Internal Rate of Return

Ravi (IBA)

IRR

• Definition:• The internal rate of return on an investment or project is

the "annualized effective compounded return rate" or rate of return that makes the net present value (NPV as NET*1/(1+IRR)^year) of all cash flows (both positive and negative) from a particular investment equal to zero.

• It can also be defined as the discount rate at which the present value of all future cash flow is equal to the initial investment or in other words the rate at which an investment breaks even.

• In more specific terms, the IRR of an investment is the discount rate at which the net present value of costs (negative cash flows) of the investment equals the net present value of the benefits (positive cash flows) of the investment.

Uses of IRR

• IRR calculations are commonly used to evaluate the desirability of investments or projects.

• The higher a project's IRR, the more desirable it is to undertake the project.

• Assuming all projects require the same amount of up-front investment, the project with the highest IRR would be considered the best and undertaken first.

• A firm (or individual) should, in theory, undertake all projects or investments available with IRRs that exceed the cost of capital. Investment may be limited by availability of funds to the firm and/or by the firm's capacity or ability to manage numerous projects.

• Because the internal rate of return is a rate quantity, it is an indicator of the efficiency, quality, or yield of an investment.

• This is in contrast with the net present value, which is an indicator of the value or magnitude of an investment.

• One of the uses of IRR is by corporations that wish to compare capital projects.

• For example, a corporation will evaluate an investment in a new plant versus an extension of an existing plant based on the IRR of each project.

• In such a case, each new capital project must produce an IRR that is higher than the company's cost of capital. Once this hurdle is surpassed, the project with the highest IRR would be the wiser investment, all other things being equal (including risk).

Calculation

Calculation NPV set at Zero – Find out r

• Internal Rate of Return Examples• Internal Rate of Return (IRR) or Discounted

Cash Flow Rate of Return measures the expected rate of returns on an investment or project based on internal factors.

• It finds widespread application to compare and rank the attractiveness of different projects. Read on for some IRR examples.

Example 1: Manual Method

• Internal Rate of Return ExamplesAssume a new bottling plant costs $25,000, including installation cost, operating at 100 percent capacity for five years, with uniform operating costs and profits:•cost of raw materials: $750•overheads such as rent, salary, energy costs and others: $1000•costs to maintain the machinery: $250•expected sales revenue per annum: $7500•effective tax rate: 10 percentThe IRR of the project can help in determining the attractiveness of the project relative to the cost of capital.

• The first step is to determine the cash flow of the project every year

• Annual cash inflow: $7500• Less: cash outflows: ($750+$1000+$250) =

$2000• Gross Profit = $7500-$2000 = $5000• Less: Tax @10 percent of gross profit = $500 • Net annual Cash Flow =$5000-$500=$4500

• The second step is to determine the present value of future cash flows

• The formula to determine future cash flows= (Cash Flow)*(1 + Interest Rate)^number of years

• Assuming the cost of capital is 5 percent for this project.• Present Value for first year = 4500*(1+5 percent) =

4500*1.05 = 4725• The cash flow can vary every year or period of calculation,

but for the sake of convenience, assume that the cash flow remains same for the entire period of the machinery’s lifecycle, that is 5 years.

• Present value for the second year = 4500*(1+5 percent)^2 = 4500*1.1025 = 4961.25

• Present value for the third year = 4500*(1+5 percent)^3 = 4500*1.1576 = 5209.20

• Present value for the fourth year = 4500*(1+5 percent)^4 = 4500*1.2150 = 5467.5

• Present value for the fifth year = 4500*(1+5 percent)^5 = 4500*1.2763 = 5743.35

• Net present value of the project = -25,000 (initial investment) + 4725 + 4961.25 + 5209.20 + 5467.5 + 5743.35 = 1106.30

• IRR is the rate at which the net present value of the investment becomes zero.

• At 5 percent, the net present value is greater than the investment, meaning that IRR is less than 5 percent, and if the project delivers a return of 5 percent, it becomes profitable.

• In a similar manner, IRR ranks two projects of similar nature.

IRR Calculation

We will use one example in order to illustrate how the internal rate of return can be calculated and the approach is. Let’s say that company A uses the internal rate of return to evaluate investment opportunities and make a decision regarding the profitability and viability of a project.There is one potential project that Company A wishes to appraise with the following characteristics:-An initial investment of $50,000 is required during the first year.-The project will last for four years and the cash inflows during these four years will be:Year 1 : $15,000Year 2: $20,000Year 3: $25,000Year 4: $18,000The company has a cost of capital of 15% and wishes to appraise this project and decide whether to proceed or not.

Internal Rate of Return Calculation with Trial and Error

• From the IRR definition, we know that the IRR is the discount rate that makes the present value of the cash flows become $nil.

• We can therefore use a trial and error approach and start increasing the discount rates until we get to a present value that is $nil.

How to Calculate the Internal Rate of Return

• As we can see from this table, a discount rate of 19% gives around $500 NPV while a 20% discount rate gives a $-462 NPV. We can therefore understand that the IRR is somewhere in the middle or around 19.5%.

Internal Rate of Return Calculation using two discount rates

• Internal Rate of Return Formula• IRR= Ra + (NPVa/(NPVa-NPVb))*(Rb-Ra)• where• Ra is the discount rate that gives the positive

net present value, • NPVa is the positive NPV,• NPVb is the negative NPV and Rb is the

discount rate that gives the negative NPV.

• The table is part of the first table and we can see that a 10% discount rate gives a positive NPV and a 20% gives a negative NPV. We can therefore use the formula above and calculate IRR as:

• IRR= 10+(11,242/(11,242+462))*(20-10)=19.6%• As you can see both methods will give the same

IRR (more or less) but most people prefer to calculate IRR by using the second approach since it involves less calculations.

Internal Rate of Return Advantages

• There are however certain advantages that IRR has which make it one of the most preferred capital appraisal methods.

• It’s an easy way to decide to accept or reject projects.• It’s a robust method that can be used to monitor how

a project is performing based on the actuals vs the budgets and how that compares to the cost of capital.

• It takes into account the time value of money compared to other methods (payback period for example) that do not.

Limitations and Disadvantages of the Internal Rate of Return

• The internal rate of return is a very robust capital appraisal method but there are certain limitations.

• For example: When a project has positive cash flows, followed by negative and then followed by positive cash flows again, there will be more than one IRR (more than solution).

• IRR is not very reliable when comparing projects that have significantly different time horizons (i.e project A will last for 5 years while project B will last for 15 years).

• Due to the limitations explained above, IRR is mostly used a decision tool (accept or reject) and not as a comparison tool (project A vs project B).