The series describes the decision-making process during selecting investment projects for implementation, with an emphasis on methods for evaluating investments. The mentioned methods comprise mainly of payback period, ROI, methods based on discounting cash flows such as Net present value, Internal rate of return or Profitability index.
More complicated described methods include Discounted payback period, Modified internal rate of return, Macaulay duration or Equivalent annual annuity approach.
Throughout the article, you will also find terms like discounting, compounding, present or future value, annuity and perpetuity etc.
Investment is both acquirement of any asset or other item with the intention to obtain a future beneficial output (i.e. the process) AND the invested amount or resource that is sacrificed for the purpose of obtaining the benefits in the future.
The terms included in the investment definition can be very wide, for example:
The investments are carried out in order to:
General problems with investments:
1. Analyse the resources that can be invested. They might include:
2. Find out investment needs, formulate possible investment project and assess them in terms of whether
3. Prepare Cost/benefit analysis (CBA) and assess the investment (NPV, IRR, payback period ...).
4. Prepare the total value of investments - e.g. the summary of all investments that have been evaluated as acceptable. If there are any similar/mutually exclusive projects , it must be decided which one will be carried out.
5. If budget is limited it must be decided which projects will be realised, which postponed and which refused.
6. Monitoring of the progress of the investment project mainly in terms of:
All investments must be in line with company goals, objectives, strategy and investment policy. They should follow the analyses of strengths, weaknesses, opportunities and threats.
Cost-benefit analysis (CBA) is the analysis that is used to summarize and evaluate costs and benefits relevant with certain decision, project or investment. The main stress is on monetary costs and benefits, but non-monetary ones shall also not be neglected. The monetary effects are often discounted to adjust them for time-value effects.
CBA is used as:
They therefore include:
They therefore do not include:
There are several quantitative methods used for investment evaluation. Each of them has its advantages and disadvantages and it is not unusual to use them in combination.
It is appropriate to use the methods which can evaluate (either in itself or in combination):
The methods include:
Payback period is the method used to evaluate investment projects. It comes out from relevant profit or cash-flows and calculates the number of years (months or other periods) during which will the invested amount be repaid from the relevant income or cash inflow. Generally, investments with shorter break-even point (i.e. payback period) are better as they represent lower risk. However, payback period shall not be the only decision criterion as profitability shall be considered as well. Therefore, this investment appraisal indicator is often combined with other indicators such as ROI, NPV or IRR.
amount of the investment / annual incremental profit or cash-flow
Return on investment (ROI) is the indicator used to evaluate the investment profitability. It is calculated as the accounting profit arising as the consequence of the investment divided by the investment costs. The higher is the calculated return, the better.
Discounted cash-flow is the technique based on the concept of time value of money on which a number of investment appraisal methods are based. It comes out from future relevant cash-flows projections, discounts them to present value which is further used to calculate for example:
Time value of money is based on the assumption that each dollar earned today is worth more than in the future, and vice versa. The reasoning behind it lies in the fact that the interest would be charged on the savings in the meantime. (29)
Time value of money is incorporated to investment appraisals via discounting and compounding methods.
Discounting is the method that transforms future value (future cash flows) into present value (PV). Because of the time value of money concept, the present value of equivalent future value is lower because money possessed now is worth more than those earned in the future (it is not certain and interest would have been charged in the meantime).
Present value (PV) is the nowadays value of future cash-flows which is calculated from future value (FV) via discounting.
Discount factor can be either calculated or easily found for each possible discount rate and year in discount tables.
Annuity is a fixed payment made at regular intervals during a specified period.
When a loan is repaid in annuity, the installment usually consists of principal repayment and interest expense where the principal repayment increase and interest expense decrease over time.
How to discount annuity cash-flow?
The discount factors over the considered years can be added to reach the annuity factor which is then applied to the annual cash-flow (not to total cash-flow!). Annuity factors can be also found in discount tables.
In case of delayed annuity, the annuity discount factor shall be applied first and the obtained amount shall be discounted back to the year zero.
Perpetuity is annuity that will be received or paid for ever.
Compounding is the method that transforms present value (current cash-flows) into future value (FV). Because of the time value of money concept, the future value of equivalent present cash-flows will be higher because interest could have been charged to the cash savings over time.
Future value (FV) is the future value of the present cash-flows. Future value is calculated from present value (present cash-flows) via compounding.
The discount factor for each considered year and discount rate can be either calculated or easily found in discount tables.
Net present value (NPV) is a method for investment appraisal that is based on discounted cash-flow methodology. It shows the amount by which shareholder´s wealth would be increased. It is calculated as the total of present values of future relevant cash-flows over the project life. It comes out from relevant future cash-flows (free cash-flow) shown for each year under consideration, discounts separately each year´s net cash-flow and calculates the total net present value (NPV) over the life of the investment project. NPV of viable project shall be positive.
Assumptions for NPV calculation shall be agreed in advance. The assumptions shall be used consistently and shall include:
Period to which will the relevant cash-flows be included
Tax effects
Income tax is assessed based on tax profits, therefore income statement items need to be prepared as well as the relevant cash-flows. It is a matter of decision to which level of detail the tax effects will be calculated. But in general, tax charges on profit figures, tax relief resulting from acquired asset´s tax depreciation and the difference obtained from sale of asset at the end of the project and disposal value shall be included.
Income tax is usually (depending on the applicable tax law) payable one year in arrears and it is therefore included in the NPV proforma with one-year delay.
Working capital changes (cash to finance additional working capital)
Increased sales usually result in increase of inventory, receivables and payables levels which in total represent cash outflow, and vice versa. It is necessary not to forget about their reversal when sales begin to decrease again. Therefore, working capital changes usually go to zero over the life of the investment.
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The following sources were used:
30. Net present value (online). Citation date: 19.1.2016. Available from www: https://en.wikipedia.org/wiki/Net_present_value
32. Obaidullah Jan, ACA, CFA. NPV vs. IRR (online). Citation date: 19.1.2016. Available from www: http://accountingexplained.com/managerial/capital-budgeting/npv-vs-irr
Discount rate is the rate of return (interest rate) used in discounted cash-flow calculations. Most often, it is cost of capital, but other rates are also possible.
Discount rate can be:
The higher is the discount rate, the lower NPV will be achieved and it is less probable that the project will be accepted.
The right choice of discount rate depends on the purpose. To decide whether the investment project will add value, WACC will be sufficient. Rate of return on alternative investment opportunity may be appropriate when deciding between mutually exclusive projects. (30)
With respect of the inflation covered, discount rate can be either:
Nominal discount rate includes inflation and can be derived by Fisher equation as:
(1 + real discount rate) * (1 + inflation rate) – 1
There are two possibilities how to incorporate inflation to NPV calculation:
With respect of the income tax rate covered, discount rate can be either:
If relevant cash-flows in the calculation include the tax effects, after-tax discount rate shall be used.
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The sources:
30. Net present value (online). Citation date: 19.1.2016. Available from www: https://en.wikipedia.org/wiki/Net_present_value
31. Obaidullah Jan, ACA, CFA. NPV and inflation (online). Citation date: 19.1.2016. Available from www: http://accountingexplained.com/managerial/capital-budgeting/npv-and-inflation
Internal rate of return is method used for investment appraisal that calculates the rate of return that is expected to be achieved by the project. IRR is related with NPV method as it is the discount rate at which NPV is zero.
CF_{1}…..cash-flow of year 1
CF_{2}…..cash-flow of year 2 (33)
IRR can alternatively be calculated by interpolation:
IRR_{1} & NPV_{1}...............lower discount rate and its NPV
IRR_{2 }& NPV_{2}...............higher discount rate and its NPV
IRR works well if cash-flows have common distribution, i.e. high cash-outflow at the beginning followed by a series of cash-inflows. But if the cash-flow distribution is uncommon (e.g. negative cash-flow during the project life), it can lead to either to NPV increase with increasing IRR (not decrease) or existence of multiple IRRs. All this can result in wrong decision. NPV should be given priority in decision-making in such cases. (32)
Advantages and disadvantages of IRR compared to NPV can be easily derived from article about advantages and disadvantages of NPV.
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Sources:
32. Obaidullah Jan, ACA, CFA. NPV vs. IRR (online). Citation date: 19.1.2016. Available from www: http://accountingexplained.com/managerial/capital-budgeting/npv-vs-irr
33. Irfanullah Jan. Internal rate of return (online). Citation date: 19.1.2016. Available from www: http://accountingexplained.com/managerial/capital-budgeting/irr
Profitability index is a method used for investment appraisal that is based on discounted cash-flow methodology. It calculates the present value of cash flows generated by the project per a unit of capital outlay. As such it is helpful in decision-making in situations when the company cannot undertake all acceptable projects due to the limited budget.
NPV / present value of investment
PI = 1 → NPV = 0 → IRR = discount rate
Modified internal rate of return (MIRR) is less frequently used method for investment appraisal that is based on discounted and compounded cash-flow methodology. It was developed to overcome the following disadvantages of internal rate of return (IRR):
There are many ways to calculate MIRR - the easiest one is based on the following steps:
1. Division of the project cash-flow into two stages:
capital outlay stage – usually the first year, but it can involve cash-outflows of further years as well
cash-inflow stage – the periods with positive cash-flow
2. Calculation of present value (PV) of capital outlay stage using the entity´s financing costs (thus discount the capital outlay/s to now; how to do it is described within the article about NPV)
3. Calculation of future value (FV) of cash-inflow stage using the entity´s cost of capital (thus compound the cash-inflows to year when the useful life of investment ends)
4. Using the formula below to calculate MIRR. (34)
The biggest disadvantage of MIRR is that it is unfamiliar and is used very rarely.
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Sources:
34. Modified Internal Rate of Return – MIRR (online). Citation date: 20.1.2016. Available from www: http://www.investopedia.com/terms/m/mirr.asp
Discounted payback period (or Adjusted payback period) is the method used to evaluate the investments. It was developed to overcome the biggest disadvantages of traditional payback period method that it ignores time value of money and is possibly calculated based on profit, not cash-flow. Discounted payback therefore comes out from the same formula, but discounts the annual relevant cash-flow to present value.
PV of investment / PV of annual differential cash-flow
However, other payback period disadvantages, except for the use of cash-flow and discounting it, remain.
Macauley duration is an indicator of bond´s sensitivity to interest changes. It can be alternatively used as a method for investment project appraisal. (35)
The steps for calculation:
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Sources:
35. Macaulay Duration (online). Citation date: 20.1.2016. Available from www: http://www.investinganswers.com/financial-dictionary/bonds/macaulay-duration-5079
Equivalent annual annuity (EAA) is the method used to decide which mutually exclusive investment project with unequal life shall be accepted.
NPV * annuity factor for the number of project life years
NPV......net present value
The project with the highest EAA shall be accepted. (36)
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Sources:
36. Equivalent Annual Annuity Approach – EAA (online). Citation date: 21.1.2016. Available from www: http://www.investopedia.com/terms/e/equivalent-annual-annuity-approach.asp
Adjusted present value (APV) is very similar method to net present value (NPV). It is used for project appraisal mainly if:
The steps for APV calculation are as follows
1. Calculate base-case NPV. It is traditional NPV calculation with one exception - unlevered cost of equity is used as discount rate (not cost of entire capital). This "base case NPV" says which value the project brings in excess of this cost of equity. Unlevered cost of equity is calculated by replacing beta of our company in traditional CAPM with unlevered beta (β_{u} ) of company facing similar business risk operating in the industry where we intend to diversify
2. Calculate net present value (NPV) of the projects side-financing effects:
+ net present value of tax relief on debt interest paid
- net present value of issue costs on equity or debt
+ net present value of tax relief on issue costs above
+/- other possible effects, e.g. subsidies
3. Add base-case NPV and the present value of side-financing effects. If > 0, the project is considered as viable. (44)
The biggest disadvantage is that it does consider the increased financial risk resulting from higher indebtedness. (44)
The company intends to diversify to the new industry with average beta of 1,25, equity/debt ratio 60:40 and expected market return 14%. Risk-free rate is 5% and the interest rate 9%. The investment value is € 500 (undepreciated, immediately expensed) and annual cash-inflows are € 150, € 200, € 200, € 100 and € 70 respectively. Project equity/debt ratio is 30:70. Income tax rate is 15%.
1. Base case NPV:
β_{u} = 1,25 / ((1+ (1-0,15) * (40/60)) = 1,25 / 1,57 = 0,8
K_{e }= 5% + 0,8 * (14% - 5%) = 12,2% (rounded to 12%)
2. NPV of the projects side-financing effects:
debt value = 70% * 500 = 350
annual interest = 9% * 350 = 31,5
tax relief on annual interest = 31,5 * 15% = 4,7
PV of tax relief on annual interest = 4,7 * 3,89 (9% annuity factor for 5 years) = 18
3. APV = 34 + 18 = + 52 ….project is viable
There are several approaches to investment project appraisals that can be undertaken if risk or uncertainty is a significant factor: