Internal Rate of Return FIN 321 Erin Kelso & Jen Wroblewski Thursday, February 1st

What is IRR? The discounted rate that equates the present value of a project’s expected cash inflows to the present value of the project’s costs The discounted rate that equates the present value of a project’s expected cash inflows to the present value of the project’s costs

What is IRR? The discount rate which sets the NPV of all cash flows equal to 0. The discount rate which sets the NPV of all cash flows equal to 0. Helps to determine the YIELD on an investment. Helps to determine the YIELD on an investment.

How do we calculate IRR? NPV = Net Present Value of the project NPV = Net Present Value of the project Initial Investment Initial Investment Ct=Cash flow at time t Ct=Cash flow at time t IRR = Internal Rate of Return IRR = Internal Rate of Return

Calculating IRR… Set the NPV = 0 Set the NPV = 0 Plug in your Cash Flows & Initial Investment Plug in your Cash Flows & Initial Investment Solve for IRR! Solve for IRR! This is the same equation used for NPV, except you know your interest rate, i. This is the same equation used for NPV, except you know your interest rate, i.

Using the Financial Calulator BA II Plus BA II Plus Go to the Cash Flow worksheet, plug in CFo, CF1, and so on… Go to the Cash Flow worksheet, plug in CFo, CF1, and so on… Go to the IRR button and click CPT (compute) and you will get your IRR! Go to the IRR button and click CPT (compute) and you will get your IRR!

So now what? Once you’ve calculated IRR Once you’ve calculated IRR  If IRR is greater than the cost of capital, then you’ve got a GOOD project on your hands (go for it!).  If IRR is less than the cost of capital, then you’ve got a BAD project on your hands (don’t undertake the project…).  If the IRR and cost of capital are equal, then you should use another method to evaluate the project!  Basically, the higher the IRR, the better the project

Example IRR Problem You are debating whether or not to invest in your best friend’s business idea, so use IRR to evaluate the project: You are debating whether or not to invest in your best friend’s business idea, so use IRR to evaluate the project: Cost of Capital: 10% Cost of Capital: 10% Initial Investment: -$200 Initial Investment: -$200 Cash Flows over the past 5 years: Cash Flows over the past 5 years: Years 1 & 2: $50 Years 1 & 2: $50 Years 3 & 4: $100 Years 3 & 4: $100 Year 5: $125 Year 5: $125

Compute IRR! A % A % B % B % C % C % D % D % E. none of the above E. none of the above

And the Answer is…. In your calculator: In your calculator: CFo=-200Enter CFo=-200Enter C01=50Enter C01=50Enter F01=2Enter F01=2Enter C02=100Enter C02=100Enter F02=2Enter F02=2Enter C03=125Enter C03=125Enter F03=1Enter F03=1Enter IRR CPT IRR CPT IRR = IRR =

Try another one… Your friend’s got another business scheme…see if you want to help him out! Your friend’s got another business scheme…see if you want to help him out! Cost of Capital: 5% Cost of Capital: 5% Initial Investment: -$1500 Initial Investment: -$1500 Cash Flows over the past 5 years: Cash Flows over the past 5 years: Years 1,2 & 3: $100 Years 1,2 & 3: $100 Year 4: $200 Year 4: $200 Year 5: $500 Year 5: $500

Compute IRR again! A. 2.61% A. 2.61% B % B % C % C % D % D % E. none of the above E. none of the above

And the answer is… In your calculator: In your calculator: CFo=-1500Enter CFo=-1500Enter C01=100Enter C01=100Enter F01=3Enter F01=3Enter C02=200Enter C02=200Enter F02=1Enter F02=1Enter C03=500Enter C03=500Enter F03=1Enter F03=1Enter IRR CPT IRR CPT IRR = IRR =

Is IRR always a good choice? IRR is useful in deciding whether or not to invest in a single project IRR is useful in deciding whether or not to invest in a single project When multiple projects are being considered, IRR is not a good investment tool to use to evaluate which project to choose. When multiple projects are being considered, IRR is not a good investment tool to use to evaluate which project to choose. The IRR calculation automatically assumes that all cash outflows are reinvested at the IRR, but doesn’t evaluate what the investor does with cash inflows, which would have an effect on the true IRR. The IRR calculation automatically assumes that all cash outflows are reinvested at the IRR, but doesn’t evaluate what the investor does with cash inflows, which would have an effect on the true IRR.

Multiple IRRs When projects have non-normal cash flows, multiple IRRs may occur When projects have non-normal cash flows, multiple IRRs may occur  A non-normal cash flow occurs when a project calls for a large cash outflow sometime during or at the end of its life There is no way to know which IRR is correct There is no way to know which IRR is correct

Sign changes in the Cash Flows IRR evaluates a project correctly when there is an initial negative cash flow, followed by a series of positive ones (-+++). IRR evaluates a project correctly when there is an initial negative cash flow, followed by a series of positive ones (-+++). If the signs are reversed (+---), that will change the accurateness of the IRR calculation. If the signs are reversed (+---), that will change the accurateness of the IRR calculation. If there are multiple sign changes in the cash flows (+-+-+) or (-+-+-), your calculation would result in multiple IRRs, also making the project very difficult to evaluate. If there are multiple sign changes in the cash flows (+-+-+) or (-+-+-), your calculation would result in multiple IRRs, also making the project very difficult to evaluate.

NPV vs. IRR NPV and IRR methods will always lead to the same accept/reject decisions for independent projects NPV and IRR methods will always lead to the same accept/reject decisions for independent projects NPV and IRR can give conflicting rankings for mutually exclusive projects (you must pick one project, you cannot accept both) NPV and IRR can give conflicting rankings for mutually exclusive projects (you must pick one project, you cannot accept both)

NPV vs. IRR NPV profiles of projects can cross when project size differences exist (the cost of one project is larger than that of the other) or when timing differences exist (most of the cash flows from one project come in the early years, while most of the cash flows from the other project come in the later years) NPV profiles of projects can cross when project size differences exist (the cost of one project is larger than that of the other) or when timing differences exist (most of the cash flows from one project come in the early years, while most of the cash flows from the other project come in the later years)

NPV vs. IRR If the cost of capital is greater than this crossover rate, the two methods give same answer If the cost of capital is greater than this crossover rate, the two methods give same answer If the cost of capital less than crossover rate, two methods give separate answers If the cost of capital less than crossover rate, two methods give separate answers

NPV vs. IRR? The NPV calculation will usually always provide a more accurate indication of whether or not a project should be undertaken or not. The NPV calculation will usually always provide a more accurate indication of whether or not a project should be undertaken or not. However, since IRR is a percentage, and NPV is shown in $$, it is more appealing for a manager to show someone a particular rate of return, as opposed to $$ amounts. However, since IRR is a percentage, and NPV is shown in $$, it is more appealing for a manager to show someone a particular rate of return, as opposed to $$ amounts.

Why do we use IRR? IRR is necessary from a capital budgeting standpoint. IRR is necessary from a capital budgeting standpoint. Just as NPV is a way to evaluate an investment, IRR provides more insight into whether or not a project/investment should be undertaken. Just as NPV is a way to evaluate an investment, IRR provides more insight into whether or not a project/investment should be undertaken. More useful for long term investments, with multiple cash flows More useful for long term investments, with multiple cash flows

Modified Internal Rate of Return Another capital budgeting tool for investments Another capital budgeting tool for investments Assumes that the project’s cash flows are reinvested at the cost of capital, not at the IRR. Assumes that the project’s cash flows are reinvested at the cost of capital, not at the IRR. This slight difference, makes the MIRR more accurate than the IRR. This slight difference, makes the MIRR more accurate than the IRR.

Any Questions? Any Questions?

Sources “Internal Rate of Return”. Wikipedia.org. “Internal Rate of Return”. Wikipedia.org. “Internal Rate of Return – IRR”. Investopedia.com. “Internal Rate of Return – IRR”. Investopedia.com.