FM Chapters 2, 3and 4: Basic Investment Appraisal Techniques and Further Discounted Cash Flow Techniques (DCF)
Compounding
-A sum invested today will earn interset. -The terminal value is the value in n years' time, of a sum invested now, at an interest rate of r%.
Exam Assumptions in Discounting
-All cash flows occur at the start or end of a year. -Initial investments occur at once (T₀) -Other cash flows start in one year's time (T₁)
Net Present Value
-All future cash flows are discounted to the present value and then added. Present Value = Future Value x Discount Factor PV= F x (1 + r)⁻ⁿ -Note: You should never include interest payments as cash flows within the NPV calculation as these are taken account of by the cost of capital.
NPV vs IRR
-Both NPV and IRR are investment appraisal techniques that discount cash flows -Both are superior to basic techniques given in Chapter Two like Payback or ROCE -The two can give conflicting advice -Only NPV can be used to distinguish between two mutually exclusive projects. -The advantage of NPV is that it tells us the absolute increase in shareholder wealth as a result of accepting the project, at the current cost of capital. -The IRR simply tells us how far the cost of capital could increase before the project would not be worth accepting.
Money Cash Flows
-Cash flows may have future inflation incorporated ("money" or "nominal terms") -Make sure you know "Money" flows are flows of actual amounts of money i.e. inflation is taken into account
Types of Cash Flows
-Current cash flows: cash flows may be expressed in today's terms ("current terms") -Money cash flows: cash flows may have future inflation incorporated ("money" or "nominal terms"). -Real cash flows: Cash flows expressed in "real" terms are money cash flows with the general rate of inflation stripped out REMEMBER: Make sure you know "Money" flows are flows of actual amounts of money i.e. inflation is taken into account
Converting from Money Cash Flow to Real Cash Flow
-Deflate using the general rate -Current and real cash flows will only be the same if the specific inflation rate for the cash flow is the same as the general inflation rate
Discount Rates and Inflation
-Discounts rates may exclude inflation ("real rate") -Or incorporate future inflation ("money rates")
Common Errors With ROCE
-Do not try and calculate ROCE using relevant cash flows - it is a profit based measure, now a cash flow based measure. -The project investment should include book values of the assets employed.
Tax-allowable Depreciation
-For tax purposes, a business may not deduct the cost of an asset from its profits as depreciation (in the way it does for financial accounting purposes) -Instead, the cost must be deducted from taxable profits in the form of tax-allowable depreciation. -Tax-allowable depreciation is calculated based on the written down value of the assets (this will either be on a reducing balance or straight line basis - read the q carefully)
Which method to use for NPV calculations with inflation?
-If there is more than one rate of inflation -> Use money method -If a question contrains both tax and inflation -> Use money mehod -If there is just one rate of inflation (and no tax) -> Use real method if cash flows are in real terms or money method if cash flows are in money terms
Discounting
-In a potential investment project, cash flows will arise at many different points in time. To make a useful comparison of the different flows, they must all be converted to a common point in time. -Discounting is the conversion of future cash flows to their value at one point in time - usually the present day.
Exam Focus: NPV calculation using a real method when there is more than one inflation value in the question (recent exam q)
-Inflate the cash flows to money cash flows -Then delflate them a the general inflation rate (to get to the real cash flows with the general inflation rate stripped out) -Then discount them using the real cost of capital
Inflation - Exam Focus Note
-Inflation features in approximately half of all exam NPV questions -The main error students make is to confuse the two main approaches for dealing with inflation -REAL METHOD -NOMINAL (Money) Method -The two methods give the same NPV
Advantages of IRR
-It considers the time value of money -It is a percentage and is therefore easily understood -It uses cash flows not profits -It considers the whole life of the prokect -It does not need the cost of capital to be known
Limitations of NPV
-It is difficult to explain to managers -It requires the knowledge of cost of capital
Real cash flows
Cash flows expressed in "real" terms are money cash flows with the general rate of inflation stripped out
Current Cash Flows
Cash flows may be expressed in today's terms ("current terms")
Finiding the discount factor in present value tables - example r=10%, n = 5
Example: Look in the 10% column and the 5-year row to find that it is 0.621 -Different discount factor for each year
Compounding formula -> future/terminal value of a given sum of money
F = P (1 + r)ⁿ where F = Future value after n periods P = Present or initial value r = Rate of interest per period n = Number of periods
Finding NPV with Inflation: Nominal (Money) Method
Money cash flows:money rate -Inflate the cash flows to find the money values (using the inflation rate) -Discount at the money rate -Useful if different cash flows are subject to differnt rates of inflation - known as 'specifc inflation'
Time Value of Money
Money received today is worth more than the same sum received in the future because of: -the potential for earning interest -the impact of inflation -the effect of risk Discounted Cash Flow (DCF) techniques take account of the time value of money when appraising investments.
Discount factor - example r=10%, n = 5
(1 + r)⁻ⁿ Example: DF= 1.1⁻⁵=0.621
DCF and Taxation: Two important tax effects to consider
(a) Tax on operating profits (b) Tax benefit from tax-allowable depreciation and a possible tax payment from a balancing charge on asset disposal
Inflation
-A general increase in prices leading to a general decline in the real value of money. -Lenders require a return made up of the real return (that required if there was no inflation) and an additional return just to keep with inflation. -Inflation aggects both future cash flows and the discount rate used.
Disadvantages of IRR
-It is not a measure of absolute profitability. -It is fairly complicated to calculate. -Interpolation only provides an estimate. -Non-convention cash flows may give rise to mutiple IRRs,w hcih means the interpolation method can't be used -Contains the inherent assumption that cash returned from the projet will be re-invested at the project's IRR, which may be unrealistic.
Exam Focus: NPV and Taxation Exam qs
-Most exam questions on NPV involve taxation -Basic idea: the presence of tax in a NPV question essentially means that there are more cash flows to include. -All relevant cash flows should have a tax consequence that also needs to be included. -TRADING CASH FLOWS: Flows such as sales, wages, etc will be taxed at the tax rate given in the question. The simplest way of dealing with these is to calculate a net total and apply the tax rate to that figure -ASSET CASH FLOWS: Initial investment witl attract tax releiief through tax-allowable depreciation. Usually 25% reducing balance, with a balancing allowanace or charge when the asset is sold or scrapped. Tip: The tax-allowable depriactiation calculation should be fairly routine and a source of easy marks in an exam,
Annuity table (sometimes referred to as a Cumulative Present Value Table) - example three-year annuity at 10%
-Provides pre-calculated annuity factors for various different discount rates over various periods -Look in the table for the 10% column and the three-year row to find 2.486
Exam focus: Showing working for cash flows inflated at different rates
-Set the NPV calculation with the cash flows down the side and time across the top -Show below workings for each figure (i.e. present value calculation table)
What does the internal rate of return (IRR) represent?
-The IRR represents the discount rate at which the NPV of an investment is zero. -As such it represents a breakeven cost of capital. -May be found by linear interpolation or extrapolation -Projects should be accepted if their IRR is greater than the cost of capital.
Present Value
-The present value (PV) is the cash equivalent now of money recievable/payable at some future date.
Payback Period
-The time taken to recoup the initial cash outlay on a project. -Organisations set target payback periods and will probably reject projects which have paybacks longer than the target.
When discounting, the rate the company should apply to take account of the time value of money may be referred to as:
-cost of capital -rate of return -discount rate -required rate -required return -weighted average cost of capital
Steps for Calculating the IRR Using Linear Interpolation
1) Calculate two NPVs for the project at two different costs of capital 2) Use the following formula to find the IRR IRR = L + [NL/NL-NH x (H-L)] Where L = lower rate of interest H = higher rate of interest NL = NPV at lower rate of interest NH = NPV at higher rate of interest
Perpetuity Factor
1/r
Limitations of Using Payback Period
A disadvantage of the payback method is that it ignores the time value of money. Payback ignores the overall profitability of a project by ignoring cash flows after payback is received. There is also no definitive investment decision rule so it is subjective (not an objective measure of what is the desirable return). -Does not ensure that shareholder wealth is maximised -Ignores timing of cash flows -Ignores returns after the payback period -It is subjective - no definitive investment decision
Limitations of Using ROCE
A major drawback of ARR is that it uses accounting profits before interest and tax rather than cash flows in order to measure return. It is a limitation that the ARR is dependent on accounting policies and there can make comparison of ARR figures across different investments very difficult. It is a disadvantage of the ROCE that it takes no account of the time value of money. Secondly, A further difficulty with the use of ARR is that it does not give a clear decision rule. -Does not ensure that shareholder wealth is maximised -Figures easily manipulated -Ignores the actual/incremental cash flows associated with the project
Strengths of Using ROCE
ARR is directly related to the performance measure Return on Capital Employed (ROCE). A key advantage of the Accounting Rate of Return is its simplicity since it makes it easy to calculate the likely effect of the project on the reported profit and loss account/balance sheet. It is also easily understood because it is expressed in terms familiar to managers (profit and capital employed). -Expressed in terms familiar to managers - profit and capital employed -Easy to calculate the likely effect of the project on the reported profit and loss account/balance sheet Managers are frequently rewarded in relation to performance against these variables -Businesses are judged on return on investment measures by financial markets
Ch 2&3 Q24 Explain and illustrate (using simple numerical examples) the Accounting Rate of Return and Payback approaches to investment appraisal, paying particular attention to the limitations of each approach. (7 marks)
Accounting rate of return (ARR) is a measure of return on investment where the annual profit before interest and tax is expressed as a percentage of the capital sum investment. Two formulae for ARR: Average Annual Profit Before Interest and Tax/Initial Capital Invested Average Annual Profit Before Interest and Tax/Average Capital Invested As there are several alternative formulae, It is important to recognise that the measure might be subject to manipulation by managers seeking approval for their investment proposals. EXAMPLE: Suppose Average Annual Profit Before Interest and Tax/Initial Capital costs x 100 A project costing £5,000,000 million, and yielding average annual profits before interest and tax of £1,250,000 would given an ARR of: £1,250,000/£5,000,00 x 100%= 25% ARR is directly related to the performance measure Return on Capital Employed (ROCE). A key advantage of the Accounting Rate of Return is its simplicity since it makes it easy to calculate the likely effect of the project on the reported profit and loss account/balance sheet. It is also easily understood because it is expressed in terms familiar to managers (profit and capital employed). A major drawback of ARR is that it uses accounting profits before interest and tax rather than cash flows in order to measure return. It is a limitation that the ARR is dependent on accounting policies and there can make comparison of ARR figures across different investments very difficult. It is a disadvantage of the ROCE that it takes no account of the time value of money. Secondly, A further difficulty with the use of ARR is that it does not give a clear decision rule. The payback method of investment appraisal is used widely in industry. The payback approach simply measures the time required for cumulative cash flows from an investment to sum to the original capital invested Like ARR, an advantage of the payback method is it is easily calculated and understood. The payback approach to investment appraisal is useful for companies that are seeking to claw back cash from investments as quickly as possible. FORMULA: Initial payment/annual cash flow OR Initial investment/annual cashflow -If cash flows are uneven the payback is calculated using the CUMULATIVE CASH FLOW over the life of the investment EXAMPLE: Original investment: £100,000 Cash flow profile: Years 1-3, £25,000 p.a. Years 4 - 5 £50,000 p.a. Year 6 - £5,000 The cumulative cash flows are therefore Year 1: £25,000 Year 2: £50,000 Year 3: £75,000 Year 4: £125,000 Year 5: £175,000 Year 6: £180,000 The original sum of £100,000 is returned via cash flows some time duing the course of Year 4. If cash flows are assumed to be even throughout the year, the cumulative cash flow £100,000 will have been earned halfway through year 4. The payback period for the investment is thus 3 years and 6 months. A disadvantage of the payback method is that it ignores the time value of money. Payback ignores the overall profitability of a project by ignoring cash flows after payback is received. There is also no definitive investment decision rule so it is subjective (not an objective measure of what is the desirable return).
Capital
An amount of finance provided to enable a business to acquire assets and sustain its operations.
Perpetuity
An annual cash flow that occurs forever - in exams it may be described as 'for the forseeable future'.
Annuity
An annuity is a constant annual cash flow for a number of years.
Average Capital Costs
Average capital = (initial capital + scrap value)/2
24) (b) (i) Explain the difference between the NPV and IRR as methods of Discounted Cash Flow Analysis (5 marks)
Discounting Cash Flow Analysis is the conversion of future cash flows to their value at one point in time - usually the present day. NPV uses discounting to calculate the present value of all cash flows associated with a project. The present value of cash outflows is then compared with the present value of cash inflows, to obtain a net present value (NPV). If the present value (PV) of cash outflows exceeds the PV of cash inflows, then the NPV will be negative. If the present value (PV) of cash inflows exceeds the PV of cash outflows, then the NPV will be negative. The rule that is applied is that invest if NPV is positive and do not invest if NPV is negative. The Internal Rate of Return (IRR) is defined as the discount rate at which the net present value equals zero. The IRR represents the effective break-even discount rate for the investment. As long as the IRR exceeds the cost of capital, then the company should invest and so, as a general rule, the higher the IRR the better. The Net Present Value is better to use to choose between two mutually exclusive projects than IRR because NPV shows gives an absolute investment decision signal. The IRR shows how far the cost of capital can go. NPV and IRR measures may sometimes contradict one another when used in relation to mutually exclusive investments. When IRR and NPV give conflicting results, the preferred alternative is the project with the highest NPV.
Accounting profits vs Cash Flows
In capital investment appraisal it is more appropriate to evaluate future cash flows than accounting profits, because: -Cash can be spent. Profits cannot actually be spent and they are only a guide to the cash that may be available. -Profit measurement is subjective, cash is real. -Cash can be used to pay dividends.
Relevant Cash Flows
For all methods of investment appraisal, with the exception of ROCE, only RELEVANT CASH FLOWS should be considered. Use future, incremental, cash-based cash flows and opportunity costs. Ignore: -sunk costs -committed costs -non-cash items -allocated items -depreciation -Future (ignore sunk costs), -Incremental (ignore committed costs and apportioned costs) -Cash-based (ignore non-cash items) -Opportunity costs (include the value of cash flow of best missed opportunities) -Ignore depreciation -Ignore interest payments on funding to avoid double counting with cost of capital -Include tax payments and receipts
Internal Rate of Return (IRR) Formula (MUST LEARN - NOT PROVIDED IN EXAM)
IRR = L + [NL/NL-NH x (H-L)] Where L = lower rate of interest H = higher rate of interest NL = NPV at lower rate of interest NH = NPV at higher rate of interest
Converting from Current Cash Flow to Money Cash Flow
Inflate using specific rate
Calculating the Payback Period
Initial payment/annual cash flow OR Initial investment/annual cashflow -If cash flows are uneven the payback is calculated using the CUMULATIVE CASH FLOW over the life of the investment
Present Value of a Perpetuity
P = Annual Cash Flow/Interest Rate P = Annual Cash Flow x 1/r
Present Value of Annuity Formula
P = Annual Cashflow x Annuity Factor P = Annual Cashflow x [1 - (1+r)⁻ⁿ]/r
Present Value Formula
PV = F /(1 + r)ⁿ = F x (1 + r)⁻ⁿ Present Value = Future Value x Discount Factor
IRR Decision Rule
Projects should be accepted if their IRR is greater than the cost of capital.
Equivalent Annual Cost
Q24 Equivalent annual cost = PV of cost of one replacement cucle/Cumulative discount factor Example Present value of cash flows ($274,582) Cumulative present value factor 3.037 Equivalent annual cost = 274,582/3.037 = $90,412
Return on Capital Employed (RoCE or Accounting Rate of Return ARR) Formula
ROCE = [Average annual profit before interest and tax/initial capital costs] x 100 -Alternatively, you may be asked to use the average capital instead of initial capital. ROCE = [Average annual profit before interest and tax/average capital costs] x 100 Average capital = (initial capital + scrap value)/2 -ROCE is expressed in percentage terms
Finding NPV with Inflation: Real Method
Real Cash Flows:Real Rate -Do not inflate cash flows. Leave them expressed in current terms (today's prices). -Discount at the real rate -Useful if given uninflated cash flows and there is a single rate of inflation
What does NPV represent?
The NPV represnt the surplus funds (after funding the investment) earned on the project, therefore: -if the NPV is positive - the project is financially viable -if the NPV is zero the project breaks even -if the NPV is negative - the project is not financially viable -if the company has two or more mutually exclusive projects under consideration it should choose the one with the highest NPV -the NPV gives the impact of the project on shareholder wealth.
Payback Approach Example: Original investment: £100,000 Cash flow profile: Years 1-3, £25,000 p.a. Years 4 - 5 £50,000 p.a. Year 6 - £5,000
The cumulative cash flows are therefore Year 1: £25,000 Year 2: £50,000 Year 3: £75,000 Year 4: £125,000 Year 5: £175,000 Year 6: £180,000 The original sum of £100,000 is returned via cash flows some time during the course of Year 4. If cash flows are assumed to be even throughout the year, the cumulative cash flow £100,000 will have been earned halfway through year 4. The payback period for the investment is thus 3 years and 6 months.
24) b ii (8 marks) non financial aspects
The optimal cycle is very three years, because this has the lowest equivalent annual cost. Non-financial aspects that need to be taken into account include, computer technology is changing very rapidly and this could mean that failure to replace annually would leave the salesmen unable to utilise the most up to date systems for business. This could negatively impact the company's competitive position.
Strengths of Using Payback Period
The payback method of investment appraisal is used widely in industry. The payback approach simply measures the time required for cumulative cash flows from an investment to sum to the original capital invested Like ARR, an advantage of the payback method is it is easily calculated and understood. The payback approach to investment appraisal is useful for companies that are seeking to claw back cash from investments as quickly as possible. -Simple to calculate and understand -Payback favours projects with quick return helps company grow minimises risk maximises liquidity -Payback uses cash flows, unlike ROCE
Advantages of NPV
Theroretically, the NPV method of investment appraisal is superior to all others. This is because: -It considers the time value of money -It is an absolute measure of return -It is based on cash flows not profits - the subjectivity of profits make them less reliable than cash flows and therefore less appropriate for decision making -It considers the whole life of the project -It should lead to maximisation of shareholders' wealth -Higher discount rates can be set of riskier projects
Annuity Factor Formula - example
[1 - (1+r)⁻ⁿ]/r 1-(1.1)⁻³/0.1 = 2.486
