## Introduction

The net present value is a more accurate method than the payback period and the accounting rate of return when choosing between two mutually exclusive projects.

The main weakness of the payback period and the accounting rate of return is that they do not consider the time value of money. The two methods may not be used to accurately account for the cost of capital. The net present value profile supports the NPV method with capturing a bigger picture using multiple discount rates.

## Payback approach

The payback approach considers the length of time that it takes to recover the amount used as capital through cash flows (Kinney and Raiborn 654). When one project needs to be selected, the project that provides the shortest time to generate the amount used for the investment is preferred.

In the payback period, longer time periods increase the uncertainty associated with the investment (Kinney and Raiborn 654). Uncertainty is a type of risk. The payback period for the Synthetic Resin project and the Epoxy Resin project are shown below.

The negative values are indicated in bracket, and the positive values are in the normal format. The payback period ends at the point where the cumulative cash flow becomes positive. The remaining amount is expressed as a percentage of the cash flow in the period that the cumulative cash flow becomes a positive value. It gives a value in the proportion of a year.

Table 1 indicates that the Synthetic Resin project has a payback period of 2 years and 6 months. Table 2 indicates that the Epoxy Resin project has 1 year and 6 months as its payback period. The Epoxy Resin project has a shorter payback period than the Synthetic Resin project, which makes the Epoxy Resin project more favourable.

The Epoxy Resin project provides less risk by having its cash flows received earlier in the project life. It is one of the advantages of the payback period because it leads to a choice that reduces uncertainty. It may make the company choose the project that may increase liquidity during the early stages of operations. Liquidity refers to the cash needed to cover routine transactions in the short run.

One of the limitations of the payback period is that it does not consider the stream of cash after the payback period. In the Synthetic Resin plan, the cash flows in Year 4 and Year 5 are ignored. The ignored period gives an additional amount of $2,500,000 for the Synthetic Resin project and $2,100,000 for the Epoxy Resin project.

Another limitation of the payback period is that it does not consider the cost of capital, which is the opportunity cost of utilizing capital. The payback period ignores the time value of money. It makes a dollar received in the first year to have the same value as a dollar received in the final year. In everyday investment processes, money borrowed is paid with an interest. Money deposited in banks provides an interest.

The capital invested in the projects could earn Day-Pro an interest by depositing it in a bank or purchasing bonds. The long-term Treasury bonds are considered risk-free. The firm could generate profit without engaging in any business.

The Epoxy and Synthetic investments have to provide a higher rate than that which can be acquired by purchasing a risk-free bond. If Day-Pro is borrowing money to invest in either of the projects, payback period cannot be used because it does not consider the cost of capital.

## Accounting Rate of Return (ARR)

ARR is an approach that measures the annual rate of receiving net income. It gives the average income as a percentage of the initial investment (Mowen, Hansen and Heitger 606). ARR is calculated by adding the net income in the five years, and dividing by the number of years. The streams of net income and the ARR are shown below.

ARR = average income/ initial investment (Mowen, Hansen and Heitger 606).

The decision process requires the projects to have a minimum ARR of 40%. None of the two projects has met the minimum requirement. The firm should not invest in any of the two projects. The problem with the decision-making process is that the minimum rate of return has been set at a very high level that the two projects or others will be unlikely to meet. Very few projects have such a high rate of return on investment.

The ARR indicates the average rate of return on the investment annually. The time value of money is not considered. Its weakness in failing to include the time value of money may divert capital from more profitable investments.

The ARR is inaccurate in a business environment where projects are usually funded with borrowed capital. The ARR fails to capture the cost of capital. Mowen, Hansen and Heitger (606) discuss that ARR’s reliance on income is a weakness because net income can be manipulated by managers.

## The Net Present Value (NPV) Profile

The NPV profile is a graph that displays how net present values are distributed for different levels of discount rates. Bierman (68) explains that the discount rates can stretch from zero to a reasonably large number of discount rates. In the calculations, the interest rates start from a discount rate of 0% to 45% (see Appendix 1 and Appendix 2).

The NPV can be plotted with fewer points, but more points increase the accuracy of the trend line. Emphasis has been laid on the horizontal axis because it holds the internal rate of return (IRR). The IRR is found at the point where the NPV is equal to zero (Hansen, Mowen and Guan 719). The NPV is equal to zero on the horizontal axis for all values of discount rates.

The NPV profile has been formed by finding the NPV at different discount rates before they are plotted. The table below and the graph are part of the NPV profile.

*Table 5 NPV Profile*

*Graph 1*

The crossover point is at a rate of about 31%. The crossover point is the discount rate at which both projects provide the same net present value. The IRR is the rate at which the curves intersect with the horizontal axis (Bierman 68). The Synthetic Resin project has an IRR of approximately 37% and the Epoxy Resin project has approximately 43%.

It becomes easier for Day-Pro to choose between the two projects depending on the side of the crossover point on which the discount rate falls. If the discount rate is less than 31%, then Synthetic Resin is more favourable because it provides a higher NPV. If the discount rate is higher than 31%, then Epoxy Resin provides a more favourable condition because it provides a higher NPV.

However, the Synthetic Resin project provides a wider range of values at which it is better than the Epoxy Resin. Epoxy Resin is favorable at higher discount rates. Most businesses use discount rates that are around 10%, which may match the cost of capital. It makes Synthetic Resin project more favorable than the Epoxy Resin project to the firm.

The main advantage of net present value is its integration of the time value of money. Day-Pro may be able to consider using borrowed capital because the NPV will account for the returns that are used to cover the interest paid on borrowed funds, and returns to owners’ equity. Hansen, Mowen and Guan (719) explain that the NPV measures the additional value that the project generates for investors in the firm.

It aligns itself with one of the objectives of the firm, which is to increase shareholders’ wealth. An NPV of zero indicates that the firm has met the cost of capital requirements (interest), and the cost of the investment (principal).

The IRR does not indicate the value that is being added to shareholders’ wealth in absolute terms. Day-Pro cannot find out the amount of wealth that will be created using IRR because it uses relative terms (Hansen, Mowen and Guan 723).

Another advantage of the NPV is that it considers all the cash flows during the operation of the business, which is different from the payback period (Peterson-Drake 1). It considers the risk in investment by using lighter weights on amounts that are further into the future. The NPV corrects the weaknesses of the payback period and the ARR.

One of the weaknesses of the NPV is that it does not provide an estimate of the annual rate of return. However, it is a weak limitation because the NPV considers capital in excess of the required rate of return.

Another weakness of the NPV method is that the required rate of return can be selected subjectively (Peterson-Drake 1). The NPV profile reduces the weakness of subjectivity by providing a wider range of possible discount rates.

## Conclusion

The NPV profile corrects the weakness of the NPV approach associated with the subjectivity of choosing the discount rate. The NPV accounts for the time value of money, which is usually applied in all sources of capital. The NPV indicates the value of wealth that is created by the project to the owners of equity. The NPV is a better method than either the payback period method or the ARR.

## Works Cited

Bierman, Harold. *An Introduction to Accounting and Managerial Finance a Merger of Equals*. Hackensack, NJ: World Scientific, 2010. Print.

Hansen, Don, Maryanne Mowen and Liming Guan. *Cost Management: Accounting and Control*. 6^{th} ed. Mason, OH: South-Western Cengage Learning, 2009. Print.

Kinney, Michael and Cecily Raiborn.* Cost Accounting: Foundations and Evolutions*. Mason, OH: Cengage Learning, 2010. Print.

Mowen, Maryanne, Don Hansen and Dan Heitger. *Cornerstones of Managerial Accounting*. 3^{rd} ed. Mason, OH: South-Western Cengage Learning, 2009. Print.

Peterson-Drake, Pamela. n.d. *Advantages and Disadvantages of Different Capital Budgeting Techniques*. n.d. Web.

## Appendix

### Appendix 1

*Discounting factors*

### Appendix 2

*Net Present Values*