Investment appraisals

Last updated: 11.11.2016

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 object of investment can be acquired both through buying or own production, construction or development
  • the asset or other item acquired may include capitalized investments (long-term assets), inventories, securities or just incurring costs
  • future beneficial output may include both quantitative or qualitative benefits:
    • quantitative:
      • additional income such as sales revenue, interest or dividends 
      • cost savings – e.g. in payroll costs or material production costs due to more efficient operation 
    • qualitative:
      • time savings – time can be devoted to more strategic issues
      • increase of market share
      • higher staff motivation or customer satisfaction
      • adoption of corporate social responsibility concept
      • easier and improved decision-making (e.g. due to more proficient economic software used)
      • more flexibility 
      • better reputation
  • the sacrificed resource can be money, time or effort


The investments are carried out in order to:

  • increase wealth
  • avoid the negative impact of inflation which reduces the purchasing power over time
  • avoid the effect of opportunity costs (when the money is not used for their best possible use)


General problems with investments:

  • sacrifice the resources now, whereas economic benefits will be obtained later
  • risk/uncertainty is involved
  • deciding between mutually exclusive investments

Steps involved in investment decision-making

1. Analyse the resources that can be invested. They might include:

  • part of equity that can be paid out – e.g. retained earnings
  • other sources – e.g. loan, issue of bonds of shares

2. Find out investment needs, formulate possible investment project and assess them in terms of whether 

  • it enhances competitive advantage and is acceptable to shareholders
  • fits with the entity´s goals, objectives, strategy, investment policy and resources available
  • there are possible alternatives

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:

  • timing
  • spending not exceeding the budget
  • achieving the planned benefits and not exceeding the risks 


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)

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:

  • a quantitative summary of changes resulting from the evaluated decision/project/investment
  • part of feasibility analysis
    • a basis for the calculation of indicators used for decision/project/investment evaluation  (such as NPV, IRR, ROI, payback period) and making a decision whether or not to accept it
  • basis for preparation project/investment plan


The relevant costs and benefits (or cash outflows and inflows) are only those that are associated with the decision/project/investment. 


They therefore include:

  • differential future costs and benefits
  • opportunity costs
  • sales value at the disposal of the investment
  • tax effects

They therefore do not include:

  • past (sunk) costs
  • irrelevant (uncontrollable) costs
  • and in case of discounted cash-flow method also:
    • non-cash costs and income
    • interest charges as they are already covered in the discount rate

Methods for investment evaluation

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):

  • payback – the shorter period, the better (lower risk)
  • investment profitability (rate of return) – the higher, the better


The methods include:

Payback period (PP)

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.


The resulting payback period for the viable investment shall be shorter than:

  • payback period defined in investment directive
  • payback period of alternative projects/investments (unless the decision criterion is profitability)


Calculation formula

amount of the investment / annual incremental profit or cash-flow



  • it is very simple
  • it is based on cash-flow (if it is) and not profit, which is easy to manipulate
  • it focuses on risk as it leads to acceptance shorter-term projects (longer projects are more risky)



  • the investment usually generates benefits also after its payback and this cash-flow is not considered
  • timing of cash-flow is irrelevant and cash-flow is not discounted, therefore time value of money is ignored – this disadvantage can partially be resolved by Adjusted (discounted) payback period method
  • the only decision criteria is time, but the alternative projects with longer payback might have much higher return



Return on investment (ROI)

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.


ROI formula is either the same or very similar to ROCE. The differences between the two indicators can reside in

  • nominator: ROI mostly uses net profit, while ROCE EBIT (but not a condition!)
  • denominator: ROI is used to evaluate the investment projects or performance of parts of the company (i.e. invested amount is in the denominator), while ROCE evaluates the profitability of the entire company (i.e. capital employed is in the denominator)


ROI formulas 


The resulting ROI for the viable investment shall be higher than

  • minimum return defined in investment directive
  • return of alternative projects/investments (unless other methods are used for evaluation)
  • in case of total profit / total investment formula higher than 1 (incremental profit is higher than the investment)


Advantages of ROI

  • ROI is easy to understand and the calculation methodology is in line with the overall company ROCE formula (if the same measure of profit is used)
  • it considers all costs and incomes incurred over the entire life of the project


Disadvantages of ROI

  • it is not based on cash-flow, but profit which is easy to manipulate
  • timing of costs and benefits is irrelevant and profit is not discounted, therefore time value of money is ignored
  • it ignores to evaluate the length of the project and longer projects are more risky – possible solution: when compared to alternative projects with different life, it can be resolved by calculating average annual ROI (i.e. by dividing ROI by the number of years included)


Discounted cash-flow (DCF)

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

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)

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.


Present value (PV) formula for perpetuity



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)

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)

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.

  • if NPV > 0 → the investment adds value to the company → can be accepted (not necessarily must be, because there can be alternative projects yielding higher NPV (30) or budget can be insufficient)
  • if NPV < 0 → the investment does not add value to the company → shall be refused


Advantages of NPV compared to investment appraisal methods not prepared on the basis of discounted cash-flow

  • it considers all relevant cash inflows and outflows over the entire life of the project
  • it is based on cash-flow, not profit which is easy to manipulate
  • considers timing of cash-flows and discounts them, therefore respects time value of money concept (gives more emphasis on earlier cash-flows)
  • allows incorporation of higher risk premium to more risky projects


Advantages of NPV compared to IRR

  • NPV considers the size of the investment, while IRR tends to prefer high return percentages irrespective of the absolute amount of investment and return
  • it is easy to incorporate different discount rates to a single NPV calculation, not to IRR (often the case in longer-term projects)
  • NPV is easier to calculate than IRR
  • NPV is based on more realistic assumption that project cash-flows will be reinvested at discount rate (mostly cost of capital), but IRR unrealistically assumes that it will be reinvested at (higher) IRR (32)
  • NPV is more advanced to IRR and shall be thus given priority if the two methods give conflicting decision. However, NPV and IRR most often lead to the same decision. But not always. The reason for differences often resides in uncommon cash-flow distribution (there is negative cash-flow also during the project life, not just at the beginning. The project might then have more IRRs or NPV can increase with increasing IRR (not vice versa as expected). Therefore, IRR can under these circumstances lead to wrong decisions. (32)

Disadvantages of NPV

  • discount rate must be calculated and it can be difficult
  • difficult to explain, specifically in the context of the used discount rate
  • NPV method itself often leads to rejection of low-value projects as these usually have lower NPV than projects with higher value
  • despite of all NPV advantages, IRR is in practice more widely used than NPV




The relevant cash-flows DO NOT INCLUDE INTEREST! Otherwise, they would be double counted – once through those interest charges and for the second time through discount factor. (30)



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
  • treatment of tax effects
  • treatment of changes in working capital (inventories, receivables, payables)
  • definition of discount rate


Period to which will the relevant cash-flows be included

  • generally:
    • if the cash-flow occurs at the beginning of the period, it shall be covered into (the end) of the previous period
    • if the cash-flow occurs at the end of the period, it shall be covered into that period
    • but if the cash-flow occurs during the period – consistent treatment must be adopted; usually taken to that period
  • it must be decided what will be the starting year (year 1) – it can be purchase of the asset or first cash inflow generated from the project
  • most often, purchase of asset (investment) is placed into the year 0 and it is therefore not discounted (or discounted with discount factor of 1) and first cash inflow generated from the project is placed to year 1
  • tax effects are usually delayed as the taxes are paid in the following year
  • working capital changes usually form part the total investment (investment value is the total of capital expenditure and initial working capital), then change with the changed sales revenues during the project life and reverse at the end of the investment useful life (however, it depends on the project type)


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. 




The following sources were used:

30. Net present value (online).  Citation date: 19.1.2016. Available from www:

32. Obaidullah Jan, ACA, CFA. NPV vs. IRR (online). Citation date: 19.1.2016. Available from www:


Discount rate

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:

  • cost of capital, most often WACC – the most common discount rate
  • specified minimum target rate of return (so called hurdle rate)
  • rate of return on alternative investment opportunity
  • company overall ROCE/ROI – compared to WACC it allows for more risks and discount rate is therefore higher
  • current or future expected market interest rate (30)

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 (money)
  • real


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:

  1. Using nominal future cash-flows (i.e. cash-flow is related to future period price level and is therefore expressed in values that already incorporate inflation) and discounting them with nominal discount rate.
  2. Using real cash-flows (i.e. cash-flow is related to the starting period price level and therefore does not consider inflation) and discounting them with real discount rate. (31)


 With respect of the income tax rate covered, discount rate can be either:

  • pre-tax
  • post-tax

If relevant cash-flows in the calculation include the tax effects, after-tax discount rate shall be used.



The sources:

30. Net present value (online).  Citation date: 19.1.2016. Available from www:

31. Obaidullah Jan, ACA, CFA. NPV and inflation (online). Citation date: 19.1.2016. Available from www:

Internal rate of return (IRR)

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.

  • if IRR > target rate (often WACC) → the investment adds value to the company → can be accepted (not necessarily must be, because there can be alternative projects yielding higher IRR or budget can be insufficient)
  • if IRR < target rate (often WACC)  → the investment does not add value to the company → shall be refused


IRR formula


CF1… of year 1

CF2… of year 2 (33)


IRR can alternatively be calculated by interpolation:

  1. Rough estimate of IRR and calculation of NPV with this rate as discount rate.
  2. Calculation of another NPV using following discount rates:
    • if NPV is positive, with a little higher discount rate
    • if NPV is negative, with a little lower discount rate (33)
  3. Calculation of IRR by using the formula:

IRR1 & NPV1...............lower discount rate and its NPV

IRR2 & NPV2...............higher discount rate and its NPV


To be drawn by the scheme 



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.




32. Obaidullah Jan, ACA, CFA. NPV vs. IRR (online). Citation date: 19.1.2016. Available from www:

33. Irfanullah Jan. Internal rate of return (online). Citation date: 19.1.2016. Available from www:

Profitability index (PI) / Benefit-cost ratio

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


  • if PI > 1 → the investment adds value to the company → can be accepted (not necessarily must be, because there can be alternative projects having higher PI or budget can be insufficient)
  • if PI < 1 → the investment does not add value to the company → shall be refused

Modified internal rate of return (MIRR)

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):

  • complex calculation
  • unrealistic assumption that the project cash-flows will be reinvested at IRR – MIRR uses cost of capital and financing costs instead (34)


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)


MIRR formula

The biggest disadvantage of MIRR is that it is unfamiliar and is used very rarely.




34. Modified Internal Rate of Return – MIRR (online). Citation date: 20.1.2016. Available from www:

Discounted payback period / Adjusted payback period

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.


Calculation formula

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

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:

  1. Preparation of the relevant cash-flow table for each period – see the possible proforma in the article about NPV.
  2. Calculation of present value of relevant cash inflows (not capital outflows!) for each period and their aggregation.
  3. Weighting each period´s relevant cash inflows (not capital outflows!) with the time factor (= the year order to which the cash inflow relates; e.g. multiplication of cash inflows in year 3 with a factor of 3) or bond´s current market value, calculation of their present value for each year and sum them up.
  4. Calculation of the duration as division of the results from step 3 by step 2:  total weighted present value of cash inflows / total present value of cash inflows (35)




35. Macaulay Duration (online). Citation date: 20.1.2016. Available from www:

Equivalent annual annuity (EAA)

Equivalent annual annuity (EAA) is the method used to decide which mutually exclusive investment project with unequal life shall be accepted.


EAA formula

NPV * annuity factor for the number of project life years present value


The project with the highest EAA shall be accepted. (36)




36. Equivalent Annual Annuity Approach – EAA (online). Citation date: 21.1.2016. Available from www:

Adjusted present value (APV)

Adjusted present value (APV) is very similar method to net present value (NPV). It is used for project appraisal mainly if:

  • the existing capital structure will be significantly changed by undertaking the project - compared to traditional NPV technique, the decision based on APV takes into account also the financial effects of specific financing structure of the project
  • here are frequently assumptions about the project financing structure - it is easy to recalculate APV with different debt parameters (44)

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 (βu ) 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:

βu = 1,25 / ((1+ (1-0,15) * (40/60)) = 1,25 / 1,57 = 0,8

Ke = 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


How to deal with risk in investment appraisals

There are several approaches to investment project appraisals that can be undertaken if risk or uncertainty is a significant factor:

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