External Rates of External Rates of ReturnReturn©Dr. Bradley C. Paul 2002 revisions 2009©Dr. Bradley C. Paul 2002 revisions 2009

Note – The procedures found in these slides can be found in numerous Note – The procedures found in these slides can be found in numerous texts dealing with the subject of engineering economics, none of which texts dealing with the subject of engineering economics, none of which was specifically used as a template for these slides. The author regards was specifically used as a template for these slides. The author regards the contents of these slides to be common knowledge to those schooled the contents of these slides to be common knowledge to those schooled in the field.in the field.

The External Rate of The External Rate of ReturnReturn Plan to divert some money to lower rate Plan to divert some money to lower rate

investments just as you would in real lifeinvestments just as you would in real life This may allow you to have sinking funds etc.This may allow you to have sinking funds etc.

Because the money you grew outside the Because the money you grew outside the project grows at a different rate - where and how project grows at a different rate - where and how much you put out when does impact the answermuch you put out when does impact the answer in general minimize the amount of cash you run in general minimize the amount of cash you run

outside the investmentoutside the investment You remember Herby and Hanna Housings You remember Herby and Hanna Housings

cash flow had the foul characteristiccash flow had the foul characteristic 40% was the right answer if they could invest some 40% was the right answer if they could invest some

of their savings from renting at 40%of their savings from renting at 40%

ERR ExampleERR Example

Herby and Hanna Housing Cash Flow for Herby and Hanna Housing Cash Flow for buying instead of rentingbuying instead of renting

Start

Year 1 Year 2 Year 3 Year 4 Year 5Year 6

More ERR MethodMore ERR Method

Look at your opportunities for short term Look at your opportunities for short term fluid investments and select a rate of fluid investments and select a rate of return for the growth of money outside return for the growth of money outside the projectthe project Lets say Herby and Hanna Housing decide Lets say Herby and Hanna Housing decide

to put their savings in a Money Market at 4%to put their savings in a Money Market at 4%

Find Your External Opportunity Rate.Find Your External Opportunity Rate.

The ERR MethodThe ERR Method

Take all initial negative cash flows and Take all initial negative cash flows and discount them back to time zerodiscount them back to time zero Herby and Hanna Housing ExampleHerby and Hanna Housing Example

-$3560 at time zero-$3560 at time zero Drops directly into the pot without any discount Drops directly into the pot without any discount

factorfactor If you have multiple negative cash flows you will If you have multiple negative cash flows you will

have several P/F factors to discount these back have several P/F factors to discount these back at the external rate.at the external rate.

Discount some forward - Discount some forward - some backsome back

Initial Negative ValuesBucket

Subsequent ValuesForward Bucket

Discounting Positive Discounting Positive Flows ForwardFlows Forward

Comparative Cash Flow if Herby External Rate InfoBuys Instead of Rents Annual % 0 4

Buying Cash "i" 0 NPV 16925.48 0.003333333Over Rent Position n P/F n forward F/P

-3560 -3560 0 1 -3560 7322.33 -3537.67 1 1 22.33 72 1.270742 28.3756661622.33 -3515.34 2 1 22.33 71 1.26652 28.2813948422.33 -3493.01 3 1 22.33 70 1.262312 28.1874367222.33 -3470.68 4 1 22.33 69 1.258119 28.0937907522.33 -3448.35 5 1 22.33 68 1.253939 28.000455922.33 -3426.02 6 1 22.33 67 1.249773 27.9074311322.33 -3403.69 7 1 22.33 66 1.245621 27.8147154122.33 -3381.36 8 1 22.33 65 1.241483 27.7223077222.33 -3359.03 9 1 22.33 64 1.237358 27.6302070322.33 -3336.7 10 1 22.33 63 1.233247 27.5384123222.33 -3314.37 11 1 22.33 62 1.22915 27.4469225842.33 -3272.04 12 1 42.33 61 1.225067 51.85706844

391.14 -2880.9 13 1 391.14 60 1.220997 477.5806078

Later Negative Flows Later Negative Flows Also Discount ForwardAlso Discount Forward

Initial Negative ValuesBucket

Subsequent ValuesForward BucketInitial Investment

Savings DiscountedForward at 4%

230.56 4283.77 59 1 230.56 14 1.047691 241.5557254-419.44 3864.33 60 1 -419.44 13 1.044211 -437.9837282-25.81 3838.52 61 1 -25.81 12 1.040742 -26.86153922

-404.84 3433.68 62 1 -404.84 11 1.037284 -419.9340261-404.84 3028.84 63 1 -404.84 10 1.033838 -418.5388965-404.84 2624 64 1 -404.84 9 1.030403 -417.1484018-404.84 2219.16 65 1 -404.84 8 1.02698 -415.7625267-404.84 1814.32 66 1 -404.84 7 1.023568 -414.3812559-404.84 1409.48 67 1 -404.84 6 1.020167 -413.004574-404.84 1004.64 68 1 -404.84 5 1.016778 -411.6324657-404.84 599.8 69 1 -404.84 4 1.0134 -410.26491615995.5 16595.3 70 1 15995.5 3 1.010033 16155.98878

ERR Problem Set UpERR Problem Set Up

Initial Negative ValuesBucket

Subsequent ValuesForward BucketInitial Investment

Future Savings andCosts Discountedforward at 4%

-404.84 2219.16 65 1 -404.84 8 1.02698 -415.7625267-404.84 1814.32 66 1 -404.84 7 1.023568 -414.3812559-404.84 1409.48 67 1 -404.84 6 1.020167 -413.004574-404.84 1004.64 68 1 -404.84 5 1.016778 -411.6324657-404.84 599.8 69 1 -404.84 4 1.0134 -410.26491615995.5 16595.3 70 1 15995.5 3 1.010033 16155.98878

0 16595.3 71 1 0 2 1.006678 00 16595.3 72 1 0 1 1.003333 0

330.18 16925.48 73 1 330.18 0 1 330.18

Sum 21482.23536

-$3560

$21,482

Solving the ERRSolving the ERR

Initial Negative ValuesBucket

Subsequent ValuesForward BucketInitial Investment

Future Savings andCosts Discountedforward at 4%

-$3560

$21,482

Now discount the future pot back into the big pot at time 0.Note this makes for a very easy IRR problem.

$3560 = 1/((1+i)73 ) * $21,482

Solve for i

(1+i)73 = $21,482/$3560

(1+ i) = 6.034^(1/73)

(1 + i) = 1.0249

i = 0.0249/monthAdapt to 1 year (1+.0249)12 = 1.3437 or 34.37%

Teachers Attitude Teachers Attitude ProblemProblem I’m a Mining and Mineral Resources EngineerI’m a Mining and Mineral Resources Engineer

Every project I do will have negative cash flows to Every project I do will have negative cash flows to build and negative at the end to reclaimbuild and negative at the end to reclaim I never see IRR work smoothly - so I don’t like itI never see IRR work smoothly - so I don’t like it

IRR assumes money outside the project IRR assumes money outside the project grows at the same rate as money in the grows at the same rate as money in the projectproject I sell mining projects because they are betterI sell mining projects because they are better

More Bad AttitudeMore Bad Attitude

I don’t like ERR eitherI don’t like ERR either I took all my money from the project and put I took all my money from the project and put

it into CDs and never invested in another it into CDs and never invested in another projectproject

If the company is for real it invests in certain If the company is for real it invests in certain types of projects repeatedly - projects are types of projects repeatedly - projects are not one and onlysnot one and onlys

ERR invested all earnings outside the ERR invested all earnings outside the project - how stupidproject - how stupid