the internal rate of return (irr) ©dr. b. c. paul 2002 revisions 2008 note – the subject covered...

The Internal Rate The Internal Rate of Return (IRR)of Return (IRR)©Dr. B. C. Paul 2002 revisions 2008©Dr. B. C. Paul 2002 revisions 2008

Note – The subject covered in these slides is considered to be “common Note – The subject covered in these slides is considered to be “common knowledge” to those familiar with the subject and books or articles knowledge” to those familiar with the subject and books or articles covering the concepts are widespread. The Spreadsheet program usedcovering the concepts are widespread. The Spreadsheet program used

Is Microsoft Excel. The spreadsheets being demonstrated were Is Microsoft Excel. The spreadsheets being demonstrated were developed by the author.developed by the author.

Back to Herby Choosing a Back to Herby Choosing a Personal Loan or Credit Personal Loan or Credit CardCard

Assume that Herby will buy the supplies Assume that Herby will buy the supplies at Smowe’s so he will not be on a credit at Smowe’s so he will not be on a credit card cash advance.card cash advance.

How do we compare two financial How do we compare two financial alternatives to the same problem when alternatives to the same problem when both will cost you money?both will cost you money?

The Cash Flow The Cash Flow Comparison TrickComparison Trick

I have a hunch Herby would rather have the bank loan to fix up his house so Iwill 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 thesame while the credit card paymentsgo down with time.

They start at -$1.79 and end at -$48.14

After the bank loan is paid offHerby would still have credit cardbills so now Herby is saving moneyby having the bank loan instead ofthe credit card.

Savings start at $57.15 and decline to$52.74 when the house sells

We’ll assume Herby would pay off thecredit card when the house sold. Byhaving the bank loan instead of the creditcard, Herby keeps money he wouldotherwise have to use to pay off the creditcard$2,499.18 - $0.

No Annuities Here – No Way I’m going to do 70 P/F calculations by Hand!

Copy the Bank Loan Copy the Bank Loan Schedule from Interest Schedule from Interest Comparison SpreadsheetComparison Spreadsheet

Do a Paste Special Values Do a Paste Special Values into a blank spreadsheetinto a blank spreadsheet

Bank Loan Cash Flow Bank Loan Cash Flow Pasted into PlacePasted into Place

Now Copy the first 69 Now Copy the first 69 payments from the credit payments from the credit cardcard

Paste It Into PlacePaste It Into Place

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

Add in the Time 0 Fee for Add in the Time 0 Fee for the Bank Loanthe Bank Loan

There isThe $200

Enter =favorite – otherEnter =favorite – otherin the next columnin the next column

Copy and Paste the Formula Copy and Paste the Formula for length of longest cash for length of longest cash flowflow

Reverse Sign to Reflect Reverse Sign to Reflect Money Going Out of Herby’s Money Going Out of Herby’s Pocket Pocket (All the numbers were positive (All the numbers were positive reflecting money going to bankers)reflecting money going to bankers)

Now I Have the3rd Cash Flow toAnalyze

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

The Values are Pasted The Values are Pasted into Class Assistantinto Class Assistant

What Interest Rate to What Interest Rate to UseUse

We’ve looked at what peoples marginal We’ve looked at what peoples marginal rate of interest may berate of interest may be

We’ve looked at feeling around with We’ve looked at feeling around with NPVs using different interest rates to see NPVs using different interest rates to see what happenswhat happens

Another tool is the IRRAnother tool is the IRR Internal Rate of ReturnInternal Rate of Return It is the interest rate that makes NPV zeroIt is the interest rate that makes NPV zero

The IRRThe IRR

The IRR is popular because it tells you The IRR is popular because it tells you what interest rate the investment makeswhat interest rate the investment makes Can make complicated cash flow into an interest rate Can make complicated cash flow into an interest rate

like is posted at a banklike is posted at a bank

Very simple flows have a formula for IRR Very simple flows have a formula for IRR but most cash flow IRRs are computed but most cash flow IRRs are computed iteratively until the NPV is 0iteratively until the NPV is 0 The way financial calculators do itThe way financial calculators do it Excel has an IRR function that works same way.Excel has an IRR function that works same way. Where going to do manual iteration this timeWhere going to do manual iteration this time

Lets Try 2%Lets Try 2%

Enter Your Annual Interest Rate as a %, but do not use the % key during data entry 2Enter the number of compounding periods in one year 12

0.001666667 (in decimal form)

Cash Flow Evaluation Index Values(Warning IRR and Payback may not function properly on unconventional cash flows)NPV 930.69482

A Positive NPV indicates too low a guess





What does this mean?





What Next?


So its gone negative.The interest rate isless than 20%, butprobably not much.



Cash Flow Evaluation Index Values(Warning IRR and Payback may not function properly on unconventional cash flows)NPV -119.87279

Lets Try 16%Lets Try 16%Enter Your Annual Interest Rate as a %, but do not use the % key during data entry 16Enter the number of compounding periods in one year 12



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

I’ll Call this Close EnoughI’ll Call this Close Enough

Enter Your Annual Interest Rate as a %, but do not use the % key during data entry 16.338Enter the number of compounding periods in one year 12


Cash Flow Evaluation Index Values(Warning IRR and Payback may not function properly on unconventional cash flows)NPV -0.0002114

Of Course Class Assistant Of Course Class Assistant Uses the IRR Function and I Uses the IRR Function and I could have just looked down could have just looked down one lineone line

Enter Your Annual Interest Rate as a %, but do not use the % key during data entry 16.338Enter the number of compounding periods in one year 12


Cash Flow Evaluation Index Values(Warning IRR and Payback may not function properly on unconventional cash flows)NPV -0.0002114IRR 16.34%

The guess method is still useful in case the computer based guesses ever return anError. I can always go back to the definition of IRR.

ConclusionConclusion Picking the bank loan instead of a credit Picking the bank loan instead of a credit

card to pay for his home repairs is like card to pay for his home repairs is like Herby investing at around 16.4% interestHerby investing at around 16.4% interest I doubt Herby has many opportunities for that I doubt Herby has many opportunities for that

kind of returnkind of return

You can see how wise choices about You can see how wise choices about needed expenses can help you to needed expenses can help you to accumulate wealthaccumulate wealth

Do not confuse this to mean that spending Do not confuse this to mean that spending money for anything makes you wealthy.money for anything makes you wealthy.

Interpreting IRRInterpreting IRR The IRR represents the rate of interest paid The IRR represents the rate of interest paid

by the project (or the selection of the by the project (or the selection of the preferred cost scenario over its alternative)preferred cost scenario over its alternative)

The IRR is compared to the Rate of Return The IRR is compared to the Rate of Return that the investor requires (or the interest rate that the investor requires (or the interest rate for the investor’s other opportunities)for the investor’s other opportunities) If the rate is greater or equal to the target rate If the rate is greater or equal to the target rate

then GO FOR ITthen GO FOR IT If not spit in the pot and walk awayIf not spit in the pot and walk away

the internal rate of return (irr) ©dr. b. c. paul 2002 revisions 2008 note – the subject covered...

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