William F. Rentz, Ph.D. and Alfred L. Kahl, Ph.D.

Telfer School of Management, University of Ottawa

**Authors: **Both authors are Associate Professors at the Telfer School of Management, University of Ottawa, Ottawa, Ontario, Canada. **Corresponding Author Email: ** akahl@uottawa.ca

### Abstract

*This narrative discusses an innovative post-secondary classroom instruction methodology using the BAIIPlus Financial Calculator iPad App for teaching the two most important corporate investment decision making rules: internal rate of return and net present value. The crucial feature of the BAIIPlus iPad App that makes this innovative teaching method possible is that the iPad App lights up a key when it is touched. Thus, students watching the computerized presentation screen immediately see each step in the decision making process as it is being demonstrated on the instructor’s iPad. Students can follow the lecture by tapping the same keys on their own calculators or iPads. Therefore, students learn by doing as well as seeing and hearing, so they retain what they learn more readily. This teaching methodology could also be used at the secondary level if classrooms are suitably equipped. Although this new innovative technique has not been in use long enough to obtain quantitative data concerning its effectiveness, the initial response from students has been very favorable and regular class attendance has increased.*

### Introduction

Teaching the internal rate of return and net present value investment decision rules in finance courses has always been difficult for both teachers and learners because students frequently find it difficult to understand the concepts involved. This paper describes an innovative teaching methodology made possible by the Texas Instruments BAIIPlus iPad App that lights up each key that is touched by the instructor so students can easily see the dynamic changes in the lecture on the computerized presentation screen as it happens. This keeps students interested in the lecture and they are able to learn the decision rules by doing the calculations along with the instructor.

#### Financial Calculators

Despite the availability of computers, financial calculators are still widely used in the financial services industry. The BAIIPlus financial calculator is one of the few calculators permitted for the Chartered Financial Analyst (CFA) professional designation exams. This designation requires at least a bachelor’s degree plus relevant experience and there are 3 separate exams before the designation can be awarded. While most finance students have their own financial calculators, many students are now using the Texas Instruments BAIIPlus Financial Calculator App with their own iPads. Both types of students may follow the instructor’s explanation of the steps involved in computing these decision rules

#### The iPad App

Before the summer of 2010, iPads did not exist but now they are ubiquitous. Mang and Wardley (2012) recommended using iPads in university classes. Cochrane, Narayan and Oldfield (2013) also suggested that instructors should integrate iPads into their classroom activities and even coined a new word, iPadagogy, for this practice. After extensive internet research only the BAIIPlus Financial Calculator iPad App created by Texas Instruments was available, so it was chosen for use during the 2014 academic year. The BAIIPlus iPad App is available from the Apple Store for both the iPad and the iPhone at a reasonable price. This App provides all the functionality of the widely used BAIIPlus financial calculator that is a relatively inexpensive tool for efficiently solving complex financial problems correctly.

### Investment Decision Rules

Graham and Harvey (2002) surveyed many chief financial officers (CFOs) in the United States and found that comparing the internal rate of return (IRR) to a required rate of return of an investment project was the most popular investment decision rule used by CFOs. This decision rule was followed very closely by the net present value (NPV) decision rule. The NPV rule compares the expected NPV of an investment project with some targeted NPV, typically zero in textbooks but not necessarily so in the real world. The Graham and Harvey (2002) survey is one of the largest ever samples of companies traded in the United States. A more recent similar but smaller Canadian study by Baker, Duttu, and Saadi (2011) found that the NPV decision rule was the most popular with Canadian CFOs but IRR was close behind. Textbooks, such as Brigham and Earhart (2014) typically discuss these decision rules in much more detail and usually agree the NPV rule is the best one for top managers to use.

Since surveys always find that decision makers use more than one method before actually deciding whether to invest or not, it appears that in practice most managers calculate at least both the IRR and NPV. These two methods are based on the estimated future net cash flows after taxes that are expected to be obtained by investing in a proposed investment project, such as, for example, building a new factory. Corporate managers usually do their best to estimate future cash flows based on their expectations about the economy over the next five or ten years. So, the estimates may turn out to by incorrect *ex post*, but they are still the best information that is available to the decision makers at the time the decision must be made. Graham (2011) suggested that students would learn finance more effectively if instructors stressed the real-world CFO practices on the assumption that this would make it more likely the students would find employment after graduation.

#### Internal Rate of Return (IRR)

The equation for the internal rate of return (IRR) is:

Where INV = Initial investment outlay, NCF = Net cash flow per period, t = time period, and n = project life

This equation can be solved with a financial calculator to obtain the discount rate that equates the present value of the expected net cash flows with the present value of the initial cost of making the investment. The decision rule is then to make the investment if the rate of return exceeds the company’s required rate of return. For corporations, the required rate of return is usually either the firm’s cost of capital (a weighted average of the various costs of debt and equity capital) or a higher hurdle rate if the investment proposal is considered to be more risky than the currently owned portfolio of assets that have resulted from previous investment decisions.

#### Net Present Value (NPV)

The equation for the net present value (NPV) is:

Where INV = Initial investment outlay, NCF = Net cash flow per period, t = time period, n = project life, and r = discount rate.

This equation can be solved with a financial calculator to obtain a dollar amount by which the present value of the expected net cash flows exceeds the present value of the initial cost of making the investment. The decision rule is to make the investment if the calculated amount is positive because this will increase the wealth of the firm’s shareholders. Thus, for this method, it is necessary to know before calculating anything what is the corporate required rate of return so it can be used as the discount rate.

### A Numerical Teaching Example

Suppose the CFO of a publicly traded corporation is considering an investment proposal requiring the purchase of a new type of equipment today for $10,000,000. This new equipment is expected to be used more efficiently to produce cash flows of: -$10,000,000 in year zero, $4,000,000 in year 1, $3,000,000 in year 2, $6,000,000 in year 3, $7,000,000 in year 4, and $5,000,000 in year 5. For investment projects of this degree of riskiness, the corporate policy is to require a rate of return of at least 20%. So, the question is, “Should the CFO make the investment?”

To use the BAIIPlus calculator App, the instructor uses the following procedure (Note that the keystrokes shown here are enclosed in brackets):

First, enter the cash flow worksheet by pressing the [CF] key

Second, clear any previous cash flow data that might be in the calculator memory by pressing the [2ND] [CLR WORK] keys.

Third, enter the cash flows by pressing the keystrokes shown in Table 1.

Table 1: Data-entry keystrokes | |

Keystrokes | Display |

[1] [0] [0] [0] [0] [0] [0] [0] [+/-] [ENTER] | CF_{0} = ‑10,000,000.00 |

[↓] [4] [0] [0] [0] [0] [0] [0] [ENTER] | C01 = 4,000,000.00 |

[↓] [↓] [3] [0] [0] [0] [0] [0] [0] [ENTER] | C02 = 3,000,000.00 |

[↓] [↓] [6] [0] [0] [0] [0] [0] [0] [ENTER] | C03 = 6,000,000.00 |

[↓] [↓] [7] [0] [0] [0] [0] [0] [0] [ENTER] | C04 = 7,000,000.00 |

[↓] [↓] [5] [0] [0] [0] [0] [0] [0] [ENTER] | C05 = 5,000,000.00 |

At this point, the BAIIPlus calculator App knows the cash flows.

Finally, to compute the IRR, press [IRR] [CPT] and the IRR of 36.35% will be displayed.

Since the computed IRR exceeds the required rate of return of 20%, the investment should be accepted.

Then to compute the NPV, press [NPV] [2] [0] [ENTER] [↓] [CPT], and the NPV of 4,274.05 will be displayed. Thus, the PV of the cash inflows exceeds the cost of the investment by $4,274.05 at a discount rate of 20%. Therefore, this investment should be accepted.

When an investment project has normal cash flows consisting of an outlay followed by a series of positive cash inflows and is independent of any other investments, the decision to accept or reject the investment will be the same whether the IRR or NPV decision rule is used. To be precise, NPV > 0 implies and is implied by IRR > the required rate of return, leading to an increase in expected wealth by accepting the investment. NPV < 0 implies and is implied by IRR < the required rate of return. In this case, the investment should be rejected because accepting it would lead to a decrease in expected wealth. In theory, one should be indifferent if NPV = 0, which implies and is implied by the IRR = the required rate of return. However, in practice, it is probably wise to reject the investment proposal in this case because there is a tendency to be overly optimistic when estimating future cash inflows.

### Conclusion

This paper discusses an innovative BAIIPlus Financial Calculator iPad App methodology for teaching the two most important corporate investment decision making rules: internal rate of return and net present value. The critical enabling feature of this innovative teaching method is the use of the Texas Instruments BAIIPlus Financial Calculator iPad App that lights up a key when it is touched. Thus, students who are following the computerized presentation immediately see each step in the decision making process as it is being demonstrated by the instructor during a lecture. Students can follow along with the calculation process on their own financial calculators or iPads. Therefore, students learn by doing as well as by seeing and hearing so they retain what they learn more readily. If the instructor has an iPad, the instructor can facilitate student learning by connecting the BAIIPlus Financial Calculator iPad App to the classroom computerized projection system.

### References

Baker, K., Dutta, S. & Saadi, S. (2011). Corporate Finance Practices in Canada: Where Do We Stand? *Multinational Finance Journal,* 15(3/4) 157-192.

Brigham, E. & Ehrhart, M. (2014). *Financial Management: Theory & Practice*, 14^{th} Ed. Mason, OH: South-Western Cengage Learning.

Cochrane, T., Narayan, V. & Oldfield, J. (2013). iPadagogy: Appropriating the iPad within Pedagogical Contexts. *International Journal of Mobile Learning,* 7(1) 48-65.

Mang, C. & Wardley, L. (2012). Effective Adoption of Tablets in Post-Secondary Education: Recommendations Based on a Trial of iPads in University. *Journal of Information Technology Education: Innovation in Practice,* 11 301-316.

Graham, J. (2011) Using CFO Surveys as a Motivational Tool to Teach Corporate Finance. *The Financial Review,* 46 193-205.

Graham, J. & Harvey, C. (2002) How Do CFOs Make Capital Budgeting and Capital Structure Decisions? *Journal of Applied Corporate Finance,* 15(1) 8-23.