Internal Rate of Return

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: 0 1 2 3 4 Cash Flows: -1,000 500 400 300 100 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: • D1 = 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 D1? • Do * (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: • 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 = Currentprice of stock

Sample Question • The University of Illinois paid dividends in the first and second year amounting to $2 and $3respectively. It then announced that dividends would be paid at a constant rate of 10%. The current 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%

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: http://people.sauder.ubc.ca/phd/barnea/documents/lecture%202%20-%202004.pdf

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.

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.

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?

Internal Rate of Return