2. The Money Pot ©Dr. B. C. Paul 2001 revisions 2008, 2011 ©Dr. B. C. Paul 2001 revisions 2008, 2011 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.

3. Where do I put the Pot?  In the examples I showed last time, I placed the pot on the time line and we picked the right magic numbers to sweep the cash into the pot  Things to look for  someone is making a decision about an investment or transaction (usually you want his/her perspective in building the cash flow)

4. Determining Where to Put the Pot  Usually the pot is placed at the point where our decision maker is going to decide whether to “Go for it”  Decision makers are going to decide by putting their nose in the money pot to see if there is enough there  This implies there must be a money pot under their nose  Usually there is a flow of money (in engineering econ problems most frequently cash moving out of his pocket) that is occurring right at the point of decision.

5. Common Money Pot Points  If I invest today – will I get enough out later to make it worth my while?  His/her hotbutton decision point is right now  Place the money pot at time 0  Someone is saving up for a big equipment replacement or retirement – they know they need a certain amount of money at some future point  His / her hotbutton point is having the right amount of money at that future point.  Place the money pot at that point in the future

6. Exception to the Money Pot at the Point of Decision Rule  Randy Ruppert is considering building a factory that makes seagull repellent for people to rub in there hair before going to the beach. (or any place where they don’t want seagulls taking dumps on them)  He will first purchase the old post office in DuQuine for $80,000  On closing he will go to the City Council to get a zoning change (he’s actually already felt out the city council on the issue)  The legal council and paper work will cost him $1200

7. Seagull Repellent  He will hire Billy Bungycord Buildings to Renovate the building.  He will pay BBB half the money up front and half when the renovation is completed at the end of the year  The total cost will be $120,000  While the building is under renovation Randy will complete the patent work on his Seagull Repellent discovery.  This will cost him $2,000 a month starting the month after closing and going the rest of the year

8. DuQuine’s New Factory  When the renovation and patent work is done at the end of the first year, Randy will place orders for his machinery from the factory ($450,000)  They will want 10% down with the order  25% down three months later when the drawings are approved and assembly begins  50% down 11 months later when the machines are ready to ship  Rest when the equipment is delivered 14 months after order.

9. Randy’s Factory  When the equipment is delivered Randy will hire Trixies Turnkey to install it. ($150,000)  Trixie wants her money up front  It will take Trixie 3 months to install the equipment  When the equipment is installed Randy will begin hiring and training workers. He doesn’t expect to see money rolling in until the third year starts. He will need $300,000 to meet payroll in the mean time.

10. Randy Goes Into Business  Randy will also begin buying inventory when he starts hiring. This will cost him $120,000.  This is often called working capital  Businesses need spare parts and raw materials to manufacture  There is a lag between when these consumables must be brought on and when revenue comes in  Sometimes also done for workers salaries

11. Things Get Going  At the beginning of year 3 he begins to enjoy earnings from the sales of Seagull Repellent. Randy’s marketers assure him that he will clear $125,000 a month.  Randy will get his money at the beginning of each year from a group of Venture Capitalists who demand a 20% Real Rate of Return (annual basis - annual compounding)

12. The Question  Will Randy Ruppert’s Seagull Repellent Factory fly?

13. General Observations  I believe that somewhere in the middle of all the horse pucky in that story is a cash flow.  Lets first decide who’s perspective we will use  Randy has a bunch of suppliers that will come and go - Nope not them  There’s Randy - he has a dream, but no money - I don’t think so (you’l be in Randy’s spot a lot of times as an engineer)  There’s the Venture Capitalists that Randy will have to sell the idea to - here’s my perspective

14. Time to start building a cash flow  I note that Randy will be getting all the money he needs for the year at the beginning of the year.  Thus all this stuff with money at the middle of the year will simplify  I just need to know how much money Randy needs at the beginning of each year  (Frequently you will find all sorts of expenses at weird times, but if you remember when the people your selling to fork over cash a lot of things will simplify)

15. Money Randy needs to Finance his First Year  Randy needs to buy the building $80,000  Randy needs to change the zoning $1,200  Randy needs half the renovation money  $60,000  Randy needs to pay patent attorneys 12 times that year ($2000 a month)  $24,000  Note that this looked a lot like an annuity but the payments didn’t correspond to compounding periods.

16. Randy Needs $165,200 now for his first years expense 0 $165,200

17. Randy Needs Money at the One Year Mark to Pay for the Next Year  Randy needs to finish paying off the contractor $60,000  As soon as the construction is done Randy will order equipment (month 12) $45,000 (10% down at order)  The drawings will be approved and ready to start equipment assembly at month 15. Randy needs another 25% $112,500

18. Randy’s Second Year Money  The equipment will be assembled at month 23 - Randy will need 50% more $225,000  Get Randy’s total money needs for the year  $60,000 + $45,000 + $112,500 + $225,000 =  $442,5000

19. Building Our Cash Flow 0 $165,200 $442,500 1

20. Randy Needs Money for his 3rd Year Operations Start  Needs to pay off equipment delivered in month 26 (last 15%) $77,500  Needs to pay Trixie to install equipment  $150,000  Needs to begin hiring and training workers  $300,000  He needs working capital $120,000  Total for year $647,500

21. Back to Our Cash Flow 0 $165,200 $442,500 1 $647,500 2

22. Randy Starts Making Money  At Beginning of Year 3, Randy makes his first $125,000 to offer investors  During that year he will make $125,000, 12 times  Since his investors are in the year end business he will report that at the beginning of year 4.  Most publically traded companies do quarterly earnings.  The pattern continues for the life of the business

23. The Cash Flow 0 1 2 3 4 5 6 7 8 9 10 …. $165,200 $442,500 $647,500 $125,000 $1,500,000 ………………………………………………...

24. Observation  A very ugly sounding problem in fact doesn’t look all that bad when reduced to a cash flow  Back to the Problem of Where Do I Put the Pot?  It’s a point of decision for the person who’s perspective is taken in the cash flow  Usually money will move at that point

25. Where Does It Happen 0 1 2 3 4 5 6 7 8 9 10 …. $165,200 $442,500 $647,500 $125,000 $1,500,000 ………………………………………………...

26. Its Sweeping Time 0 1 2 3 4 5 6 7 8 9 10 …. $165,200 $442,500 $647,500 $125,000 $1,500,000 ………………………………………………... What Magic Number do I need to use to sweep this flow into the pot? No Number - its already ready to drop into the pot

27. More Sweeping 0 1 2 3 4 5 6 7 8 9 10 …. $165,200 $647,500 $125,000 $1,500,000 ………………………………………………... What Number for these two investments? $442,500

28. Looking at Our Investors Investment  165,200  442,500 * P/F (because 442,500 is in the future and is being swept back to the left to our pot)  How many compounding Periods? 1  n=1  What interest rate?  Our investors want 20% real ROR that means no inflation  Is our analysis no inflation?  Is our compounding period the same as the time listed for the interest rate?  i = 0.2

29. The Investors Strike Again  $165,200  $442,500 * 0.83333 = $368,750  $647,500 * P/F 0.2, n  What is n  P/F = 0.69444  $647,500 * 0.69444 = $449,653  Total Investor Commitment  $165,200 + $368,750 + $449,653 = $983,603

30. The Mystery of the Missing Money  We just said our investors were committing $983,603 to the project  In fact the total amount of money they came up with is $1,255,200  What Happened?  Our investors have opportunities to invest their money at 20% Real ROR. They can make a commitment to Randy without turning over all the money now. That means they can get some gratification elsewhere before turning over the money.

31. Time to Sweep some Positive Doe in 0 1 2 3 4 5 6 7 8 9 10 …. $442,500 $125,000 $1,500,000 ………………………………………………... Investors have $983,603 in the pot How Much Positive Doe will it take to make our investors happy? What magic number should I use to sweep that first $125,000 into the pot P/F 0.2,3

32. I Smell An Annuity! 0 1 2 3 4 5 6 7 8 9 10 …. $1,500,000 ………………………………………………... Investors have $983,603 in the pot $125,000*.5787 = $72,338 $1,500,000 * A/P Lets Cancel Wait a minute - We Can’t Cancel Things Like That!

33. My Problem Today  I know the Annuity - I need to get a present value.  The wrong symbol is on top  Last time I had this problem I just flipped it  Lets do it again  Our new hero - P/A  As before the formula is just flipped  Called Present Value of an Annuity or Series Present Worth

34. What Does P/A Do?  It takes an annuity and converts a whole bunch of repeating values into a single present value  To Use It Take One Payment from the Annuity to get the amount  P = P/A*(one annuity payment)  Do Not! Add up all the money in the annuity and then use P/A to multiply that total.

35. How Might the FE Test Your Understanding of P/A?  If a business needs a 9% rate of return, what is the maximum amount of money that can be invested right now in a project that will generate $300,000 per year for 10 years starting next year?  A- $3,000,000  B- $3,270,000  C- $1,925,000  D- $4,558,000

36. What to Recognize  $300,000 * P/A 9%,10 years = Answer  (Obviously we will not invest more than what the future revenue is worth right now)

37. We Could Get P/A from the Formula but I’m just Going to Show the Table this time. $300,000 * 6.418 = $1,925,000

38. Picking Off the Answer  A- $3,000,000  B- $3,270,000  C- $1,925,000  D- $4,558,000  Our Calculations say $1,925,000  Pick C  And we are one step closer to our FE

39. Now Back to Our Seagull Repellent 0 1 2 3 4 5 6 7 8 9 10 …. $1,500,000 ………………………………………………... Investors have $983,603 in the pot $72,338 $1,500,000 * P/A Wait a minute - Whats the test for an annuity?

40. Characteristics of an Annuity  Series of equal payments or cash flows  Check  The cash flows occur at the end of the compounding periods  Check (or at least because we lumped up the monthly cash flows to year end pay backs)  The first cash flow occurs one compounding period in the future.  We’re

41. Oh What Ever Shall We Do? 0 1 2 3 4 5 6 7 8 9 10 …. $1,500,000 ………………………………………………... Investors have $983,603 in the pot $72,338 123 4 Remember - I told you the pot is USUALLY placed at the point of decision so the investor can stick his nose in it to count the money

42. This would be a good time to break the rule 0 1 2 3 4 5 6 7 8 9 10 …. $1,500,000 ………………………………………………... Investors have $983,603 in the pot $72,338 I’m going to put a fake bucket right here. Now that cash flow is an annuity!

43. Lets Get Our Magic Number  P/A i,n  The interest rate is 20%  i = 0.2  n is the number of compounding periods and payments  So n =

44. The ##@!! Problem Forgot to Tell me How Long the Factory will Run  Not an uncommon problem  Most people planning for a successful business don’t try to figure out when it will fail  We could look at life of equipment, but that may just be a replacement time  would work nice if we were evaluating a piece of equipment for the factory or even building a bridge or section of interstate

45. The Perpetual Annuity Trick  P/A i,n=∞ ≈1/i  P= 1,500,000/0.2 = $7,500,000

46. Application Time 0 1 2 3 4 5 6 7 8 9 10 …. $1,500,000 ………………………………………………... Investors have $983,603 in the pot $72,338 $1,500,000 * 5

47. Now there is just one little problem 0 1 2 3 4 5 6 7 8 9 10 …. Investors have $983,603 in the pot $72,338 $7,500,000 I’ve got a big chuck of my money in a pot in the wrong place What magic number should I use to sweep the little pot of money into the big pot? P/F 0.2, 3 = 0.5787 $7,500,000 * 0.5787

48. Investors Check Out the Pot Investors have $983,603 in the pot Value of Future Earnings $4,412,588 Our Gut Feeling is that this investment is looking real good

49. A Couple Of Classy Check Out the Pot Tools  Tool #1  Add up everything - both positive and negative  Total comes out at $3,428,985  The sweep it all into one pot and check out the total technique is called Net Present Value  NPV  Book Calls it NPW for Net Present Worth

50. The NPV Tool  With NPV we set our required ROR and use that value for i in all the magic numbers we use to sweep the money into our pot.  If the total is zero that means that the positive earnings were worth as much as our investment  we are happy and buy the project

51. Evaluating NPV  If the total is positive that means the earnings are worth more than we hoped for.  We slobber all over everything and buy the project.  If the total is negative that means the earnings didn’t justify our investment  We have ways of dealing with such a pot

52. Next Tool  Present Value Ratio  Take all the investments (negative flows) and sweep them back into the pot as red ink  Take all the positive earnings and sweep them back into the pot as earnings  Divide the Positive earnings by the Investment (red ink)  The resulting number is a present value ratio  Book calls it (Benefit-Cost Ratio)

53. Evaluating Present Value Ratio  If the project made as much money as the investment - the value will be 1  If the project made more money than the investment - the value will be more than 1  For our Seagull Repellent Factory the value is 4.486 (Which means we made ungodly globs of money)  If the numerator is smaller than the denominator our investment didn’t get paid back

54. Money Pot at Future Time  We encountered this with Fursee Forsight  We used F/P numbers to move all her borrowed money forward in time to graduation  Act of creating a sum in the future is called a Net Future Value

55. Differences with NFV  Unlike NPV and PVR there is no fixed criteria  NFV is usually compared against some problem specific target amount to see if we got enough  Can also be used to compare several courses of action  (More on that latter)

56. Using Class Assistant to Help Randy Ruppert We enter the interest rate We enter the number of Compounding periods/year We enter our Cash flow Out comes our answer

57. But Class Assistant Can’t do an infinite cash flow  Engineers often don’t try to get the right answer - just close enough to make it work  P/F tells us how much future earnings are worth to us  at 20% interest  P/F is 0.40187 for cash 5 years in the future  P/F is 0.16151 for cash 10 years in the future  P/F is 0.02608 for cash 20 years in the future  Cash more than 20 years in the future is worth less than 2 cents on the dollar

58. The Mineral Inventory Effect  Experts publish papers about world running out of resources in 20 years  Read a very convincing paper  Of course it was from 1926  About every 20 years panic  End of WWII  1970s

59. Whats Happening  Costs money now to find oil or minerals  What you find becomes part of your reserves  What happens when it costs more to find reserves than the NPV of the reserves you find?  Reserves are following economic considerations

60. Cutting Off Long Cash Flows Before we Puke  Generally about the first 20 or so years of a cash flow will determine what its worth  (At least to engineering accuracy)  Our solution is to just make up a point to cut-off the annuity that’s long enough to not make any difference  I’ll make n=20

61. So You Won’t Feel Left Out  Do Homework #5  Problem gives you two cash flows and has you calculate the NPVs  Being able to do NPVs will be a basic calculation for Engineering Econ going forward