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Relationship between IRR & NPV


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Relationship between IRR & NPV

  1. 1. Financial Management Assignment 1 Relationship between IRR & NPV IRR & Modified IRR By Zeeshan Valliani (12543) MBA Executive July 14th, 2012
  2. 2. Relationship between IRR & NPVIRR – Internal Rate of ReturnNPV - Net Present ValueNPV and IRR, are measures that are used to evaluate a potential capital project or investment.With both IRR and NPV, we evaluate a stream of expected cash inflows and outflows to helpdetermine if we should make a specific investment or not. The IRR indicates the potential growthpercentage of the investment. The NPV, on the other hand, indicates the value of a projectsincome potential today.CalculationsIRR gives insight into the potential profitability of an investment when the NPV still equals zero.The IRR is also commonly known as the discount rate. When we compare potential investments, ahigher IRR usually indicates a better investment choice.FormulaInitial Cash Outlay = CF1/(1 + IRR)^1 + CF2/(1 + IRR)^2 + ... + CFn/(1 + IRR)^n.In this formulation, CF stands for cash flow. Each expected future cash flow must be divided by (1+ IRR) raised to the nth power, where n equals the number of years after the initial cash outlaywhen the cash inflow is expected to occur. For fractional years, you must raise the value inparentheses to the fractional power. If you will have three cash flows expected in one, two and fourand a half years after the initial cash outlay respectively, the denominators will be (1 + IRR), (1 +IRR)^2 and (1 + IRR)^4.5, respectively.Amounts of ReturnConsider the minimum rate of return you find acceptable. For an investor, the IRR must at leastequal the minimum amount of return expected for a particular investment. If the IRR does not meetthis minimum, look for another investment. The NPV, on the other hand, shows the investmentsvalue in todays dollars. The NPV will equal zero if the investments future discounted income,minus the initial cash outflow of the project, does not carry any present-day value.Break-Even PointWhen measuring an investments profitability through the IRR, always consider the break-evenpoint of that investment. The IRR assumes that your investment will generate neither a loss nor acash profit and that future income from the investment will occur only at specific milestones andmonetary values during the lifetime of the investment.Predetermined Return RateWhen calculating the NPV, compare what you invested today with the present value of the cashreceipts expected in the future. Use the NPV calculation to discount all the future income streamsbased on the expected rate of return. For example, if you want to earn a minimum return of 4percent on your investment, discount each of the future income payments using this percentage to
  3. 3. determine the present-day value of the investment. Subsequently, to obtain the NPV calculation,add all the discounted future income payments and subtract this sum from the projects initial cashoutflow.Relationship between IRR & Modified IRRIRR – Internal Rate of ReturnModified IRR– Modified Internal Rate of ReturnThe modified internal rate of return is the same concept as the internal rate of return. Thedifference between the two indicates that the formula has been slightly modified to get a morerealistic idea of how lucrative a deal you are considering.The internal rate of return normally considers only the initial investment. A modified calculationadds another variable to the equation by considering the rate of return on money that is re-invested.So, if there is an investment with a high yield, but the money will be invested with a regular return,the modified internal rate of return will reflect the true value of the venture.It is the rate of return that a project generates to cover its costs -- taking into account the time valueof money. IRR, as a methodology, has limitations that modified IRR attempts to address. Theacceptance rule is the same for basic and modified: Accept the project if IRR is greater than therequired return on the project. A modified IRR of 25 percent or greater is often acceptable.CalculationsMIRR is calculated as follows:where n is the number of equal periods at the end of which the cash flows occur (not the number ofcash flows), PV is present value (at the beginning of the first period), FV is future value (at the endof the last period).The formula adds up the negative cash flows after discounting them to time zero using the externalcost of capital, adds up the positive cash flows including the proceeds of reinvestment at theexternal reinvestment rate to the final period, and then works out what rate of return would causethe magnitude of the discounted negative cash flows at time zero to be equivalent to the futurevalue of the positive cash flows at the final time period.Relation to Capital Budgeting and NPVModified IRR is a common investment criterion in capital budgeting decisions (e.g., which fixedassets to buy, products to launch or markets to enter). The most effective investment criterion,
  4. 4. however, is the net present value approach, or NPV. In essence, NPV is the difference between aprojects market value and its cost; thus, acceptable projects are those with positive NPV. Aprojects market value is the sum of its discounted future cash flows. IRR relates to NPV in that it isthe rate of return at which a projects NPV is zero.IRR Problem No. 1: Negative Cash FlowsWhen a project has negative future cash flows, solving for the rate at which NPV is zero yieldsmultiple IRRs; this is also known as the multiple rates of return problem. You cannot tell whichrate is the correct IRR -- perhaps both or neither. To address this, compute the present value ofnegative future cash flows at first and add it to the cost of the project. Next, set NPV to zero andsolve for the "modified" IRR.IRR Problem No. 2: Comparing Mutually Exclusive ProjectsModified IRR and the NPV approach produce conflicting recommendations when comparingmutually exclusive projects. This often occurs for projects with low required rates of return. Thereason is timing of cash flows: At low discount rates, deferred cash flows are more valuable. Aproject with significant cash flows around the end of its life yields a lower modified IRR comparedto a similar project with significant cash flows around the beginning of its life. Ultimately, theproject with the highest NPV is always the value-maximizing choice.Qualitative ConsiderationsDo not forget to consider the strategic implications of undertaking a project. A seeminglyprofitable project can destroy value over the long run as a company loses its competitive advantagein the market. This calls for a wider assessment of a project, taking into account potential changesin the business environment, strategic position relative to the competition, and real options (i.e.options embedded in the project). Examples of real options include the option to delay, expand orabandon a project.