Internal Rate of ReturnWhat We Will CoverWhat is Internal Rate of Return?IRR for Common StocksSample QuestionSample Question ContinuedPractice QuestionIRR for Zero Growth ModelsSlide 9IRR for Constant Growth ModelsSlide 11IRR for Multiple Growth ModelSlide 13Slide 14Crossover RateSlide 16DisadvantagesDisadvantages ContinuedSlide 19ConclusionInternal Rate of ReturnAndrew Jain and Ravinder SaidhaWhat We Will Cover•What is Internal Rate of Return?•Formula to calculate IRR for:•Projects / Common Stocks•Zero-Growth Models•Constant Growth Models•Multiple Growth Models•Crossover Rate•Independent & Mutually Exclusive Projects•Advantages and Disadvantages of IRR•ConclusionWhat is Internal Rate of Return?•Another way of making a capital budgeting decision•Is calculated when the Net Present Value is set equalto Zero•There are four model types we will cover:•Projects / Common Stocks•Zero Growth •Constant Growth•Multiple GrowthIRR for Common Stocks•Formula0)1(...)1()1(22110NNIRRCFIRRCFIRRCFCFNPVNtttIRRCF00)1(Sample QuestionTime Period: 0 1 2 3 4Cash Flows: -1,000 500 400 300 100PV of theinflows discounted at IRR-1,000NPV = 0Sample Question Continued•Can only find IRR by trial and error•IRR = 14.49%0)1(...)1()1(22110NNIRRCFIRRCFIRRCFCFNPV4321)1(100)1(300)1(400)1(50010000IRRIR RIRRIRR Practice QuestionProfessor Stephen D'Arcy is planning to invest $500,000 in to his own insurance company, but is unsure about the return he will gain on this investment. He produces estimated cash flows for the following years:•Year 1: $200,000•Year 2: $250,000•Year 3: $300,000How do you find his internal rate of return for this investment?•A•B•C•D•E This is a trick question321)1(000,300)1(000,250)1(000,200000,500IRRIRRIRR 321)1(000,300)1(000,250)1(000,200000,500IRRIRRIRR 123)1(000,300)1(000,250)1(000,200000,500IRRIRRIRR 321)1(000,300)1(000,250)1(000,200000,500IRRIRRIRR IRR for Zero Growth Models•A zero growth model is when dividends per share remain the same for every year•Formula:•Where:•D1 = Dividend paid•P = Current price of stockPDIRR1Sample Question•Andrew is prepared to pay his stockholders $8 for every share held. The current price that his stock is currently held for is $65. What is his internal rate of return?•IRR = 12.3%65$8$IRRIRR for Constant Growth Models•A constant growth model is when thedividend per share grows at the same rateevery year•Formula is similar to zero growth, exceptyou have to add growth:gPDIRR 1Sample Question•Rav paid $1.80 in dividends last year. He has forecasted that his growth will be 5%per year in the future. The current share price for his company is $40. What is his IRR?What is D1?Do * (1 + Growth Rate)$1.80 * (1+5%) = $1.89IRR = 9.72%05.040$89.1$IRRIRR for Multiple Growth Model•A multiple growth model is when dividends growthrate varies over time•The focus is now on a time in the future after which dividends are expected to grow at a constant rate g•Unfortunately, a convenient expression similar to the previous equations is not available for multiple-growth models. You need to know what the current price of the stock is to find IRR•Formula:•Where:•Dt = Dividend payments before dividends are made constant•Dt+1 = Dividend payment after dividends are set to a constant rate•t = time dividends are paid at•T = time that dividends are made constant•P = Current price of stockTtNtttIRRgIRRDIRRDP)1)(()1(11Sample Question•The University of Illinois paid dividends in the first and second year amounting to $2 and $3 respectively. It then announced that dividends would be paid at a constant rate of 10%. Thecurrent price of the stock is $55.•We know:•D1 = $2•D2 = $3•P = 55•T = 2 (as after second year, dividends become constant)•We need to find D3:•$3 * (1+10%) = $3.30 •IRR = 14.9%221)1)(1.0(30.3$)1(3$)1(2$55IRRIRRIRRIRR Practice Question•Professor Stephen D'Arcy is the CEO of a large insurance firm, AIG. He is prepared to pay $10 in dividends for the first three years, in which after the third year, the growth rate in dividends will be 10%. If the stock currently sells for $100, how do you find his internal rate of return?•A•B•C•D•E I have no idea what you want me to do4321)1)(1.0(11$)1(10$)1(10$)1(10$100IRRIRRIRRIRRIRR 4321)1)(1.0(31.13$)1(1.12$)1(11$)1(10$100IRRIRRIRRIRRIRR 3321)1)(1.0(11$)1(10$)1(10$)1(10$100IRRIRRIRRIRRIRR 3321)1)(1.0(10$)1(10$)1(10$)1(10$100IRRIRRIRRIRRIRR Crossover Rate•The crossover rate is defined as the rate at which the NPV’s of two projects are equal.Source: http://people.sauder.ubc.ca/phd/barnea/documents/lecture%202%20-%202004.pdfInternal Rate of Return•Advantages•Doesn’t require a discount rate to calculatelike NPV calculations•Disadvantages•Lending vs. Borrowing•Multiple IRRs•Mutually Exclusive projects.Disadvantages•Lending vs. Borrowing•Example: Suppose you have the choice between projects A and B. Project A requires an investment of $1,000 and pays you $1,500 one year later. Project B pays you $1,000 up front but requires you to pay $1,500 one year later.Project C_0 C_1 IRRNPV at 10%A -1,000 +1,500 +50% +364B +1,000 -1,500 +50% -364Disadvantages Continued•Multiple IRR’s•In certain situations, various rates will cause NPV to equal zero, yielding multiple IRR’s.•This occurs because of sign changes in the associated cash flows.•In a case where there are multiple IRR’s, you should choose the IRR that provides the highest NPV at the appropriate discountrate.Disadvantages Continued•Mutually exclusive projects can be misrepresented by theIRR rule.•Example: Project C requires an initial investment of $10,000 and yields a inflow of $20,000 one year later. Project D requires an initial investment of $20,000 and yields an inflow of $35,000 one year later. It would appear that we shouldchoose project C due to its higher IRR. Project D, however, has the higher NPV.Project C_0 C_1 IRR (%)NPV at 10%C -10,000 +20,000 100 +8,182D -20,000 +35,000 75 +11,818Conclusion•There are various types of models for calculating