefully.
1.4.2 Typical assumptions which may be stated in questions are as follows.
(a) An assumption about the timing of payments will have to be made.
(i) Half the tax is payable in the same year in which the profits are earned and half in the following year.
(ii) Tax is payable in the year following the one in which the taxable profits are made. Thus, if a project increase taxable profits by $10,000 in year 2, there will be a tax payment, assuming tax at (say) 30%, of $3,000 in year 3.
(iii) Tax is payable in the same year that the profits arise.
(b) Net cash flows from a project should be considered as the taxable profits arising from the project.
1.5 Capital allowances (tax-allowable depreciation, or writing down allowances (WDAs) or depreciation allowances)
1.5.1 Capital allowance is used to reduce taxable profits, and the consequent reduction in a tax payment should be treated as a cash saving from the acceptance of a project.
1.5.2 There are two assumptions about the time when capital allowance start to be claim.
(a) It can be assumed that the first claim occurs at the start of the project (at year 0).
(b) Alternatively it can be assumed that the first claim occurs later in the first year.
Question 1A company is considering whether or not to purchase an item of machinery costing $40,000 in 2015. It would have a life of four years, after which it would be sold for $5,000. The machinery would create annual cost savings of $14,000.
The machinery would attract tax-allowable depreciation of 25% on the reducing balance basis which could be claimed against taxable profits of the current year, which is soon to end. A balancing allowance or charge would arise on disposal. The tax rate is 30%. Tax is payable half in the current year, half one year in arrears. The after-tax cost of capital is 8%.
Tax-allowable depreciation is first claimed against year 0 profits.
Should the machinery be purchased?
Solution:
1.6 Tax exhaustion
1.6.1 In most tax systems, capital expenditure is set off against tax liabilities so as to reduce the taxes a company pays and to encourage investment.
1.6.2 The effect of capital allowances can be from the definition of after-tax earnings
After-tax earnings = Earnings before tax – tax liability
Where tax liability = Tax rate × (Earnings before tax – capital allowances)
1.6.2 There will be circumstances when the capital allowances in a particular year will equal or exceed before tax earnings. In such a case the company will pay no tax.
1.6.3 In most tax systems unused capital allowances can be carried forward indefinitely, so that the capital allowance that is set off against the tax liability in any one year includes not only the writing down allowance for the particular year but also any unused allowances from previous years.
Question 2Suppose that a company has invested $10 million in a plant. The first year allowance is 40 percent, whereas the remaining amount is written down over a period of four years. The tax rate is 30 percent. Earnings before tax over a five year period are as follows:
Year 1 / Year 2 / Year 3 / Year 4 / Year 5
$m / $m / $m / $m / $m
3 / 2.5 / 3.5 / 3.8 / 4.2
(a) Calculate the tax liability every year and the after-tax earnings.
(b) Calculate the impact on earnings if the first year allowance is 60 percent.
Solution:
2. Capital Rationing
2.1 Meaning of capital rationing
2.1.1 In order to invest in all projects with a positive NPV a company must be able to raise funds as and when it needs them: this is only possible in a perfect capital market.
2.1.2 In practice capital markets are not perfect and the capital available for investment is likely to be limited or rationed. The causes of capital rationing may be external (hard capital rationing) or internal (soft capital rationing).
2.2 Soft and hard capital rationing
2.2.1 Capital rationing occurs when funds are not available to finance all wealth-enhancing projects. There are two types of capital rationing:
(a) Soft capital rationing – is internal management-imposed limits on investment expenditure. Such limits may be linked to the firm’s financial control policy.
(b) Hard capital rationing – relates to capital from external sources. Agencies (e.g. shareholders and bank) external to the firm will not supply unlimited amounts of investment capital, even though positive NPV projects are identified.
2.2.2 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) Capital expenditure budgets may restrict spending.
(f) Managers may prefer slower organic growth in order to remain in control of the growth process and so avoid rapid growth.
(g) Managers may want to make capital investments compete for funds in order to week out weaker or marginal projects.
2.2.3 Hard capital rationing may arise for one of the following reasons.
(a) Raising money through the stock market may not be possible if share prices are depressed.
(b) There may be restrictions on bank lending due to government control.
(c) Lending institutions may consider an organization to be too risky to be granted further loan facilities.
(d) The costs associated with making small issues of capital may be too great.
2.3 Relaxation of capital constraints
2.3.1 If an organization adopts a policy that restricts funds available for investment (soft capital rationing), the policy may be less than optimal. The organization may reject projects with a positive NPV and forgo opportunities that would have enhanced the market value of the organization.
2.3.2 A company may be able to limit the effects of hard capital rationing and exploit new opportunities.
(a) It may 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, for example:
(i) Venture capital
(ii) Debt finance secured on the assets of the project
(iii) Sale and leaseback of property or equipment
(iv) Grant aid
(v) More effective capital management
2.4 Single period capital rationing
(Jun 09)
2.4.1 The simplest and most straightforward form of rationing occurs when limits are placed on finance availability for only one year.
2.4.2 There are two possibilities with this single-period rationing situation.
(a) Divisible projects – The nature of the proposed projects is such that it is possible to undertake a fraction of a total project. For instance, if a project is established to expand a retail shop by opening a further 100 shops, it would be possible to take only 30% (that is 30 shops) or any other fraction of the overall project.
(b) Indivisible projects – with some projects it is impossible to take a fraction. The choice is between undertaking the whole of the investment or none of it (for instance, a project to build a ship, or a bridge or an oil platform).
2.4.3 When capital rationing occurs in a single period, projects are ranked in terms of profitability index.
2.4.4 / Profitability Index (PI)Profitability index is the ratio of the PV of the project’s future cash flows (not including the capital investment) divided by the present value of the total capital investment.
PI = / PV of future cash flows
Initial investment
Example 2
Suppose that ABC Co is considering four projects, W, X, Y and Z. Relevant details are as follows.
Project / Investment required / PV of cash inflows / NPV / PI / Ranking as per NPV / Ranking as per PI
$ / $ / $
W / (10,000) / 11,240 / 1,240 / 1.12 / 3 / 1
X / (20,000) / 20,991 / 991 / 1.05 / 4 / 4
Y / (30,000) / 32,230 / 2,230 / 1.07 / 2 / 3
Z / (40,000) / 43,801 / 3,801 / 1.10 / 1 / 2
Without capital rationing all four projects would be viable investments. Suppose, however, that only $60,000 was available for capital investment. Let us look at the resulting NPV if we select projects in the order of ranking per NPV.
By NPV:
Project / Priority / Outlay / NPV
Z / 1st / 40,000 / 3,801
Y (balance)* / 2nd / 20,000 / 1,487 / (2/3 of $2,230)
60,000 / 5,288
By PI:
Project / Priority / Outlay / NPV
W / 1st / 10,000 / 1,240
Z / 2nd / 40,000 / 3,801
Y / 3rd / 10,000 / 743 / (1/3 of $2,230)
60,000 / 5,784
* Projects are divisible. By spending the balancing $20,000 on project Y, two thirds of the full investment would be made to earn two thirds of the NPV.
2.5 Single period rationing with non-divisible projects
2.5.1 If the projects are not divisible then the method shown above may not result in the optimal solution. Another complication which arises is that there is likely to be a small amount of unused capital with each combination of projects. The best way to deal with this situation is to use trial and error and test the NPV available from different combinations of projects. This can be a laborious process if there are a large number of projects available.
Example 3ABC Co has capital of $95,000 available for investment in the forthcoming period. The directors decide to consider projects P, Q and R only. They wish to invest only in whole projects, but surplus can be invested. Which combination of projects will produce the highest NPV at a cost of capital of 20%?
Project / Investment required / PV of inflows at 20%
$000 / $000
P / 40 / 56.5
Q / 50 / 67.0
R / 30 / 48.8
Solution:
The investment combinations we need to consider are the various possible pairs of projects P, Q and R.
Projects / Required investment / PV of inflows / NPV from projects
$000 / $000 / $000
P and Q / 90 / 123.5 / 33.5
P and R / 70 / 105.3 / 35.3
Q and R / 80 / 115.8 / 35.8
The highest NPV will be achieved by undertaking projects Q and R and investing the unused funds of $15,000 externally.
2.6 Multi-period capital rationing