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Rate of Return and the Cost of Capital

Rate of Return and the Cost of Capital. A big rate of return means you have to come up with a lot of extra money to get the investors to put-off their Dairy Queen Blizzards A small ROR means you only need a little extra. So Why All This Rate of Return Business?.

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Rate of Return and the Cost of Capital

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  1. Rate of Return and the Cost of Capital • A big rate of return means you have to come up with a lot of extra money to get the investors to put-off their Dairy Queen Blizzards • A small ROR means you only need a little extra

  2. So Why All This Rate of Return Business? • Remember all engineering econ problems involve • Write down the money that goes in and out of the project for each year in order (get your cash flow) • Multiply each number in the cash flow by a magic number • Add up the total and see whether the money pile is big enough • Rate of Return Tells you how big the money pile has to be

  3. Example • If I put $1.00 in the bank at 5% interest, how much money will I have next year when I take the money out • 5% of $1.00 is 5 cents • I will have $1.05 • If I leave the money in the bank another year I will get 5% interest on $1.05 not just $1.00 • At the end of the year I will have (1.05)(1.05)= 1.1025

  4. Example continued • If I leave the money in another year I will get 5% interest on $1.1025 • (1.1025)(1.05) = 1.1576 • and again the next year (1.1576)(1.05) = 1.2155 • My interest is “Compounding” • Note that if I only got 5% each year on my dollar I would only have $1.20 • The sneaky trick with interest is to multiply, not add (multiplication takes care of compounding)

  5. Compounding Period • In the previous example I got my interest every year and then I started compounding the interest on the interest. • Why does the interest have to compound once a year - it doesn’t • Ever noticed CD rates at Banks 4.6% interest with a 4.75% yield? • They pay interest and compound it over shorter times so that by the end of the year the ROR is higher than the interest rate • Interest Rates are Usually Reported on an Annual Basis

  6. The Credit Card Rip-Off • Sammy Sucker gets a credit card offer from Spin on My Finger Bank and Trust • The interest rate is 18% (but they’ll give him a 5% purchase credit toward a new Turbo charged Volkswagon Beetle that will make all the girls think he is sexy) • Sammy goes out and maxes out his credit card at $10,000 • We’ll ignore his monthly minimum payments for a while

  7. Sammy gets ------- • Spin on My Finger Bank and Trust divides the interest rate over 12 months • 18%/12 months = 1.5% per month • Month #1 Sammy doesn’t pay off his card • 1.5% of $10,000 • (10000)*(1.015) = $10,150 or $10,150- $10,000 is $150 of interest

  8. Sammy’s Adventure • Month #2 Sammy doesn’t pay off his credit card • Spin on My Finger Bank and Trust compounds the interest • $10,150*(1.015) = $10,302.25 • Month #3 Sammy doesn’t pay off his credit card • $10,302.25 * (1.015) = $10,456.78

  9. This is Sammy’s Adventure - Not Ours • I really love these calculations but if I have to do them 12 times I’m going to puke • Enter Super formula • Note that all I’m doing is multiplying the original debt $10,000 by 1.015 • Note that 1.015*1.015 is just (1.015)2 • Note that 1.015*1.015*1.015 is just (1.015)3 • Note that 1.015 is just 1 plus the interest rate • Magic formula (1 + i)n • where i is the interest rate • and n is the number of compounding periods

  10. Now Lets Return to Sammy’s Saga • After 1 year how much does Sammy owe? • He’s had 12 compounding periods at 1.5% interest each time • The magic formula is (1.015)12 = 1.1956 • Apply the formula to Sammy’s Debt • $10,000 * 1.1956 = $11,956 • Note that Sammy paid • 1.1956 - 1 = 0.1956 or 19.56% interest because of compounding - not 18%

  11. What Else is New • Note that Sammy’s spending $10,000 is a cash flow number • Note that we multiplied a cash flow number by a magic number • Oh Cool! We just did our first engineering cash flow problem!

  12. Magic Numbers • There are many kinds of magic numbers • This one came from the formula (1 + i)^n • This one told us what the future debt would be from a present amount of money that Sammy Sucker spent • This magic number is called a Future Value of a Present Amount factor • Common notation is F/P

  13. Lets Pick on Sammy Some More • Say Sammy Sucker goes all the way through College (he’s a little dense so it takes him 7 years) and never pays off that credit card • Sammy has gone 7 * 12 compounding periods (84) • Our formula says (1 + i {0.015})84 = 3.49259 • Sammy owes $34,925.90

  14. F/P Factors • You can see that the exact value of the magic F/P number depends on the interest rate and the number of compounding periods. • We sometimes write F/Pi,n • Thus the F/P magic number for the end of 12 months would have been F/P1.5, 12 • The factor for after 7 years F/P1.5,84

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