- Calculate the NPV of all cash outflows using the borrowing rate.
- Calculate the NFV of all cash inflows using the investing rate.
- Calculate r by the equation:
Payback Period
Payback period method is the only method, in this essay’s discussion, which not based on discount cash flow. It is the number of years required to recover the original investment in a project. (CFA curriculum, 2011, p.12) It can be calculated as:
This method is popular among CFOs, due to its simplicity in both understanding and communicating. Instead of having a restricted criterion, unlike NPV or IRR, whether to accept a certain project merely depends on a company’s own target payback period.
The main argument against payback period method is that it fails to consider the time value of money. In other words, we are not actually ‘breakeven’ in that breakeven point calculated by payback period method, but have lost amount of money due to the cost of capital or inflation. Therefore, by using discounted cash flow, people try to improve the traditional payback period method to develop a new method, called discounted payback period method. In general, the discounted payback period is always greater, and more accurate, than payback period.
NPV v IRR
NPV and IRR have a lot of similarity, because that they are both based on discount cash flow. More specifically, they both consider the time value of money and future cash flow. Therefore they both can be used, and have been used, as a main criterion in decision-making.
However, there can be ranking conflicts between NPV and IRR in the cases of two mutually exclusive projects in some circumstances, which makes us consider which method is preferred between NPV and IRR.
Generally speaking, NPV is more preferable than IRR in several ways. First of all, we should consider that the actual growth of company is in monetary unit instead of in percentage, and IRR ignores the size or the scope of a potential investment. When dealing with two mutually exclusive investment proposals, only using IRR method can be extremely misleading. For example, 50% return on a $1,000 investment generates more money, than 100% return on a $10 investment. In this case, NPV method should be chosen rather than IRR. But in realistic, this kind of situation is very rare, as companies have increasing opportunities. Stock selection for instance, we would still rather prefer 100% on a $10 investment because we can invest the rest of money in other opportunities as long as they are not mutually exclusive.
Second of all, the most vital limitation of IRR is its simplicity. As I have mentioned above, the discount rate in NPV method contains a wide range of factors, like opportunity cost, cost of capital, risk premium, inflation, interest rate et. While using IRR method merely need to estimate a require rate of return, based on whether experience or expectation. In this case, the NPV method can literally provide more accurate result than IRR method. However, IRR's major limitation is also its greatest strength: it uses one single discount rate to evaluate every investment. (Investopedia, 2011) Besides, when facing a great number of projects, evidence suggests that directors prefer to use IRR because it is easier to understand and communicate.
Thirdly, we should consider the reinvestment rate assumption. Bothe the NPV rule and the IRR rule make implicit assumptions about the reinvestment rate. The NPV rule assumes that shareholders can reinvest their money at the market-determined opportunity cost of capital, while IRR rule assumes that investors can reinvest their money at the IRR for future project. In this case, it is obvious that NPV method is more logical, because NPV criterion uses the most realistic discount rate, the opportunity cost of funds (CFA curriculum, 2011, p.19).
Fourthly, we need to look at the timing problem. As every project is the opportunity cost of itself delayed in time, the gain of waiting should be taken in to account. For example, if a company need debt capital to invest a project, it is better to wait for a lower interest rate. In this case, NPV can more easily shows the change of value of project.
Finally, the multiple IRR problem should be noticed. For conventional projects, this problem cannot occur. However, for nonconventional projects, there could be, mathematically, more than one IRR or none IRR. In this case, we should use modified IRR analyst to estimate IRR, or try to use another method to evaluate the projects.
However, we should also consider the cost of investment appraisal and the complexity of usage, which are crucial in practice but sadly ignored by most pure academic study. Although investors should use NPV as a prior method, IRR method is more simple and easy to use, which makes IRR more popular than NPV. Nevertheless, in practice, we should choose a method more suitable to the specific company.
NPV v Discounted Payback Period (DPP)
There is no doubt that discounted cash flow method, e.g. NPV, is more accurate than non-discounted cash flow method, e.g. payback period, by taking into account the time value of money. However, can discounted payback period, which is also a discounted cash flow method by considering the time value of money and risk, replace NPV method?
As a matter of fact, DPP is more often used by small business (Bhandari, 2008, p.3), as this technique concentrates on cash flows, which are more objective than profit because that the long-term survival of small company depends heavily on its liquidity. Evidence suggests that sole traders may prefer a project with both lower NPV and DPP (Grinyer, 2003, p3), rather than another projects with tremendous NPV but would not generate any cash in the first 10 years, as they need money to meet their daily needs.
Another advantage of DPP is its simplicity in both computation and understanding, which allows quick and simple calculations that reduce the time and cost required for the initial screening of projects (Grinyer, 2003, p5). Especially in large corporation, it can easily facilitate communications among management.
However, using merely DPP to evaluate an investment opportunity is obviously not enough, because that it always ignores these cash flows beyond the payback period. As the traditional payback period is shorter than discounted payback period, it would ignore even more cash flows. Therefore, DPP method can only reflect liquidity of a project instead of profitability, i.e. it cannot show whether the projects would gain the company’s value. For example, if a project can recover its initial cost in one year, but would make a loss every year thereafter, should we accept this project? Of Couse no. But its payback period will still be one year, which sounds pretty reasonable.
The other disadvantage of DPP is that it might cause conflict between junior and senior managers (Grinyer, 2003, p3). One potential reason could be that they are not given equivalent information. For example, project risks for subordinate managers are likely to be greater than those for their superiors, as the subordinate managers have fewer opportunities diversify the risk. Therefore, subordinate managers are more willing to accept the projects with shorter payback period to reduce their risk, regardless they may have lower NPV. Furthermore, subordinates managers may wish a quick promotion, by increasing short-term cash flows and reduce that of long term.
In practice, payback period is rarely used as a main method in investment appraisal, as it only evaluates the liquidity of projects. However, DPP can help management by supporting NPV or IRR. For example, if we have two projects with same NPV, the project with shorter payback period would be preferred, as longer recover time would generate more uncertainty.
Limitations of NPV
The main limitation of NPV analysis is the difficulty of accurately forecasting future cash follow and discount rate (Michel, 2009). On one hand, a wide range of variables can affect future cash flow, like economic context, government policy, industry rotation, or even the project itself. Furthermore, a large group usually has a tremendous range of projects, and it is problematic to distinguish the cash flow from each project. On the other hand, discount rate depends on amount of influential factors from interest rate to inflation, to find a specific value is nearly impossible. The best analyst can do is to find a range of NPV by selecting higher and lower discount rates.
Another limitation is that, there is no possible way to measure the uncertainty risk, as it only provides the amount of cash flow possibly, and ignore the possibility to gain it. Even though we can add risk premium in NPV method, it is far from accurate because that risk premium is not normally proportional to present value of project. In fact, proportional change only appears when investors have unlimited capital and a well-diversified profile (Shimko, 2001). If an investor’s capital is limited, which is more likely, specific risk must be taken into account, which makes simply adding risk premium into discount rate inappropriate.
There are some other limitations of NPV in certain circumstances. For instance, when dealing with high-risk project or the market being overheated, the NPV method would obtain a value of project less than zero due to its high-risk premium. However, investors would usually not stop trading in this case based on greater fool theory, or because they simply believe the project is not absolutely worthless.
One Step Further: NPV-at-Risk
As ignoring risk could lead to a inaccurate, or even wrong, results, analyst find a way to adjust NPV so that it can reflect the specific risk of a project, i.e. NPV-at-Risk. This method takes the following factors into account (Ye, 2002):
- All the possible returns resulting from uncertainty;
- The time value of money;
- The impact of financing methods
- Various risks associated with projects.
The definition of NPV-at-Risk is a particular NPV generated from a project at some specific confidence level. Therefore, the decision rules can be derived that the project is acceptable with a confidence level if NPV-at-Risk at the given confidence is greater than zero (Ye, 2002).
The major requirement in using this method is the availability of date for statistical analysis. By using these data, analysts can adjust a project’s specific risk to its NPV, therefore yields more accurate result to help them in investment appraisal.
Conclusion
The integrity of a corporation’s capital budgeting processes is important to analysts so that is crucial to find an appropriate way in investment appraisal. Therefore, a successful method should demonstrate two things: the degree to which management embraces the goal of shareholder wealth maximization, and its effectiveness in pursuing that goal (CFA curriculum, 2011). By fulfilling these two criteria, NPV method still remains as the most useful method in investment appraisal. Although IRR and DPP have several flaws, they can be used as supportive methods due to its simplicity in both understanding and communicating. In practice, analyst usually combines several methods in order to achieve a more accurate result.
Appendix 1
Level I Volume 4 Corporate Finance and Portfolio Management, (2011) 6th Edition. Pearson Learning Solutions p. G-33
Appendix 2
References:
Bhandari, S. (2008) ‘Discounted Payback: A Criterion for Capital Investment Decisions’
Grinyer, J. (2003) ‘Managerial Advantages of Using Payback as a Surrogate for NPV’, the engineering economist
Level I Volume 4 Corporate Finance and Portfolio Management, (2011) 6th Edition. Pearson Learning Solutions p. G-33
Michel, G. (2009) Net Present Value Analysis: A primer for Finance Officers.
Shimko, D. (2001) ‘NPV No More: RPV for Risk-based Valuation’
Ye, S. (2002) ‘NPV-AT-RISK METHOD IN INFERASTRUCTURE PROJECT INVESTMENT EVALUATION’
![Investment appraisal methods. Evidence[1] suggests that, NPV (net present value), IRR (internal rate of return), and payback period are the three most popular method used by companies in decision-making. In this essay, the three methods would be discussed](https://mbt-essays-prod-public.s3.eu-west-1.amazonaws.com/926411/listing/926411_1.jpg)
