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  • Writer's pictureAgnes Sopel

Making capital investment decisions - PP, ARR, NPV and IRR

Updated: May 8, 2023


In this blog we will assess on how business should assess potential investments in new plant, machinery, buildings and other long-term assets.


Investment decisions


One of the most essential features of investment decisions is time. We determine the outlay which is typically a single large amount of money and the benefits arrive in a series of small amounts over a certain period.


Large amounts of resources are often involved and laying out a significant proportion of resources. Additionally, relatively long timescales are involved and there is a room for things to go wrong. Once decision is undertaken, it is difficult to bail out of it.


The level of annual net investment is different from one business to another. Expenditure of additional non-current assets can vary. But investment involves a significant outlay of current assets to support it.


Investment decisions must be consistent with the overall strategy of the organisation. Generally to maximise the wealth of the owners.


These investment decisions are important and need to be appropriately evaluated and used.

Organisations may use "Accounting rate of return" , "Payback period", Net Present Value" and/or "Internal rate of return".


Businesses may use variance of these methods. Small businesses may rely on 'gut feeling" of managers..


Successful businesses set a clear strategic framework for the selection of investment projects. The best investment projects are those, that use business internal strengths, for example, skills, experience or access to finance. This combined with the opportunities available can make for great strategic decisions and give competitive advantage.


Let's summarise the most common assessment methods with more examples.


Accounting Rate of Return (ARR)


This method takes the average profit that an investment will generate expressed in a percentage of the average investment made over the life of the project.


To calculate ARR, we need two pieces of information:


  1. Annual average operating profit

  2. The average investment

The formula is as follows:


ARR = (Average annual operating profit / Average investment to earn that profit) X100%


For example, we have a cost of new machine of £100,000 with disposal value of £20,000. If the average annual operating profit for 5 years is £40,000 (before depreciation) - ( lets say 1st year £20,000 + 2nd year - £40,000 , 3rd year - £60,000, 4th year £20,000 and 5th year - £20,000) and we use straight 'line depreciation charge' ( it is equal the annual amounts ((£100,000 - £20,000)/5) of £16,000, then the average annual operating profit would be £24,000. So the average investment would be the "Cost of machine" + "Disposal value" / 2 = (£10,000 + £20,000 )/ 2 = £60,000


The ARR therefore is (£24,000 / £60,000) X 100% = 40%


Generally, for project to be accepted a target ARR needs to be achieved. When there are competing projects, the one with higher rate would be chosen. In the example, for the 40% to be accepted, we need to compare if it is acceptable for the business.


If another company, for example consider an investment of ten delivery vans with cost of £15,000 each with annual running cost of £50,000 for each van including delivery driver's salary. The vans are expected to operate for 6 years with a disposal of £3,000 per van.

Comparable carrier, will charge £530,000 per year for the next 6 years.


We can calculate the ARR for the vans. The vans will save the business £30,000 per year (£530,000 - (£50,000 X 10).



Source: Atrill P., 2019, "Accounting for non-accounting students", Pearson Education UK


The total annual depreciation expense with 'straight line method', would be £20,000 ((£150,000 - £30,000)/6). Therefore, the average annual savings (after depreciation) os £10,000 (£30,000 - £20,000)


We can calculate the average investment ((£150,000 + £30,000)/2) of £90,000.

Then the ARR would be £10,000 / £90,000 = 11.1%


ARR takes the approach to measure business performance, it looks at operating profit and costs of assets. The ARR target could be based on the overall ROCE achieved for the entire business so it is based on the industry average ROCE.


ARR, however, does not take into consideration of the time factor and the cost of financing the project. If competing projects return the same ARR, we could choose the shortest project to achieve the return.


ARR is based on the accounting profits, but measuring the profits cash flows are important. Accounting profits would be more appropriate to assess an achievement. We must also ensure that ARR target is specified. If not objective target is specified it will depend on the judgement of the managers.


Payback Period (PP)


This is another method for apprising possible investments. This is the time taken for initial investment to be repaid. This method takes into account and deals with cash rather then accounting profit.


For example with the cost of machine of £100,000 and operating profits:


  1. 1st year - £20,000

  2. 2nd year - £40,000

  3. 3rd year - £60,000

  4. 4th year - £60,000

  5. 5th year - £20,000

And disposal value of £20,000


All of those figures are the amounts of cash paid and received.


The payback period can be calculated of the cumulative cash flows.



Source: Atrill P., 2019, "Accounting for non-accounting students", Pearson


The cash flow becomes positive at the end of 3rd year, and the PP would be 2 2/3 years.


Generally, for a project to be acceptable, it should have a payback period no longer then the maximum payback period set by the business. If there is two or more competing projects, the one with shortest payback period should be accepted.


For example, a company has a payback period of of 4 years. Below are the inflows and outflows that are expected to be.



Source: Atrill P., 2019, "Accounting for non-accounting students", Pearson


The payback period here is 5 years.


The logic of using PP is that projects that can recoup their costs quickly are economically more attractive then those with longer payback periods. This method is quick and easy to calculate. It is an improvement from ARR as it uses cashflow and takes time into account. It does, however, ignore the payback after the accounting period which could be higher and more beneficial then the payback time.


This method is concerned with how quickly the initial investment can be recouped, but it does not account for longer period. Cash arising after the payback period may be important.


The PP method provides a way of dealing with risk and it is not concerned with maximising the wealth of the business owners.


Net Present Value (NPV)


We need methods to account for both the costs and benefits of an investment opportunity as well as make a logical allowance for timing of those costs and benefits.



For example with the cost of machine of £100,000 and operating profits:


  1. 1st year - £20,000

  2. 2nd year - £40,000

  3. 3rd year - £60,000

  4. 4th year - £60,000

  5. 5th year - £20,000

And disposal value of £20,000


If we give it a financial objective of maximising owners wealth. We can simply compare the cash inflows (£220,000) to cash outflows (£100,000). We can then make a simple assumption that we should go ahead with the project as it generates £120,000. However, it cannot be as simple, because cash outflows arise immediately and inflows in different times.

Here, the time is important because today £100 may not be worth £100 in 5 years time. Income forgone represents an opportunity costs. An investment must exceed the opportunity cost so it is worthwhile.


We know that an investment exposes us to risk as things may not turn out as expected. We can determine the risk premium and we cannot simply compare cash inflows and outflows in different times. If for example, the sample company could invest the money in another project with 20% return a year. The business should be prepared to accept a lower amount if it could be received immediately. This is it should be prepared to accept amount that, with year's income will grow to £20,000.


Therefore, we need to calculate a present value (PV) for each year of the investment.


Source: Atrill P., 2019, "Accounting for non-accounting students", Pearson


Now, to assess on whether the project is acceptable, we need to calculate NPV. As we can see the NPV is positive, so we should accept the project and buy the machine.

To deduct each PV, we have taken the relevant cashflow and multiplied by 1/(1+r)n, but we can use table below to calculate the same factor.



It is called, discount factor. If a project has a negative value this means that the present value of benefits from investments are less then the initial outlay.

The VPN is the opportunity cost finance and it offers a better approach then ARR and PP. This is mainly because it accounts for the timing of the cashflows, all of the relevant cashflows and is aligned with the business objectives.

NPV is known for one of the most logical methods to make business decisions about investments and productive assets. It accounts for value discounted of all future cashflows from the project or asset concerned.


Internal Rate of Return (IRR)


This method is closely related to NPV as it involves the discounted cashflows. The IRR of an investment is the discount rate that, when applied to future cashflows will produce NPV of zero. It represents the yield of the investment.


IRR cannot usually be calculated directly and trial and error is normally adopted.


Let's try a higher rate of 30% for our example.



Source: Atrill P., 2019, "Accounting for non-accounting students", Pearson


We have reduced NPV to -£1.88. Since the IRR is the discount rate that will give us NPV at zero, we can already conclude that the IRR will be around 30%.


Generally for a project to be accepted, it must meet the minimum IRR requirements. This is often known as 'hurdle rate' . Where there are competing projects, the one with higher IRR should be selected.


IRR for investment projects can be considerate. A study of returns made on the London Stock exchange shows an average return of 5.5%.


With IRR method, all cashflows are taken into account as well as time is logically handled. However, this method does not directly answer the question of wealth generation and can lead to wrong decisions being made.


Summary


When undertaking an investment appraisals we should bear in mind:


* Relevant costs. We should take into account only all the relevant costs. This means that all past costs and common future costs should be ignored.


* Taxation. We need to be interested in after-tax returns. Profits from projects will be taxed and the tax rate is often significant. It is, therefore, an important consideration when making investment decisions.


* Cash flows, not profit flows. Some assessments may only consist figures related to profits and this need to be adjusted for cashflows, for example including depreciation.


* Working capital adjustment. Project may increase the trade receivables and inventories less payables).


* Year-end assumption. The assumption that cashflows arise at the end of the year. This assumption is unrealistic.


* Interest payments. When using NPV and IRR interests payed should not be taken into account in deriving cashflows. Discounting already takes into account the interest.






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