B1. Discounted cash flow techniques

Question 1

The net present value (NPV) of a project.

Answer 1

The net present value (NPV) of a project: the sum of the discounted cash flows less the initial investment. If the inflows are more than the outflows, it is called a positive NPV. All future cash flows are discounted to take into account time value of money. This “discounting” takes into account not only the time value of money but also the required return to share and debt holders. This means that if NPV is positive (even after discounting the future cash flows) then the return is above not only the time value of money but also above what the shareholders and debt holders require. So, they will be happy and the company value (and hence share price) will rise by the +NPV amount (divided by the number of shares).

Question 2

Relevant costs NPV

Answer 2

The figures in NPV working must be incremental cash flows that are relevant to the decision being considered:
• Cash flows only – e.g. depreciation and allocated overheads should be ignored
• Future amounts - costs which have already been incurred are ignored.
• Finance related cash flows - normally excluded from project appraisal because discounting accounts for the minimum return required by any equity investors.
• Opportunity costs – these need to be included; these are costs incurred, or revenues lost, from diverting existing resources from their existing use.

Question 3

Working Capital NPV

Answer 3

Projects need funds to finance the level of working capital requires (inventory). The relevant cash flows are the incremental cash flows from one year’s requirement to the next. At the end of the project, the full amount invested will be released.
• Always start at T0
• Just account for increase or decrease
• Final year it all comes back as income
• The working capital line should always total zero

Question 4

Inflation real vs nominal

Answer 4

Inflation.
• Real terms – at current prices
• Nominal or money – adjusted for inflation.

Question 5

Inflation has two impacts on NPV:

Answer 5

• Cash flow – cash inflows will increase, making the project more attractive
• Discount factor – the cost of capital will increase, making the project less attractive
• Present value – the net impact on the NPV may be minimal.

Question 6

Specific and general inflation rates.

Answer 6

• Specific Inflation rate - Impacts all the individual cash flow items – each cash flow is affected by a specific rate.
• General rate of inflation - Impacts the investors’ overall required rate of return.

Question 7

NPV Ignoring inflation.

Answer 7

If there is one rate of inflation, inflation has no impact on the NPV of a domestic investment. In this case it is normally quicker to ignore inflation in the cash flows (i.e. real cash flows) and to use an uninflated (real) cost of capital (rarely examined).

Question 8

NPV Including inflation

Answer 8

It will normally be the case that cash flows inflate at a variety of different rates. If so, inflation will have an impact on profit margins and therefore inflation must be included in the cash flows and the cost of capital. Cash flows will need to be inflated by their specific inflation rates. However, investors will anticipate inflation, so the cost of capital will normally include inflation. So, there will be no need to adjust the cost of capital for the general rate of inflation unless it is stated to be in ‘real terms’ (rare but if happens use formula, which is provided)
(1+real cost of capital) x(1+general inflation rate)
=(1+inflated cost of capital)

Question 9

NPV Corporation tax

Answer 9

Corporation tax can have two impacts on project appraisal:
• The tax will need to be paid on the cash profits from the project. The effect of taxation will not necessarily occur in the same year as the relevant cash flow that causes it (normally payable one year later).
• Tax will be saved if tax allowable depreciation (WDA) can be claimed.
These impacts can be built into project appraisal as a single cash flow showing the tax paid after tax allowable depreciation is taken into account. However, care must be taken to add back TAD because it is not in itself a cash flow.
In the final year a balancing allowance or charge will be claimed to reduce the written down value of asset to zero (after accounting for any scrap value).

Question 10

NPV Tax exhaustion.

Answer 10

There will be circumstances when TAD in a particular year will equal or exceed before-tax profits. In most tax systems, unused TAD can be carried forward so that it is set off against the tax liability in any one year includes not only TAD for that year but also any unused TAD from previous years.

Question 11

Capital rationing

Answer 11

Shareholder wealth is maximised if a company undertakes all possible positive NPV projects. However, capital is not always available to allow this to happen. Capital rationing is a situation in which 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.

There are 2 reasons for this:
• Hard capital rationing is brought by external factors, such as a limited availability of new external finance.
• Soft capital rationing is brought about by internal factors and decisions by management. This is contrary to the rational view of shareholder wealth maximisation.

Question 12

Hard capital rationing may arise for one of the following reasons:

Answer 12

• Raising new finance through the stock market may not be possible if share prices are depressed.
• There may be restrictions on bank lending due to government control.
• Lending institutions may consider an organization to be too risky to be granted further loan facilities.
• The costs associated with making small issues of capital may be too great.

Question 13

Soft capital rationing may arise for one of the following reasons:

Answer 13

• Management may be reluctant to issue additional share capital because of concern that this may lead to outsiders gaining control of the business.
• Management may be unwilling to issue additional share capital if it will lead to a dilution of earnings per share
• Management may not want to raise additional debt capital because they do not wish to be committed to large fixed interest payments.
• Management may wish to limit investment to a level that can be finance solely from retained earnings.
• One of the main reasons suggested for soft capital rationing is that managers wish to create an internal market for investment funds. It is suggested that requiring investment projects to compete for funds means that weaker or marginal projects, with only a small chance of success, are avoided. This allows a company to focus on more robust investment projects where the chance of success is higher. This cause of soft capital rationing can be seen as a way of reducing the risk and uncertainty associated with investment projects, as it leads to accepting projects with greater margins of safety.

Question 14

Divisible vs Indivisible projects

Answer 14

Divisible projects are those which can be undertaken completely or in fractions. Indivisible projects are those which must be undertaken completely or not at all.

Question 15

Single-period capital rationing with divisible projects.

Answer 15

With single-period capital rationing, investment funds are a limiting factor in the current period. The total return will be maximised if management follows the decision rule of maximising the return per unit of the limiting factor. They should therefore select those projects whose cash inflows have the highest present value per $1 of capital invested, i.e. rank the projects according to their profitability index.
Profitability index=
(NPV of project)/(Initial cash outflow)

Question 16

Single-period capital rationing with non-divisible projects.

Answer 16

The main problem if projects are non-divisible 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 available.

Question 17

Multi period capital rationing.

Answer 17

Where capital rationing exists over a number of years, mathematical models are used to find the optimal combination of divisible or individual projects to invest in (linear programming).
Need to be able to formulate the problem and to interpret solution.

The steps to answer these questions are:
• Do the Objective function (i.e. write down all the projects NPVs and their names next to them e.g. maximize P1XNPV+P2XNPV+P3XNPV)
• Do the Constraints function (i.e. write down all the costs of each project and say they should be less than the cash available e.g. P1XCOST+P2XCOST+P3XCOSTP1,P2,P3>1)
• Feed into computer, results with 1 means select and 0 reject.

Question 18

Practical methods of dealing with capital rationing.

Answer 18

Practical methods of dealing with capital rationing. A company may be able to limit the effects of capital rationing and exploit new opportunities.
• It might seek joint venture partners with which to share projects.
• As an alternative to direct investment in a project, the company may be able to consider licensing or franchising agreement with another enterprise.
• It may be possible to contract out parts of a project to reduce the initial capital outlay required.
• The company may seek new alternative sources of capital.

Question 19

Risk & Uncertainty.

Answer 19

Before deciding on a project, managers will want to be able to make a judgement on the possibility of receiving a return below the projected NPV, i.e. the risk or uncertainty of the project.
Risk refers to the situation where probabilities can be assigned to a range of expected outcomes arising from an investment project and the likelihood of each outcome occurring can therefore be quantified.
Uncertainty refers to the situation where probabilities cannot be assigned to expected outcomes. Investment project risk therefore increases with increasing variability of returns, while uncertainty increases with increasing project life.

Question 20

There are 4 main techniques for analysis of risk and uncertainty:

Answer 20

• Sensitivity Analysis
• Probability Analysis (expected values)
• Simulation
• Adjusted Payback

Question 21

Probability analysis.

Answer 21

Probability analysis refers to the assessment of the separate probabilities of a number of specified outcomes of an investment project. A probability analysis of expected cash flows can often be estimated and used both to calculate an expected NPV and to measure risk. A probability distribution of expected cash flows can often be estimated, recognising there are several possible outcomes, not just one.
This could then be used to:
• Calculate an expected value (EV) of the NPV.
• Measure risk for example in the following ways:
o By calculating the worst possible outcome and its probability;
o By calculating the probability that the project will fail to achieve a positive NPV
o By calculating the standard deviation of the NPV
In this way, the downside risk of the investment could be determined and incorporated into the investment decision.
The term ‘probability’ refers to the likelihood or chance that a certain event will occur, with potential values ranging from 0 (the event will not occur) to 1 (the event will definitely occur).

Question 22

Calculating an EV.

Answer 22

The formula for calculating an EV is:
EV=∑px
Where
p = the probability of an outcome
x = the value of an outcome.

Question 23

Problems with EV

Answer 23

The EV does not necessarily represent what the outcome will be, nor does it represent the most likely result. What it really represents is the average pay off per occasion if the project were repeated many times (i.e. a ‘long-run’ average). There are two main problems with using EV to make decisions in this way:
• The project will only be carried out once. It could result in a sizeable loss and there may be no second chance to win our money back.
• The probabilities used are simply subjective estimates of our belief, on a scale from 0 to 1. There is probably little data on which to base these estimates.

Question 24

Sensitivity analysis.

Answer 24

Sensitivity analysis assesses how the net present value of an investment project is affected by changes in project variables. Considering each project variable in turn, the change in the variable required to make the net present value zero is determined, or alternatively the change in net present value arising from a fixed change in the given project variable. In this way the key or critical project variables are determined
Management should review critical variables to assess whether or not there is a strong possibility of events occurring which will lead to a negative NPV. They should also pay particular attention to controlling those variables to which the NPV is particularly sensitive, once the decision has been taken to accept the investment.

Question 25

Calculation of sensitivity.

Answer 25

A simple approach to deciding which variables the NPV is particularly sensitive to is to calculate the sensitivity of each variable.
Sensitivity margin=
NPV/(PV of project variable)×100%

The lower the sensitivity margin, the more sensitive the decision to the particular parameter being considered, i.e. small changes in the estimate could change the project decision from accept to reject.

Question 26

Weakness of Sensitivity Analysis

Answer 26

• It assumes that changes to variables can be made independently (in isolation), e.g. material prices will change independently of other variables. This is unlikely. If material prices went up the firm would probably increase selling price at the same time and there would be little effect on NPV. Or management may be more interested in the combination of the effects of changes in two or more key variables.
• It only identifies how far a variable need to change. It does not look at the probability of such a change.
• Critical factors may be those over which managers have no control.
• It is not an optimising technique. It provides information on the basis of which decisions can be made. It does not point directly to the correct decision.

Question 27

Payback period.

Answer 27

The payback period is the length of time that it takes for a project to recoup its initial cost out of the cash receipts that it generates. The payback period is expressed in years. This method focuses on liquidity rather than the profitability of a product. It is good for screening and for fast moving environments. However, project should not be evaluated on the basis of payback alone. If project gets through the payback test, it ought to then be evaluated with a more sophisticated investment appraisal technique that takes into consideration the total return over the full investment period. The basic premise of the payback method is that the more quickly the cost of an investment can be recovered, the more desirable is the investment.

Question 28

Payback period calculation

Answer 28

Constant annual cash flows
Payback period=(Initial Investment)/(Actual cash flow)
Uneven annual cash flows. In practice, cash flows from a project are unlikely to be constant. Where cash flows are uneven, payback is calculated by working out the cumulative cash flow over the life of the project.

Question 29

Payback period advantages

Answer 29

• Simplicity –it is easily understood and is easily calculated.
• It can be used as a screening device as a first stage in eliminating obviously inappropriate projects prior to more detailed evaluation.
• It is useful in certain situations:
o Rapidly changing technology –If new plant is likely to be scrapped in a short period because of obsolescence, a quick payback is essential.
o Improving investment conditions –When investment conditions are expected to improve in the near future, attention is directed to those projects which will release funds soonest, to take advantage of the improving climate.
• Payback favours projects with a quick return – It is often argued that these are to be preferred for three reasons:
o Rapid project payback leads to rapid company growth, but in fact such a policy will lead to many profitable investment opportunities being overlooked because their payback period does not happen to be particularly swift
o Rapid payback minimises risk (the logic being that the shorter the payback period, the less there is that can go wrong). Not all risks are related to time, but payback is able to provide a useful means of assessing time risks (and only time risks). It is likely that earlier cash flows can be estimated with greater certainty.
o Rapid payback maximises liquidity – but liquidity problems are best dealt with separately, through cash forecasting
• Cash flows –Unlike the other traditional methods it uses cash flows, rather than profits, and so is less likely to produce an unduly optimistic figure distorted by assorted accounting conventions

Question 30

Payback period disadvantages

Answer 30

• Project returns may be ignored – cash flows arising after the payback period are totally ignored and therefore the total project return. Payback ignores profitability and concentrates on cash flows and liquidity.
• Time value of money. Another criticism of payback method is that it does not consider the time value of money. A cash inflow to be received several years in the future is weighed equally with a cash inflow to be received right now.
• Project profitability is ignored payback takes no account of the effects on business profits and periodic performance of the project, as evidenced in the financial statements.
• It may lead to excessive investment in short-term projects. Unfortunately, a shorter payback period does not always mean that one investment is more desirable than another. For example it doesn’t look at the whole life of the project

Question 31

Discounted payback period.

Answer 31

The discounted payback period is the length of time before the cumulative PV of cash inflows from the projects begins to exceed the initial outflow. The cash flows are first discounted using an appropriate discount rate that reflects the risk profile of the project. The cumulative discounted cash flow can then be calculated in the same manner as the cumulative cash flow is for the standard payback calculation.
The approach has all the perceived advantages of the payback period method of investment appraisal: it is easy to understand and calculate, and it provides a focus on liquidity where this is relevant. In addition, however, it also take into account the time value of money.
It does differ from NPV in that the discount rate used is the unadjusted cost of capital whereas NPV uses an adjusted rate to reflect project risk and uncertainty. Another advantage over traditional payback is that it has clear accept or reject criterion. Using DPP, a project is acceptable if it pays back within its lifetime. DPP still shares one disadvantage with the payback period method: cash flows which occur after the payback period are ignored (even though more of them are included).

Question 32

Risk Adjusted Discount Rates

Answer 32

The discount rate reflects either:
• the cost of borrowing funds in the form of a loan rate or
• the underlying required return of the business (i.e. the return required by the shareholder),
• or a mix of both

If an individual investment or project is perceived to be more risky than existing investments, the increased risk could be used as a reason to adjust the discount rate. This is a key concept in investment appraisal. Applying the existing discount rate or cost of capital to an investment assumes that the existing business and gearing risk of the company will remain unchanged. If the project is significant in size and likely to result in additional risks then a project specific or risk-adjusted discount rate should be used.

The application of an increased discount rate is often successful in eliminating marginal projects. The addition to the usual discount rate is called the risk premium.

Question 33

Project duration as risk measure

Answer 33

Project duration: a measure of the average time over which a project delivers its value. Project duration shows the reliance of a project on its later cash flows, which are less certain than earlier cash flows; it does this by weighting each year of the project by the % of the present value of the cash inflows received in that year. Unlike payback, this measure of uncertainty looks at all of a project’s life.
Although duration can be the same as the project life, it will normally be different. The lower the project duration the lower the risk/uncertainty of the project.
This can be calculated as:
(1xPV_1+2xPV_2+3xPV_3)/(PV_1+PV_2+PV_3)

Question 34

Monte Carlo simulation.

Answer 34

Monte Carlo simulation is a model which will include all combinations of the potential variables associated with the project. It results in the creation of a distribution curve of all possible cash flows which could arise from the investment and allows for the probability of the different outcomes to be calculated (including negative NPV).

The steps involved are as follows:
• Specify all major variables (market, operating costs etc)
• Specify the relationship between those variables to calculate NPV (sales revenue=market size x market share x selling price)
• Using a probability distribution, simulate each environment.
• The results of a simulation exercise will be a probability distribution of NPVs. Instead of choosing between expected values, decision makers can now take the dispersion of outcomes and the expected return into account.

Question 35

Advantages and disadvantages of simulation

Answer 35

Advantages of simulation.
• It includes all possible outcomes in the decision-making process
• It is a relatively easily understood technique
• It has a wide variety of applications (inventory control, component replacement, corporate models, etc.)
• Works in complex situations which are difficult to model mathematically in other ways.
Drawbacks of simulation.
• Models can become extremely complex and the time and costs involved in their construction can be more than is gained from the improved decisions
• Probability distributions may be difficult to formulate

Question 36

Value at risk

Answer 36

Value at risk is the maximum likely loss over a set period (with only an x% chance of being exceeded). It is a measure of how the market value of an asset is likely to decrease over a certain time. Value at risk is measured by using normal distribution theory.
Value at risk = amount at risk to be lost from an investment under usual conditions over a given holding period, at a particular “confidence level”. Confidence levels are often set at either 95% (in which case the Value in risk will provide the amount that has only a 5% chance of decline) or at 99% (when the Value in risk considers a 1% chance of loss of value).

Question 37

Value at risk calculation

Answer 37

Calculation.
Z=(X-μ)/σ
X= result we are considering
µ=mean
σ=standard deviation
Establishing Z from normal distribution table.
At a 95% (0.95) confidence level, 1.65 is the value for a one tailed 5% probability of decline (i.e. 0.95 - 0.50 = 0.45 = 0.4505 from the normal distribution table)
At a 99% (0.99) confidence level, 2.33 is the value for a one tailed 1% probability of loss of NPV (i.e. 0.99 - 0.50 = 0.49 = 0.4901 from the normal distribution table).

Question 38

Value at risk for a project

Answer 38

Value at risk can be quantified for a project using simulation to calculate the project’s standard deviation. Standard deviation relates to a period of time (e.g. year), but the value at risk may be over a different time period (e.g. life of project). In this context, the standard deviation may need to be adjusted by multiplying by the square root of the time period, i.e.
95% value at risk=
1.645 x standard deviation of project x√(time period of the project)

Question 39

Value at risk drawbacks

Answer 39

• Value at risk is based on a normal distribution, which assumes that virtually all possible outcomes will be within three standard deviations of the mean and that success and failure are equally likely. Neither is likely to be true for a one-off project.
• Value at risk is also based around the calculation of a standard deviation and again this is hard to estimate in reality since it is based on forecasting the possible spread of the results of a project around an average.

Question 40

Internal Rate of Return (IRR)

Answer 40

Internal Rate of Return (IRR) of any investment: the discount rate at which the NPV is equal to zero. Alternatively, the IRR can be thought of as the return that is delivered by a project. A project will be accepted if its IRR is higher than the required return as shown by the cost of capital.

Question 41

Calculation of IRR.

Answer 41

It can be estimated as follows:
Calculate NPV of the project at any reasonable rate (e.g. cost of capital)
Calculate the project NPV at any other rate (If previous NPV is positive, increase the discount rate to get a smaller NPV and vice versa).
Calculate IRR using the formula:
IRR=a+NPVₐ/(NPVₐ-NPVb ) x(b-a)

Where 
a=lower cost of capital
B=higher cost of capital
NPVₐ=NPV at the lower cost of capital
NPVb =NPV at the higher cost of capital

Question 42

Interpreting the IRR.

Answer 42

The IRR provides a decision rule for investment appraisal, but also provides information about the riskiness of a project – i.e. the sensitivity of its returns. The project will only continue to have a positive NPV whilst the firm’s cost of capital is lower than the IRR. A project with a positive NPV at 14% but an IRR of 15% for example, is clearly sensitive to:

• an increase in the cost of finance
• an increase in investors’ perception of the potential risks
• any alteration to the estimates used in the NPV appraisal.

Question 43

Advantages of IRR

Answer 43

• IRR considers the time value of money. The current value earned from an investment project is therefore more accurately measured.
• IRR is a percentage and therefore easily understood. Although managers may not completely understand the detail of the IRR, the concept of a return earned is familiar and the IRR can be simply compared with the required return of the organisation.
• IRR uses cash flows, not profits. These are less subjective.
• IRR considers the whole life of the project rather than ignoring later flows.
• IRR a firm selecting projects where the IRR exceeds the cost of capital should increase shareholders’ wealth. This holds true provided the project cash flows follow the standard pattern of an outflow followed by a series of inflows.

Question 44

Disadvantages of IRR

Answer 44

• It is not a measure of absolute profitability. A project of $1,000 invested now and paying back $1,100 in a year’s time has an IRR of 10%. If a company’s required return is 6%, then the project is viable according to the IRR rule but most businesses would consider the absolute return too small to be worth the investment.
• Interpolation only provides an estimate. The cost of capital calculation itself is also only an estimate and if the margin between required return and the IRR is small, this lack of accuracy could actually mean the wrong decision is taken.
• Non-conventional cash flows may give rise to no IRR or multiple IRRs.
• IRR ignores the size of a project, so smaller with higher IRR can be chosen instead of bigger project which will generate more wealth.

Question 45

Modified internal rate of return.

Answer 45

IRR assumes that the cash flows after the investment phase (time 0) are reinvested at the project’s IRR. A better assumption is that the funds are reinvested at the investor’s minimum required return (WACC). If this re-investment assumption is used the alternative, modified version of IRR can be calculated (MIRR). Modified internal rate of return - gives a measure of the return from a project. MIRR gives a measure of the maximum cost of finance that the firm could sustain and allow the project to remain worthwhile.

Question 46

Calculation of MIRR

Answer 46

Calculation of MIRR
MIRR=
((PV return phase)/(PV investment phase))^(1/n) x
(1+r_e )-1

re – cost of capital
n-number of time periods

If project return > company cost of finance ⇒ Accept project. The extent to which the MIRR exceeds the cost of capital is called return margin and indicates the extent to which a new project is generating value.

Question 47

The MIRR procedure

Answer 47

The MIRR assumes a single outflow at time 0 and a single inflow at the end of the final year of the project. The procedures are as follows:
• Step 1. Convert all investment phase outlays as a single equivalent payment at time 0. Basically, bring all investment costs to year 0. Where necessary, any investment costs arising after time 0 must be discounted back to time 0 using the company’s cost of capital.
• Step 2. All net cash flows generated by the project after the initial investment (i.e. the return phase cash flows) are converted to a single net equivalent terminal receipt at the end of the project’s life, assuming a reinvestment rate equal to the company’s cost of capital.
• Step 3. The MIRR can then be calculated using number of methods.

Question 48

Advantages of MIRR

Answer 48

• Eliminates the possibility of multiple internal rates of return.
• Addresses the reinvestment rate issue i.e. it does not make the assumption that the company’s reinvestment rate is equal to whatever the project IRR happens to be.
• Provides rankings which are consistent with the NPV rule (which is not always the case with IRR).
• Provides a % rate of return for project evaluation.
• It is claimed that non- financial managers prefer a % result to a monetary NPV amount, since a % helps measure the “headroom” when negotiating with suppliers of funds.

Question 49

Capital investment monitoring system

Answer 49

It is used to monitor the ongoing progress of a capital investment project once the decision to proceed has been taken. The CIMS will:

• set a plan of how the project is to proceed and budget for the project
• set project milestones and when they need to be achieved by
• consider potential external and internal risks to the project (contingency plans will be drawn up to deal with them)

Question 50

Capital investment monitoring system benefits

Answer 50

• it ensures project meets its budgeted revenue and expenditure
• it helps ensures project is completed on time and identified risk factors are still valid
• it identifies a critical path of linked activities which are vital to deliver project on time
• can be used as means of communication between project managers and monitoring team.