# How to Calculate IRR on TI-84

How to calculate IRR on TI-84? The internal rate of return (IRR) is a metric used in financial analysis to estimate the profitability of potential investments. IRR is a discount rate that makes the net present value (NPV) of all cash flows equal to zero in a discounted cash flow analysis. IRR calculations rely on the same formula as NPV does. Keep in mind that IRR is not the actual dollar value of the project. It is the annual return that makes the NPV equal to zero.

Generally speaking, the higher an internal rate of return, the more desirable an investment is to undertake. IRR is uniform for investments of varying types and, as such, can be used to rank multiple prospective investments or projects on a relatively even basis. In general, when comparing investment options with other similar characteristics, the investment with the highest IRR probably would be considered.

## REASON FOR IRR

The ultimate goal of IRR is to identify the rate of discount, which makes the present value of the sum of annual nominal cash inflows equal to the initial net cash outlay for the investment. Several methods can be used when seeking to identify an expected return, but IRR is often ideal for analyzing the potential return of a new project that a company is considering undertaking.

Think of IRR as the rate of growth that an investment is expected to generate annually. Thus, it can be most similar to a compound annual growth rate (CAGR). In reality, an investment will usually not have the same rate of return each year. Usually, the actual rate of return that a given investment ends up generating will differ from its estimated IRR.

## WHAT ARE THE EXAMPLES OF IRR

Assume a company is reviewing two projects. Management must decide whether to move forward with one, both, or neither. Its cost of capital is 10%. The cash flow patterns for each are as follows:

Project A

• Initial Outlay = $5,000 • Year one =$1,700
• Year two = $1,900 • Year three =$1,600
• Year four = $1,500 • Year five =$700

Project B

• Initial Outlay = $2,000 • Year one =$400
• Year two = $700 • Year three =$500
• Year four = $400 • Year five =$300

The company must calculate the IRR for each project. Initial outlay (period = 0) will be negative. Solving for IRR is an iterative process using the following equation:

$0 = Σ CFt ÷ (1 + IRR)t where: • CF = net cash flow • IRR = internal rate of return • t = period (from 0 to last period) -or-$0 = (initial outlay * −1) + CF1 ÷ (1 + IRR)1 + CF2 ÷ (1 + IRR)2 + … + CFX ÷ (1 + IRR)X

Using the above examples, the company can calculate IRR for each project as:

IRR Project A

$0 = (−$5,000) + $1,700 ÷ (1 + IRR)1 +$1,900 ÷ (1 + IRR)2 + $1,600 ÷ (1 + IRR)3 +$1,500 ÷ (1 + IRR)4 + \$700 ÷ (1 + IRR)5

### How to Calculate IRR

1. Using the formula, one would set NPV equal to zero and solve for the discount rate, which is the IRR.
2. The initial investment is always negative because it represents an outflow.
3. Each subsequent cash flow could be positive or negative, depending on the estimates of what the project delivers or requires as a capital injection in the future.
4. However, because of the nature of the formula, IRR cannot be easily calculated analytically and instead must be calculated iteratively through trial and error or by using software programmed to calculate IRR (e.g., using Excel).1

### What Is IRR Used for?

In capital planning, one popular scenario for IRR is comparing the profitability of establishing new operations with that of expanding existing operations. For example, an energy company may use IRR in deciding whether to open a new power plant or to renovate and expand an existing power plant.

While both projects could add value to the company, it is likely that one will be the more logical decision as prescribed by IRR. Note that because IRR does not account for changing discount rates, it’s often not adequate for longer-term projects with discount rates that are expected to vary.

IRR is also useful for corporations in evaluating stock buy back programs. Clearly, if a company allocates substantial funding to repurchasing its shares, then the analysis must show that the company’s own stock is a better investment—that is, has a higher IRR—than any other use of the funds, such as creating new outlets or acquiring other companies.

Individuals can also use IRR when making financial decisions—for instance, when evaluating different insurance policies using their premiums and death benefits. The general consensus is that policies that have the same premiums and a high IRR are much more desirable.

Note that life insurance has a very high IRR in the early years of policy—often more than 1,000%. It then decreases over time. This IRR is very high during the early days of the policy because if you made only one monthly premium payment and then suddenly died, your beneficiaries would still get a lump sum benefit.

Another common use of IRR is in analyzing investment returns. In most cases, the advertised return will assume that any interest payments or cash dividends are reinvested back into the investment. What if you don’t want to reinvest dividends but need them as income when paid? And if dividends are not assumed to be reinvested, are they paid out, or are they left in cash? What is the assumed return on the cash? IRR and other assumptions are particularly important on instruments like annuities, where the cash flows can become complex.

Finally, IRR is a calculation used for an investment’s money-weighted rate of return (MWRR). The MWRR helps determine the rate of return needed to start with the initial investment amount factoring in all of the changes to cash flows during the investment period, including sales proceeds.

### Limitations of IRR

IRR is generally ideal for use in analyzing capital budgeting projects. It can be misconstrued or misinterpreted if used outside of appropriate scenarios. In the case of positive cash flows followed by negative ones and then by positive ones, the IRR may have multiple values. Moreover, if all cash flows have the same sign (i.e., the project never turns a profit), then no discount rate will produce a zero NPV.

Within its realm of uses, IRR is a very popular metric for estimating a project’s annual return; however, it is not necessarily intended to be used alone. IRR is typically a relatively high value, which allows it to arrive at an NPV of zero. The IRR itself is only a single estimated figure that provides an annual return value based on estimates. Since estimates in IRR and NPV can differ drastically from actual results, most analysts will choose to combine IRR analysis with. Scenarios can show different possible NPVs based on varying assumptions.

As mentioned, most companies do not rely on IRR and NPV analyses alone. These calculations are usually also studied in conjunction with a company’s WACC and an RRR, which provides for further consideration.

Companies usually compare IRR analysis to other tradeoffs. If another project has a similar IRR with less up-front capital or simpler extraneous considerations, then a simpler investment may be chosen despite IRRs.

In some cases, issues can also arise when using IRR to compare projects of different lengths. For example, a project of a short duration may have a high IRR, making it appear to be an excellent investment. Conversely, a longer project may have a low IRR, earning returns slowly and steadily. The ROI metric can provide some more clarity in these cases, although some managers may not want to wait out the longer time frame.

### WHAT IS TI-84

The TI-84 Plus graphing calculator is ideal for high school math and science. Its MathPrint technology engages students by enabling them to enter fractions and equations in proper notation so they see it on the display exactly as it’s printed in texts and on the board.

## How to Calculate IRR on TI-84

Solving for the IRR on TI-84 is done in a similar way, except that we’ll use the IRR function. This function is defined as: