Internal Rate of ReturnInternal Rate of Return

FIN 321FIN 321

Erin Kelso & Jen WroblewskiErin Kelso & Jen Wroblewski

Thursday, February 1stThursday, February 1st

What is IRR?What is IRR?

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

What is IRR?What is IRR?

The discount The discount rate which sets rate which sets the NPV of all the NPV of all cash flows cash flows equal to 0.equal to 0.

Helps to Helps to determine the determine the YIELD on an YIELD on an investment.investment.

How do we calculate IRR?How do we calculate IRR?

NPV = Net Present Value of the NPV = Net Present Value of the projectproject

Initial Investment Initial Investment Ct=Cash flow at time tCt=Cash flow at time t IRR = Internal Rate of ReturnIRR = Internal Rate of Return

Calculating IRR…Calculating IRR…

Set the NPV = 0Set the NPV = 0 Plug in your Cash Flows & Initial Plug in your Cash Flows & Initial

Investment Investment Solve for IRR!Solve for IRR! This is the same equation used for This is the same equation used for

NPV, except you know your interest NPV, except you know your interest rate, i.rate, i.

Using the Financial CalulatorUsing the Financial Calulator

BA II PlusBA II Plus Go to the Cash Flow worksheet, plug Go to the Cash Flow worksheet, plug

in CFo, CF1, and so on…in CFo, CF1, and so on… Go to the IRR button and click CPT Go to the IRR button and click CPT

(compute) and you will get your IRR!(compute) and you will get your IRR!

So now what?So now what?

Once you’ve calculated IRR Once you’ve calculated IRR If IRR is greater than the cost of capital, then If IRR is greater than the cost of capital, then

you’ve got a you’ve got a GOODGOOD project on your hands (go for project on your hands (go for it!).it!).

If IRR is less than the cost of capital, then you’ve If IRR is less than the cost of capital, then you’ve got a got a BAD BAD project on your hands (don’t project on your hands (don’t undertake the project…).undertake the project…).

If the IRR and cost of capital are equal, then you If the IRR and cost of capital are equal, then you should use another method to evaluate the should use another method to evaluate the project!project!

Basically, the higher the IRR, the better the Basically, the higher the IRR, the better the projectproject

Example IRR ProblemExample IRR Problem

You are debating whether or not to You are debating whether or not to invest in your best friend’s business invest in your best friend’s business idea, so use IRR to evaluate the project:idea, so use IRR to evaluate the project:

Cost of Capital: 10%Cost of Capital: 10% Initial Investment: -$200Initial Investment: -$200 Cash Flows over the past 5 years: Cash Flows over the past 5 years:

Years 1 & 2: $50Years 1 & 2: $50 Years 3 & 4: $100Years 3 & 4: $100 Year 5: $125Year 5: $125

Compute IRR!Compute IRR!

A. 15.36%A. 15.36% B. 31.20%B. 31.20% C. -17.29%C. -17.29% D. 26.04%D. 26.04% E. none of the aboveE. none of the above

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

Try another one…Try another one…

Your friend’s got another business Your friend’s got another business scheme…see if you want to help him scheme…see if you want to help him out!out!

Cost of Capital: 5%Cost of Capital: 5% Initial Investment: -$1500Initial Investment: -$1500 Cash Flows over the past 5 years:Cash Flows over the past 5 years:

Years 1,2 & 3: $100Years 1,2 & 3: $100 Year 4: $200Year 4: $200 Year 5: $500Year 5: $500

Compute IRR again!Compute IRR again!

A. 2.61%A. 2.61% B. -9.66%B. -9.66% C. 10.65%C. 10.65% D. -21.79%D. -21.79% E. none of the aboveE. none of the above

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

Is IRR always a good choice?Is IRR always a good choice?

IRR is useful in deciding whether or not to IRR is useful in deciding whether or not to invest in a single projectinvest in a single project

When multiple projects are being When multiple projects are being considered, IRR is not a good investment considered, IRR is not a good investment tool to use to evaluate which project to tool to use to evaluate which project to choose.choose.

The IRR calculation automatically assumes The IRR calculation automatically assumes that all cash outflows are reinvested at the that all cash outflows are reinvested at the IRR, but doesn’t evaluate what the IRR, but doesn’t evaluate what the investor does with cash inflows, which investor does with cash inflows, which would have an effect on the true IRR.would have an effect on the true IRR.

Multiple IRRsMultiple IRRs

When projects have non-normal cash When projects have non-normal cash flows, multiple IRRs may occurflows, multiple IRRs may occur A non-normal cash flow occurs when a project A non-normal cash flow occurs when a project

calls for a large cash outflow sometime during calls for a large cash outflow sometime during or at the end of its lifeor at the end of its life

There is no way to know which IRR is There is no way to know which IRR is correctcorrect

Sign changes in the Cash FlowsSign changes in the Cash Flows

IRR evaluates a project correctly when there IRR evaluates a project correctly when there is an initial negative cash flow, followed by a is an initial negative cash flow, followed by a series of positive ones (-+++).series of positive ones (-+++).

If the signs are reversed (+---), that will If the signs are reversed (+---), that will change the accurateness of the IRR change the accurateness of the IRR calculation.calculation.

If there are multiple sign changes in the cash If there are multiple sign changes in the cash flows (+-+-+) or (-+-+-), your calculation flows (+-+-+) or (-+-+-), your calculation would result in multiple IRRs, also making would result in multiple IRRs, also making the project very difficult to evaluate.the project very difficult to evaluate.

NPV vs. IRRNPV vs. IRR

NPV and IRR methods will always NPV and IRR methods will always lead to the same accept/reject lead to the same accept/reject decisions for independent projectsdecisions for independent projects

NPV and IRR can give conflicting NPV and IRR can give conflicting rankings for mutually exclusive rankings for mutually exclusive projects (you must pick one project, projects (you must pick one project, you cannot accept both) you cannot accept both)

NPV vs. IRRNPV vs. IRR

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

NPV vs. IRRNPV vs. IRR

If the cost of If the cost of capital is greater capital is greater than this than this crossover rate, crossover rate, the two methods the two methods give same answergive same answer

If the cost of If the cost of capital less than capital less than crossover rate, crossover rate, two methods give two methods give separate answersseparate answers

NPV

Cost of capital

Crossover rate

NPVA

NPVB

NPV vs. IRR?NPV vs. IRR?

The NPV calculation will usually The NPV calculation will usually always provide a more accurate always provide a more accurate indication of whether or not a project indication of whether or not a project should be undertaken or not.should be undertaken or not.

However, since IRR is a percentage, However, since IRR is a percentage, and NPV is shown in $$, it is more and NPV is shown in $$, it is more appealing for a manager to show appealing for a manager to show someone a particular rate of return, someone a particular rate of return, as opposed to $$ amounts.as opposed to $$ amounts.

Why do we use IRR?Why do we use IRR?

IRR is necessary from a capital IRR is necessary from a capital budgeting standpoint.budgeting standpoint.

Just as NPV is a way to evaluate an Just as NPV is a way to evaluate an investment, IRR provides more investment, IRR provides more insight into whether or not a insight into whether or not a project/investment should be project/investment should be undertaken.undertaken.

More useful for long term More useful for long term investments, with multiple cash flowsinvestments, with multiple cash flows

Modified Internal Rate of ReturnModified Internal Rate of Return

Another capital budgeting tool for Another capital budgeting tool for investmentsinvestments

Assumes that the project’s cash Assumes that the project’s cash flows are reinvested at the cost of flows are reinvested at the cost of capital, not at the IRR.capital, not at the IRR.

This slight difference, makes the This slight difference, makes the MIRR more accurate than the IRR.MIRR more accurate than the IRR.

Any Questions?Any Questions?

SourcesSources

““Internal Rate of Return”. Internal Rate of Return”. Wikipedia.org. Wikipedia.org. http://en.wikipedia.org/wiki/Internal_rate_of_returnhttp://en.wikipedia.org/wiki/Internal_rate_of_return

““Internal Rate of Return – IRR”. Internal Rate of Return – IRR”. Investopedia.com. Investopedia.com. http://www.investopedia.com/terms/i/irr.asphttp://www.investopedia.com/terms/i/irr.asp