## The Comparison of Irr and Npv

Question 1. Calculation of Payback, NPV and IRR. 3 (i) Calculation for Project 13 (ii) Calculation for Project 24 (iii) Calculation for Project 35 (iv) Calculation for Project 46 (v) Calculation for Project 57 (vi) Calculations summary8 Question 2. Assessment of the proposals9 Question 3. Other factors to be considered11 Question 4. The comparison of IRR and NPV12 References14 Bibliography15 Question 1. Calculation of Payback, NPV and IRR. (i) Calculation for Project 1: Year| Net cash flow (? ) | Cumulative net cash flow (? )| Discount factors| Present value (? )| | | | 10%| 20%| 25%| 10%| 20%| 25%| 1-2| 0| 0| | | | | | | | 73,000| 73,000| 0. 751| 0. 579| 0. 512| 54,823| 42,267| 37,376| 4| 73,000| 146,000| 0. 683| 0. 482| 0. 410| 49,859| 35,186| 29,930| 5| 73,000| 219,000| 0. 621| 0. 402| 0. 328| 45,333| 29,346| 23,944| Total present value| 150,015| 106,799| 91,250| Less: Initial investment | 100,000| 100,000| 100,000| Net present value (NPV) = Total present value – Initial [email protected]% = ? 50,015| 50,015| 6,799| (8,750)| Payback period=3+ ? 100,000-? 73,000? 73,000= 3. 37 years or 0. 37 * 12 months = 3 year and 4. 4 months | Internal rate of return (IRR) =positive rate+(positive NPVpositive NPV + negative NPV* ? ange of rates)* ignore the negative sign=20%+? 6,799? 6,799 + ? 8,750 ? (25% – 20%)= 22. 2%| Conclusion: As the NPV of ? 50,015 is positive, the project 1 can be accepted. The IRR of 22. 2% which is above the minimum rate of return (10%) bring us to the same conclusion. Payback period shows that 3 years and 4. 4 months is necessary for the project to pay back initial investment of ? 100,000. (ii) Calculation for Project 2: Year| Net cash flow (? )| Discount factors| Present value (? )| | | 10%| 20%| 25%| 10%| 20%| 25%| Annuity for 5 years| 66,000| 3. 791| 2. 991| 2. 690| | | | Initial investment| 180,000| 180,000| 180,000|

Net present value (NPV) of an annuity= Net cash flow * Discount factor – Initial investment = ? 66,000 * Discount factor – ? 180,[email protected]% = ? 70,206| 70,206| 17,406| (2,460)| Payback period of an annuity=Initial investmentNet cash flow per year=? 180,000? 66,000= 2. 7 years or 0. 7 * 12 months = 2 years and 8. 4 months| Internal rate of return (IRR) =positive rate+(positive NPVpositive NPV + negative NPV* ? range of rates)* ignore the negative sign=20%+? 17,406 ? 17,406 + ? 2,460 ? (25% – 20%)= 24. 4%| Conclusion: As the NPV of ? 70,206 is positive, the project 2 can be accepted. The IRR of 24. % which is above the minimum rate of return (10%) bring us to the same conclusion. Payback period shows that 2 years and 8. 4 months is necessary for the project to pay back initial investment of ? 180,000. (iii) Calculation for Project 3: Year| Net cash flow (? )| Cumulative net cash flow (? )| Discount factors| Present value (? )| | | | 10%| 30%| 35%| 10%| 30%| 35%| 1| 145,000| 145,000| 0. 909| 0. 780| 0. 740| 131,805| 113,100| 107,300| 2| 145,000| 290,000| 0. 826| 0. 600| 0. 550| 119,770| 87,000| 79,750| 3-5| 0| 0| | | | | | | Total present value| 251,575| 200,100| 187,050|

Less: Initial investment | 200,000| 200,000| 200,000| Net present value (NPV) = Total present value – Initial [email protected]% = ? 51,575| 51,575| 100| (12,950)| Payback period=1+ ? 200,000 – ?145,000? 145,000 = 1. 4 years or 0. 4 * 12 months = 1 year and 4. 8 months| Internal rate of return (IRR) =positive rate+(positive NPVpositive NPV + negative NPV* ? range of rates)* ignore the negative sign=30%+? 100? 100 + ? 12,950 ? (35% – 30%)= 30. 0%| Conclusion: As the NPV of ? 51,575 is positive, the project 3 can be accepted. The IRR of 30% which is above the minimum rate of return (10%) bring us to the same conclusion.

Payback period shows that 1 year and 4. 8 months is necessary for the project to pay back initial investment of ? 200,000. (iv) Calculation for Project 4: Year| Net cash flow (? )| Discount factors| Present value (? )| | | 10%| 25%| 30%| 10%| 25%| 30%| Annuity for 5 years| 16,000| 3. 791| 2. 690| 2. 480| | | | Initial investment| 40,000| 40,000| 40,000| Net present value (NPV) of an annuity= Net cash flow * Discount factor – Initial investment = ? 16,000 * Discount factor – ? 40,[email protected]% = ? 20,656| 20,656| 3,040| (320)| Payback period of an annuity=Initial investmentNet cash flow per year=? 0,000? 16,000= 2. 5 years or 0. 5 * 12 months = 2 year and 6 months| Internal rate of return (IRR)=positive rate+(positive NPVpositive NPV + negative NPV* ? range of rates)* ignore the negative sign=25%+? 3,040? 3,040 + ? 320 ? (30% – 25%)= 29. 5%| Conclusion: As the NPV of ? 20,656 is positive, the project 4 can be accepted. The IRR of 29. 5% which is above the minimum rate of return (10%) bring us to the same conclusion. Payback period shows that 2 years and 6 months is necessary for the project to pay back initial investment of ? 40,000. (v) Calculation for Project 5: Year| Net cash flow (? | Discount factors| Present value (? )| | | 10%| 95%| 100%| 10%| 95%| 100%| Annuity for 5 years| 70,000| 3. 791| 1. 010| 0. 970| | | | Initial investment| 70,000| 70,000| 70,000| Net present value (NPV) of an annuity= Net cash flow * Discount factor – Initial investment = ? 70,000 * Discount factor – ? 70,[email protected]% = ? 195,370| 195,370| 700| (2,100)| Payback period of an annuity=Initial investmentNet cash flow per year=? 70,000? 70,000= 1 year | Internal rate of return (IRR)=positive rate+(positive NPVpositive NPV + negative NPV* ? range of rates)* ignore the negative sign=95%+? 700? 700 + ? ,100 ? (100% – 95%)= 96. 3%| Conclusion: As the NPV of ? 195,370 is positive, the project 5 can be accepted. The IRR of 96. 3% which is above the minimum rate of return (10%) bring us to the same conclusion. Payback period shows that 1 year is necessary for the project to pay back initial investment of the ? 70,000. (vi) Calculations summary: | Initial investment| Payback period| [email protected]%| IRR| Project 1| ? 100,000| 3 years and 4. 4 months| ? 50,015| 24. 2%| Project 2| ? 180,000| 2 years and 8. 4 months| ? 70,206| 24. 4%| Project 3| ? 200,000| 1 years and 4. 8 months| ? 51,575| 30. 0%| Project 4| ? 0,000| 2 years and 6 months| ? 20,656| 29. 5%| Project 5| ? 70,000| 1 year| ? 195,370| 96. 3%| Question 2. Assessment of the proposals. According to Proctor (2009), a situation in which a company has several possible projects with positive NPV and is not able to invest resources in all of them, is known as “capital rationing”. It is not possible to allocate limited funds based on NPV, IRR and Payback methods, which were calculated above. In order to maximise shareholder’s wealth project proposals should be ranked based on Profitability index (PI), as defined as follows: PI= NPVInitial investment ? 00% The PI of every project is summarized in the table below and their relative rankings are presented in column “Rank”. As it can be seen, the Project 5 carries the highest ranking while Project 3 is ranked below all other projects. | Initial investment| [email protected]%| PI| Rank| Project 1| ? 100,000| ? 50,015| 0. 50| 3| Project 2| ? 180,000| ? 70,206| 0. 39| 4| Project 3| ? 200,000| ? 51,575| 0. 26| 5| Project 4| ? 40,000| ? 20,656| 0. 52| 2| Project 5| ? 70,000| ? 195,370| 2. 79| 1| Taking into account the key figures of the proposals including limited resources of ? 00,000 and the possibility to divide the project into two phases without the requirement to implement both phases, the following projects combination is proposed to be undertaken. Allocation of the capital investment ? 300,000: 1. Project 5 (both phases): ?70,000? 230,000 NPV = ? 195,370 2. Project 4 (both phases): ?40,000? 190,000 NPV = ? 20,656 3. Project 1 (both phases): ?100,000? 90,000 NPV = ? 50,015 4. Project 2 (only first phases): (? 90,000) NPV = =? 70,260? 180,000 ? ?90,000 = ? 35,103 Aggregate NPV = ? 195,370 + ? 20,656 + ? 50,015 + ? 35,103 = ? 301,144 Conclusion: Investment of ? 00,000 in combination of projects presented above will create aggregate NVP of ? 301,144, which will maximize the shareholder’s value. Question 3. Other factors to be considered. There are other factors that the directors may consider before coming to final conclusion regarding the project proposals. Apart from financial factors, which can be assessed using quantitative techniques, it is also important to consider non-financial drivers. It is not always possible to quantitatively evaluate such components, but they can have a significant impact on the implementation of any project (Berry and Jarvis, 2007).

A brief review of the scientific literature on investment appraisals suggests that there are many different types of qualitative factors. Significant amongst these include: Political factors at micro and macro level or negative / positive political attitudes such as relevant government regulations and policies may seriously affect a project implementation (Brown and Reilly, 2009). Ungson & Wong (2008) argue that country and market specific economic factors including the likelihood of recession, market opportunities and threats, competition, customers and suppliers might also have critical influence on project success.

On the other hand, studies undertaken by Dayananda (2002) conclude that company specific factors such as cost management, internal controls, corporate reputation, brand value and the risk associated with capital financing might carry substantial importance for project future. Dayananda (2002) also emphasizes importance of human factor such as quality of management, corporate values and employee morale, recruiting and training personnel procedures, employee safety and employee turnover for successful implementation of projects.

Equally important might be environmental impact of the project including pollution control and environment protection (Ungson and Wong, 2008) as well as technological factors comprising innovations and new technology. In conclusion, it is the responsibility of the managers to consider various factors applicable to the projects including quantitative, qualitative, psychological and social factors as well as a managers’ intuition before making a final investment decision. Question 4. The comparison of IRR and NPV.

There have been many studies which have determined that amongst discounted cash flow (DCF) techniques for investment appraisals, the IRR method is most commonly used in practice. According to Pike (1996), although companies often used both techniques IRR was favoured. He found in the UK in 1992 around 81% of business enterprises used IRR as compared to 74% which used NPV (cited in Drury, 2006, p. 406). The main reasons of IRR popularity are worth being examined in detail. The key advantage of IRR is the ease of understanding by users.

It produces clear conclusion related to the return on investment in percentages rather than in absolute terms. For managers this representation is more preferable, because they can compare it with an expected return on different investments (Vance, 2002). According to Vance (2002), the IRR measures the efficiency with which the capital is employed by managers and guides them in selecting those projects that satisfy the minimum required level of return to capital. Moreover, Vance has also referred to IRR as a measure of “cushion” in making investment decision.

According to his finding if the cost of capital is 12% and project has IRR of 15%, 3% can be considered as a “cushion” against the risks related during project implementation. It should be also noticed that unlike NPV, IRR does not use estimated future rate of return. Instead, it gauges a discount rate under which NPV equals the initial investment. As a result IRR is more precise, since predicting future discount rate is difficult (Dyson, 2010). In addition, Weetman (2010) argues that by using IRR, large companies with international operations can use different rates of return in order to reflect the risk attributable to any specific country.

On the other hand, latest studies report that NPV has become recently the most widely used approach for investment appraisal. According to Arnold and Hatzopouloulos (2000), around 97% of all large firms in the UK in 2000 used NPV for the purpose of investment appraisal as compared to 84% others which used IRR (cited in Drury, 2006, p. 406). In order to achieve better understanding reasons for superiority of NPV over IRR should be further investigated. The IRR has two problems that can occur in a minority of mutually exclusive projects and cause the conflict between NPV and IRR rankings (Lucey, 2003).

First of all, the IRR assumes that cash inflows will be reinvested at the project’s rate of return, whereas the NPV assumes reinvestment at cost of capital. NPV’s assumption related to reinvestment at the cost of capital is generally better, because it is closer to real practice while assumption foreseeing reinvestment at IRR’s may cause conflict, especially when evaluating mutually exclusive projects (Horngren, et al. , 2009). Secondly, depending on the pattern of cash inflows it is possible to have more than one IRR value, while there is always only one NPV value.

Achieving more than one IRR might take place when a company has unconventional cash flows; e. g. when positive cash inflows during the first two years are followed by negative cash outflow the next year. In this case, it is not clear which IRR should be used for comparison with the cost of capital. As a result IRR may result in a misleading outcome (Horngren, et al. , 2009). Related to IRR`s serious weaknesses discussed above several other shortcomings of this method have been referred to in recent literature. One of them is the inability of IRR to take into account the scale of investment (Atrill and McLaney, 2009).

This is important when it is necessary to chose only one out of several mutually exclusive projects with different investment sizes. Under such conditions, IRR might give a preference to the project with higher IRR but with by far smaller amount of shareholder value created. The IRR can also be calculated for only one project, while the NPV can be used for quantifying performance of a portfolio of projects based on the analysis of each of them separately (Horngren, et al. , 2009). Moreover, Atrill and McLaney (2009) state that IRR cannot be used in situation with different discount rates during the life of project.

This is because it is unknown how to choose a single discount rate when several rates of return apply in different years and subsequently how to compare it with the required rate in order to make accept / reject decision. However, it is possible to apply NVP technique, because it uses different rates of return every year. In addition to this, the IRR method cannot be calculated precisely. It is derived from estimation techniques which give only an approximate rate of return (Dyson, 2010). In conclusion, both the NPV and IRR methods can be widely used for investment appraisal purposes.

They provide the same results in accept / reject decisions and in the majority of ranking investment. However, when rankings conflict in mutually exclusive projects managers should rely on the NPV ranking (Lucey, 2003). According to Atrill and McLaney (2009) in practice businesses prefer to use several techniques of capital budgeting. References 1. Atrill, P. and McLaney, E. , 2009. Management Accounting for Decision Makers. 6rd ed. Italy: Person Education Limited. 2. Berry, A. and Jarvis, R. , 2007. Accounting in a Business Context. 4rd ed. UK: Thomson Learning. 3. Brown, K. C. and Reilly, F. K. , 2009.

Analysis of Investment and Management of Portfolios. 2rd ed. Canada: South-Western Cengage Learning. 4. Dayananda, D. , Irons, R. , Harrison, S. , Herbohn, J. and Rowland, R. , 2002. Capital Budgeting: Financial Appraisal of Investment Projects. [pdf] UK: Cambridge University Press. Available at: http://assets. cambridge. org/97805218/17820/excerpt/9780521817820_excerpt. pdf [Accessed 24 May 2011]. 5. Drury, C. , 2006. Cost and Management Accounting. 6rd ed. China: Sough-Western Gengate Learning. 6. Dyson, J. R. , 2010. Accounting for Non-Accounting Students. 8rd ed. Italy: Pearson Education Limited. . Horngren, C. T. , Datar, S. M. , Foster, G. , Rajan, M. and Ither, G. , 2009. Cost Accounting: A Managerial Emphasis. 13rd ed. US: Prentice Hall. 8. Lucey, T. , 2003. Quantitative Techniques. 6rd ed. UK: Thomson Learning. 9. Proctor, R. , 2009. Management Accounting for Business Decisions. 3rd ed. UK: Pearson Education Limited. 10. Ungson, G. R. and Wong, Y. Y. , 2008. Global Strategic Management. US: M. E. Sharpe. 11. Vance, D. E. , 2002. Financial Analysis and Decision Making: Tools and Techniques to Solve Financial Problems and Make Effective Business Decisions. US: McGraw-Hill Professional. 2. Weetman, P. , 2010. Management Accounting. 2rd ed. Italy: Pearson Education Limited. Bibliography 1. Curwin, J. and Slater, R. , 2008. Quantitative Methods for Business Decisions. 6rd ed. Singapore: South-Western Cengage Learning. 2. Drury, C. , 2005. Management Accounting for Business. 3rd ed. UK: Thomson Learning. 3. Lucey, T. , 2007. Management Accounting. 5rd ed. UK: Thomson Learning. 4. McLaney, E. and Atrill, P. , 2010. Accounting: An Introduction. 5rd ed. Italy: Person Education Limited. 5. Wood, F. and Sangster, A. , 2008. Business Accounting Vol. 2. 11rd ed. US: Prentice Hall.