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# Accounting Rate of Return

### 1.0 INTRODUCTION

Investment appraisal also called capital budgeting is a planning process used to assess whether the capital expenditure on a particular project will be beneficial for the organization or not. These techniques can be used to evaluate projects in both the private and public sector companies. Many formal methods are used in capital budgeting but the most commonly used are Accounting Rate of Return (ARR), Payback Period, Discounted Payback Period, Net Present Value (NPV) and Internal Rate of Return (IRR). These techniques will help the company to answer to some questions like how long will it be before the investment starts to yield returns? How long will it take to pay back the investment? These methods use the incremental cash flows from each one of the potential investment, or project Techniques based on accounting earnings and accounting rules. In another word these are some decision making tools for the organization. (businesslink website 2010)[1]

### 2.0 Accounting Rate of Return (ARR)

Accounting Rate of return is a method of estimating the rate of return from an investment using a straight-line approach (not discounted or compounded). The investment inflows are totalled and the investment costs subtracted to derive the profit. The profit is divided by the number of years invested, then by the investment cost, to estimate an annual rate of return. This method is not as sophisticated as the discounted approach, which is used by modern accountants. (Refer to appendix1)

The most important advantage of ARR is its simplicity. This makes it relatively easy to understand and to calculate. This method is also realistic and easy to construct. There is in addition a connection with some accounting measures that are commonly used. The Average Rate of Return is comparable to the Return on Capital Employed or return on investment; this may make the business planners to understand the ARR easily. The ARR is expressed in percentage terms and this, again, may make it easier for managers to use. It takes all the years into account when making an investment decision.(Moneyterms website 2010)[2]

First of all, the ARR does not take into account the time value of money the value of cashflows that means it does not diminish with time. Secondly, the profit concept can be very subjective, varying with specific accounting practice and the capitalisation of project costs. As a result, the ARR calculation for identical projects would be likely to result in different outcomes from business to business. Thirdly, there is no definitive signal given by the ARR to help managers decide whether or not to invest. This lack of a guide for decision making means that investment decisions remain subjective.(allbusiness website 2010)[3]

### 3.0 Discounted payback method

Discounted payback method is an investment tool which calculate the number of years it will takes for an investment to recover its initial cost after taking into account, interest, inflation and other matters affected by the time value of money, in order to be worthwhile to the investor. It differs a little bit from the payback period rule, which only accounts for cash flows resulting from an investment and does not take into account the time value of money.(Refer to appendix 2)

The discounted payback method takes into consideration the time value of money and the riskiness of the projects through the cost of capital. When the project has a long payback that means your capital is tied up, therefore you can easily determine from which project your capital is not going to be tied up by choosing the one who will take less time to get your investment back. It uses the cash flows which are more objective compare to profits.(financethinkanddone website 2010)[4]

This method ignores the cash flows beyond the discounted payback period good project may be rejected. It's also required and estimates of the cost of capital in order to calculate payback. It is not expressed in terms of percentage and therefore it may be difficult to know the return on investment.

### 4.0 Net present value

The Net Present Value method calculates the present values for all future cash flows of projects. The discount rate can be the Weighted Average Cost of Capital (Ko) or it could be any cost of capital depending on the risk of the project in consideration. This type of appraisal technique is regarded superior to the Accounting Rate of Return and the payback period, however there are certain assumptions, on which this technique is based, making its evaluation less reliable. The net present value includes all cash flows including initial cash flows such as the cost of purchasing an asset, while a present value does not.( Refer to appendix 3)

The net present value use cash flows hence it is a liquidity measure. It takes into account time value of money that is why the cash flows are discounted. The overall projects returns are assessed and it also considers the risk of future cash flows through the cost of capital.

The Net Present Value calculation is very sensitive to the discount rate and a small change in the discount rates can causes a large change in the NPV. As the estimation of the appropriate discount rate is uncertain, this makes NPV result very uncertain. NPV also often relies on unsure forecasts of future cash flows. It might be difficult to determine the rate of discount especially when multiple source of finance is used.

### 5.0 Internal rate of return

Internal Rate of Return is a method use to calculate the rate at which the NPV of a project equals to zero. According to this method when the cost of capital of a company is more than the IRR, the project will be rejected and if it is lower than the cost of capital it is likely to be accepted. IRR and NPV concepts are linked because we calculate the NPV first and then we use that result to calculate the IRR.

This technique takes into consideration the overall returns for the whole project duration. It takes in consideration the time value of money and use cash flows which are more objective than profits. Because it is expressed in form of percentage and it is in the form of return. Easy and understandable, it does not have the drawbacks of the ARR and the payback period, both of which ignore the time value of money.

IRR can lead to conflicting decisions a project with a higher positive NPV can have a lower IRR compare to another project with a lower positive NPV but higher IRR So unless the calculated IRR is a reasonable rate for reinvestment of future cash flows, it should not be used as a index to accept or reject a project. It may not give the value maximizing decision when used to choose projects when there is capital rationing. We cannot use it in a situation in which the sign of the cash flows of a project change more than once during the project life. (Muhammad Ansar, 2002)[5]

### 6.0 Financial factors

Financial factors are all those factors were money is involved. As the business environment keeps on changing, managers need to thoroughly scan the environment before investing in a project. The reason is to identify the major factors that can be detrimental to the organization from reaping the potential rewards from theses particulars investments proposals. This will help the organization to views and identify threats and opportunities while improving long and short term planning. These factors include Forex, inflation and taxation.

### 6.1 Forex

The purpose of the foreign exchange market Forex is to support international trade and investment from one country to another one. The foreign exchange market allows businesses to convert one currency to another foreign currency. For instance, it permits the U.S. businesses to import European goods and pay Euro, even though the business's income is in US Dollar. Some experts, however, believe that the unrestricted speculative movement of currencies by large financial institutions such as hedge funds impedes the markets from correcting global current account imbalances. This carry trade may also disadvantage some counties in term of loss of competitiveness. (Efficientforextrading website, 2010)[6]

### 6.2 Inflation

Inflation is an increase in the general level of prices of goods and services in the economy of a country over a period of time. When the price level rises, each unit of currency buys less goods and services; therefore, annual inflation is also an erosion in the purchasing power of money in that particular country with a loss of real value in the internal medium of exchange and unit of account in the economy. The main measure of price inflation is the inflation rate, the annualized percentage change in a general price index over time.(investopedia website 2010)[7]

### 6.3 Taxation

Taxation is very important for investors all over the world it is one of the key element that they are looking at therefore the board of directors of Polasian will look closely at it. The profit of the organization will be taxed. They will be also interested to know if there is any tax incentive given by the government for a new set up company in that country. Taxation should be taken in consideration in order to make an investment for a project. IN the UK the corporate tax is 28%.(hmrc website 2010)[8]

### 7.0 Non financial factors

Although the financial case for making an investment is a vital part of the decision-making process, non-financial factors can also be important and need to be taking into account while deciding for an investment. The key non-financial factors can include:

* meeting the requirements of current and future legislation

* matching industry standards and good practice

* improving staff morale, making it easier to recruit and retain employees

* improving relationships with suppliers and customers

* developing the capabilities of your business, for example by building skills and experience in new areas or strengthening management systems

* anticipating and dealing with future threats, for example by protecting intellectual property against potential competition

For example, you might need to take into account the environmental impact of a potential investment. To some degree, this may be reflected in financial factors: for example, the energy savings offered by new machinery. But other things such asthe effect onyour reputation will also be important.(Accountantnextdoor website, 2010) [9]

### Appendix 1: Accounting rate of return (ARR)

Proposal 1

Proposal 2

Proposal3

Periods

Net cash flows £000

Net cash flows £000

Net cash flows £000

1

70

200

(60)

2

(120)

(400)

0

3

380

473

(140)

4

840

(6)

910

5

840

270

910

6

620

780

429

7

1500

1030

140

8

660

890

180

Total

4790

3237

2369

Average profits:

Proposal 1 Proposal 2 Proposal 3

4790 / 8 = £598.75 3237 / 8 = £404.625 2369 / 8 = £ 296.125

ARR Proposal 1 ARR Proposal 2 ARR Proposal 3

598.75 / 1700 = 0.3522 404.625 / 1700 = 0.2380 296.125 / 1700 = 0.1742

Or 35.22% Or 23.8% Or 17.42%

### A) Cost of capital

Cost of equity Ke = + g

= + 0.02

Ke = 0.0608 or 6.08%

Cost of preference share capital Kp = X 100

= X 100

Kp = 5%

Cost of debt with tax Kd = (1- t) X 100

= (1- 0.28) X 100

Kd = 2%

Weighted average cost of capital Ko

Ko = + +

Ko = 4.9%

### B) Discounted payback

Proposal 1

Periods

Net cash flows £000

Discounted at 4.9%

Present value £000

Cumulative £000

0

(1700)

1

(1700)

(1700)

1

70

0.953288847

66.73021926

(1633.27)

2

(120)

0.908759625

(109.051155)

(1742.32)

3

380

0.866310415

329.1979575

(1413.12)

4

840

0.825844056

693.7090069

(719.414)

5

840

0.787267927

661.305059

(58.1089)

6

620

0.750493734

465.3061153

407.1972

7

1500

0.715437306

1073.15596

1480.353

8

660

0.682018405

450.132147

1930.485

The payback period of proposal 1 is 5 years 2months

(-58.1089 / 465.3061153 × 12) = 2months

### Proposal 2

Periods

Net cash flows £000

Discounted at 4.9%

Present value £000

Cumulative £000

0

(1700)

1

(1700)

(1700)

1

200

0.953288847

190.6577693

(1509.34)

2

(400)

0.908759625

(363.50385)

(1872.85)

3

473

0.866310415

409.7648261

(1463.08)

4

(6)

0.825844056

(4.955064335)

(1468.04)

5

270

0.787267927

212.5623404

(1255.47)

6

780

0.750493734

585.3851128

(670.089)

7

1030

0.715437306

736.9004256

66.81156

8

890

0.682018405

606.9963801

673.8079

The payback period of proposal 2 is 6 years 11 months (-670.089 / 736.9004256 × 12) = 11 months

### Proposal 3

Periods

Net cash flows £000

Discounted at 4.9%

Present value £000

Cumulative £000

0

(1700)

1

(1700)

(1700)

1

(60)

0.953288847

-57.19733079

-1757.2

2

0

0.908759625

0

-1757.2

3

(140)

0.866310415

-121.283458

-1878.48

4

910

0.825844056

751.5180908

-1126.96

5

910

0.787267927

716.4138139

-410.549

6

429

0.750493734

321.9618121

-88.5871

7

140

0.715437306

100.1612229

11.57415

8

180

0.682018405

122.7633128

134.3375

The payback period of proposal 3 is 6 years 11 months

(-88.5871 / 100.1612229 × 12) = 11 months

### NPV Proposal 1

Periods

Net cash flows £000

Discounted at 4.9%

Present value £000

0

(1700)

1

(1700)

1

70

0.953288847

66.73021926

2

(120)

0.908759625

(109.051155)

3

380

0.866310415

329.1979575

4

840

0.825844056

693.7090069

5

840

0.787267927

661.305059

6

620

0.750493734

465.3061153

7

1500

0.715437306

1073.15596

8

660

0.682018405

450.132147

NPV

1930.485

NPV Proposal 2

Periods

Net cash flows £000

Discounted at 4.9%

Present value £000

0

(1700)

1

(1700)

1

200

0.953288847

190.6577693

2

(400)

0.908759625

(363.50385)

3

473

0.866310415

409.7648261

4

(6)

0.825844056

(4.955064335)

5

270

0.787267927

212.5623404

6

780

0.750493734

585.3851128

7

1030

0.715437306

736.9004256

8

890

0.682018405

606.9963801

NPV

673.8079

NPV proposal 3

Periods

Net cash flows £000

Discounted at 4.9%

Present value £000

0

(1700)

---

(1700)

1

(60)

0.953288847

-57.19733079

2

0

0.908759625

0

3

(140)

0.866310415

-121.283458

4

910

0.825844056

751.5180908

5

910

0.787267927

716.4138139

6

429

0.750493734

321.9618121

7

140

0.715437306

100.1612229

8

180

0.682018405

122.7633128

NPV

134.3375

### Negative NPV Proposal1

Periods

Net cash flows £000

Discounted at 22%

Present value £000

0

(1700)

1

(1700)

1

70

0.819672131

57.37704918

2

(120)

0.671862403

(80.62348831)

3

380

0.550706887

209.2686172

4

840

0.451399088

379.1752339

5

840

0.369999252

310.7993721

6

620

0.303278076

188.032407

7

1500

0.248588587

372.8828801

8

660

0.203761137

134.4823502

NPV

(128.6055787)

### Negative NPV Proposal 2

Periods

Net cash flows £000

Discounted at 22%

Present value £000

0

(1700)

1

(1700)

1

200

0.819672131

163.9344262

2

(400)

0.671862403

(268.744961)

3

473

0.550706887

260.4843577

4

(6)

0.451399088

(2.708394528)

5

270

0.369999252

99.89979816

6

780

0.303278076

236.5568991

7

1030

0.248588587

256.0462443

8

890

0.203761137

181.3474116

NPV

(773.18421)

### Negative NPV Proposal 3

Periods

Net cash flows £000

Discounted at 22%

Present value £000

0

(1700)

1

(1700)

1

(60)

0.819672131

(49.18032787)

2

0

0.671862403

0

3

(140)

0.550706887

(77.09896423)

4

910

0.451399088

410.7731701

5

910

0.369999252

336.6993197

6

429

0.303278076

130.1062945

7

140

0.248588587

34.80240214

8

180

0.203761137

36.6770046

NPV

(877.2211)

IRR = A +

IRR Proposal 1

IRR = 0.049 +

IRR= 20.92%

IRR Proposal 2

IRR = 0.049 +

IRR = 12.86%

IRR Proposal 3

IRR = 0.049 +

IRR = 7.17%

### References

Muhammad Ansar (2002) What are investment appraisal techniques? Ed helium

Graeme Pietersz (2006) accounting rate of return [Online].Retrieved from: http://moneyterms.co.uk/arr/ [Accessed 6th April 2010].

Stephen A. Ross (2007) Discounted Payback Period to evaluate Capital Budgeting Proposals [Online]. Retrieved from: http://finance.thinkanddone.com/discounted-payback-period.html [Accessed 6th April 2010].

David Romer (2004) Reducing inflation: motivation and strategy [Online]. Retrieved from: http://www.investopedia.com/terms/i/inflation.asp [Accessed 8th April 2010].

Allen Taylor (2009) Investment appraisal non financial factors that every accountant and manager should consider [Online]. Retrieved from: http://www.accountantnextdoor.com/investment-appraisal-8-non-financial-factors-that-every-accountants-and-managers-should-consider/ [Accessed 8th April 2010].

[2] Graeme Pietersz (2006) accounting rate of return [Online].Retrieved from: http://moneyterms.co.uk/arr/ [Accessed 6th April 2010].

[4] Stephen A. Ross (2007) Discounted Payback Period to evaluate Capital Budgeting Proposals [Online]. Retrieved from: http://finance.thinkanddone.com/discounted-payback-period.html [Accessed 6th April 2010].

[5] Muhammad Ansar (2002) What are investment appraisal techniques? Ed helium

[7]David Romer (2004) Reducing inflation: motivation and strategy [Online]. Retrieved from: http://www.investopedia.com/terms/i/inflation.asp [Accessed 8th April 2010].

[9] Allen Taylor (2009) Investment appraisal non financial factors that every accountant and manager should consider [Online]. Retrieved from: http://www.accountantnextdoor.com/investment-appraisal-8-non-financial-factors-that-every-accountants-and-managers-should-consider/ [Accessed 8th April 2010].

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