Internal Rate of Return Andrew Jain and Ravinder Saidha

What 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 Conclusion

What is Internal Rate of Return? Another way of making a capital budgeting decision Is calculated when the Net Present Value is set equal to Zero There are four model types we will cover: Projects / Common Stocks Zero Growth Constant Growth Multiple Growth

IRR for Common Stocks Formula

Sample Question Time Period:01234 Cash Flows: -1, PV of the inflows discounted at IRR -1,000 NPV = 0

Sample Question Continued Can only find IRR by trial and error IRR = 14.49%

Practice Question Professor 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: $300,000 How do you find his internal rate of return for this investment? A B C D E This is a trick question

IRR for Zero Growth Models A zero growth model is when dividends per share remain the same for every year Formula: Where: D 1 = Dividend paid P = Current price of stock

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%

IRR for Constant Growth Models A constant growth model is when the dividend per share grows at the same rate every year Formula is similar to zero growth, except you have to add growth:

Sample 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 D 1 ?  D o * (1 + Growth Rate)  $1.80 * (1+5%) = $1.89  IRR = 9.72%

IRR for Multiple Growth Model A multiple growth model is when dividends growth rate 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: D t = Dividend payments before dividends are made constant D t+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 stock

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%. The current price of the stock is $55. We know: D 1 = $2 D 2 = $3 P = 55 T = 2 (as after second year, dividends become constant) We need to find D 3 : $3 * (1+10%) = $3.30 IRR = 14.9%

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 do

Crossover Rate The crossover rate is defined as the rate at which the NPV’s of two projects are equal. Source:

Internal Rate of Return Advantages Doesn’t require a discount rate to calculate like 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. ProjectC_0C_1IRR NPV at 10% A-1,000+1,500+50%+364 B+1,000-1,500+50%-364

Disadvantages 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 discount rate.

Disadvantages Continued Mutually exclusive projects can be misrepresented by the IRR 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 should choose project C due to its higher IRR. Project D, however, has the higher NPV. ProjectC_0C_1IRR (%) NPV at 10% C-10,000+20, ,182 D-20,000+35, ,818

Conclusion There are various types of models for calculating IRR including common stock, zero growth, constant growth, and multiple growth. Despite the disadvantages covered, IRR is still a much better measure than the payback method or even return on book. When applied correctly, IRR calculations yield the same decisions that NPV calculations would. In cases where IRR causes conflicts in decision-making, it is more useful to use NPV.

Questions?