1. External Rates of Return ©Dr. Bradley C. Paul 2002 revisions 2009 Note – The procedures found in these slides can be found in numerous texts dealing with the subject of engineering economics, none of which was specifically used as a template for these slides. The author regards the contents of these slides to be common knowledge to those schooled in the field.

2. The External Rate of Return  Plan to divert some money to lower rate investments just as you would in real life  This may allow you to have sinking funds etc.  Because the money you grew outside the project grows at a different rate - where and how much you put out when does impact the answer  in general minimize the amount of cash you run outside the investment  You remember Herby and Hanna Housings cash flow had the foul characteristic  40% was the right answer if they could invest some of their savings from renting at 40%

3. ERR Example  Herby and Hanna Housing Cash Flow for buying instead of renting Start Year 1 Year 2 Year 3 Year 4 Year 5 Year 6

4. More ERR Method  Look at your opportunities for short term fluid investments and select a rate of return for the growth of money outside the project  Lets say Herby and Hanna Housing decide to put their savings in a Money Market at 4%  Find Your External Opportunity Rate.

5. The ERR Method  Take all initial negative cash flows and discount them back to time zero  Herby and Hanna Housing Example  -$3560 at time zero  Drops directly into the pot without any discount factor  If you have multiple negative cash flows you will have several P/F factors to discount these back at the external rate.

6. Discount some forward - some back Initial Negative Values Bucket Subsequent Values Forward Bucket

7. Discounting Positive Flows Forward

8. Later Negative Flows Also Discount Forward Initial Negative Values Bucket Subsequent Values Forward Bucket Initial Investment Savings Discounted Forward at 4%

9. ERR Problem Set Up Initial Negative Values Bucket Subsequent Values Forward Bucket Initial Investment Future Savings and Costs Discounted forward at 4% -$3560 $21,482

10. Solving the ERR Initial Negative Values Bucket Subsequent Values Forward Bucket Initial Investment Future Savings and Costs Discounted forward 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/month Adapt to 1 year (1+.0249) 12 = 1.3437 or 34.37%

11. Teachers Attitude Problem  I’m a Mining and Mineral Resources Engineer  Every project I do will have negative cash flows to build and negative at the end to reclaim  I never see IRR work smoothly - so I don’t like it  IRR assumes money outside the project grows at the same rate as money in the project  I sell mining projects because they are better

12. More Bad Attitude  I don’t like ERR either  I took all my money from the project and put it into CDs and never invested in another project  If the company is for real it invests in certain types of projects repeatedly - projects are not one and onlys  ERR invested all earnings outside the project - how stupid