The Internal Rate of Return (IRR) ©Dr. B. C. Paul 2002 revisions 2008 Note – The subject covered in these slides is considered to be “common knowledge” to those familiar with the subject and books or articles covering the concepts are widespread. The Spreadsheet program used Is Microsoft Excel. The spreadsheets being demonstrated were developed by the author.

Back to Herby Choosing a Personal Loan or Credit Card  Assume that Herby will buy the supplies at Smowe’s so he will not be on a credit card cash advance.  How do we compare two financial alternatives to the same problem when both will cost you money?

The Cash Flow Comparison Trick I have a hunch Herby would rather have the bank loan to fix up his house so I will get the cash flow from choosing the bank loan instead of the credit card Herby pays a $200 loan application fee $0 - $200 Bank loan payments stay the same while the credit card payments go down with time. They start at -$1.79 and end at -$48.14 After the bank loan is paid off Herby would still have credit card bills so now Herby is saving money by having the bank loan instead of the credit card. Savings start at $57.15 and decline to $52.74 when the house sells We’ll assume Herby would pay off the credit card when the house sold. By having the bank loan instead of the credit card, Herby keeps money he would otherwise have to use to pay off the credit card $2, $0. No Annuities Here – No Way I’m going to do 70 P/F calculations by Hand!

Copy the Bank Loan Schedule from Interest Comparison Spreadsheet

Do a Paste Special Values into a blank spreadsheet

Bank Loan Cash Flow Pasted into Place

Now Copy the first 69 payments from the credit card

Paste It Into Place

Add the Payoff Amount to the Credit Card when the House Sells

Add in the Time 0 Fee for the Bank Loan There is The $200

Enter =favorite – other in the next column

Copy and Paste the Formula for length of longest cash flow

Reverse Sign to Reflect Money Going Out of Herby’s Pocket (All the numbers were positive reflecting money going to bankers) Now I Have the 3 rd Cash Flow to Analyze

Copy My Third Cash Flow (I’m going to Paste into Class Assistant)

The Values are Pasted into Class Assistant

What Interest Rate to Use  We’ve looked at what peoples marginal rate of interest may be  We’ve looked at feeling around with NPVs using different interest rates to see what happens  Another tool is the IRR  Internal Rate of Return  It is the interest rate that makes NPV zero

The IRR  The IRR is popular because it tells you what interest rate the investment makes  Can make complicated cash flow into an interest rate like is posted at a bank  Very simple flows have a formula for IRR but most cash flow IRRs are computed iteratively until the NPV is 0  The way financial calculators do it  Excel has an IRR function that works same way.  Where going to do manual iteration this time

Lets Try 2% A Positive NPV indicates too low a guess

Lets Try 6% What does this mean?

Lets Try 12% What Next?

Lets Try 20% So its gone negative. The interest rate is less than 20%, but probably not much.

Lets Try 16% We’re Getting Close Its between 16% and 20% and closer to 16%

I’ll Call this Close Enough

Of Course Class Assistant Uses the IRR Function and I could have just looked down one line The guess method is still useful in case the computer based guesses ever return an Error. I can always go back to the definition of IRR.

Conclusion  Picking the bank loan instead of a credit card to pay for his home repairs is like Herby investing at around 16.4% interest  I doubt Herby has many opportunities for that kind of return  You can see how wise choices about needed expenses can help you to accumulate wealth  Do not confuse this to mean that spending money for anything makes you wealthy.

Interpreting IRR  The IRR represents the rate of interest paid by the project (or the selection of the preferred cost scenario over its alternative)  The IRR is compared to the Rate of Return that the investor requires (or the interest rate for the investor’s other opportunities)  If the rate is greater or equal to the target rate then GO FOR IT  If not spit in the pot and walk away