The Money PotThe 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 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 knowledge” to those familiar with the subject and books or articles covering the concepts are widespread. concepts are widespread.

Where do I put the Pot?Where do I put the Pot?

In the examples I showed last time, I In the examples I showed last time, I placed the pot on the time line and we placed the pot on the time line and we picked the right magic numbers to sweep picked the right magic numbers to sweep the cash into the potthe cash into the pot

Things to look forThings to look for someone is making a decision about an someone is making a decision about an

investment or transaction (usually you want investment or transaction (usually you want his/her perspective in building the cash flow)his/her perspective in building the cash flow)

Determining Where to Put Determining Where to Put the Potthe Pot

Usually the pot is placed at the point where Usually the pot is placed at the point where our decision maker is going to decide our decision maker is going to decide whether to “Go for it”whether to “Go for it” Decision makers are going to decide by putting their Decision makers are going to decide by putting their

nose in the money pot to see if there is enough therenose in the money pot to see if there is enough there This implies there must be a money pot under their noseThis implies there must be a money pot under their nose

Usually there is a flow of money (in Usually there is a flow of money (in engineering econ problems most frequently engineering econ problems most frequently cash moving out of his pocket) that is cash moving out of his pocket) that is occurring right at the point of decision.occurring right at the point of decision.

Common Money Pot Common Money Pot PointsPoints

If I invest today – will I get enough out later to If I invest today – will I get enough out later to make it worth my while?make it worth my while? His/her hotbutton decision point is right nowHis/her hotbutton decision point is right now Place the money pot at time 0Place the money pot at time 0

Someone is saving up for a big equipment Someone is saving up for a big equipment replacement or retirement – they know they replacement or retirement – they know they need a certain amount of money at some future need a certain amount of money at some future pointpoint His / her hotbutton point is having the right amount His / her hotbutton point is having the right amount

of money at that future point.of money at that future point. Place the money pot at that point in the futurePlace the money pot at that point in the future

Exception to the Money Pot Exception to the Money Pot at the Point of Decision Ruleat the Point of Decision Rule

Randy Ruppert is considering building a factory Randy Ruppert is considering building a factory that makes seagull repellent for people to rub in that makes seagull repellent for people to rub in there hair before going to the beach.there hair before going to the beach. (or any place (or any place where they don’t want seagulls taking dumps on them)where they don’t want seagulls taking dumps on them)

He will first purchase the old post office in He will first purchase the old post office in DuQuine for $80,000DuQuine for $80,000

On closing he will go to the City Council to get On closing he will go to the City Council to get a zoning change a zoning change (he’s actually already felt out the (he’s actually already felt out the city council on the issue)city council on the issue) The legal council and paper work will cost him The legal council and paper work will cost him

$1200$1200

Seagull RepellentSeagull Repellent He will hire Billy Bungycord Buildings to He will hire Billy Bungycord Buildings to

Renovate the building.Renovate the building. He will pay BBB half the money up front and half when He will pay BBB half the money up front and half when

the renovation is completed at the end of the yearthe renovation is completed at the end of the year The total cost will be $120,000The total cost will be $120,000

While the building is under renovation While the building is under renovation Randy will complete the patent work on his Randy will complete the patent work on his Seagull Repellent discovery.Seagull Repellent discovery. This will cost him $2,000 a month starting the month This will cost him $2,000 a month starting the month

after closing and going the rest of the yearafter closing and going the rest of the year

DuQuine’s New FactoryDuQuine’s New Factory

When the renovation and patent work is done When the renovation and patent work is done at the end of the first year, Randy will place at the end of the first year, Randy will place orders for his machinery from the factory orders for his machinery from the factory ($450,000)($450,000) They will want 10% down with the orderThey will want 10% down with the order 25% down three months later when the drawings are 25% down three months later when the drawings are

approved and assembly beginsapproved and assembly begins 50% down 11 months later when the machines are ready to 50% down 11 months later when the machines are ready to

shipship Rest when the equipment is delivered 14 months after order.Rest when the equipment is delivered 14 months after order.

Randy’s FactoryRandy’s Factory

When the equipment is delivered Randy will hire When the equipment is delivered Randy will hire Trixies Turnkey to install it. ($150,000)Trixies Turnkey to install it. ($150,000) Trixie wants her money up frontTrixie wants her money up front It will take Trixie 3 months to install the It will take Trixie 3 months to install the

equipmentequipment When the equipment is installed Randy will begin When the equipment is installed Randy will begin

hiring and training workers. He doesn’t expect to hiring and training workers. He doesn’t expect to see money rolling in until the third year starts. He see money rolling in until the third year starts. He will need $300,000 to meet payroll in the mean will need $300,000 to meet payroll in the mean time.time.

Randy Goes Into BusinessRandy Goes Into Business

Randy will also begin buying inventory when Randy will also begin buying inventory when he starts hiring. This will cost him $120,000.he starts hiring. This will cost him $120,000. This is often called working capitalThis is often called working capital Businesses need spare parts and raw materials Businesses need spare parts and raw materials

to manufactureto manufacture There is a lag between when these consumables There is a lag between when these consumables

must be brought on and when revenue comes inmust be brought on and when revenue comes in Sometimes also done for workers salariesSometimes also done for workers salaries

Things Get GoingThings Get Going

At the beginning of year 3 he begins to At the beginning of year 3 he begins to enjoy earnings from the sales of Seagull enjoy earnings from the sales of Seagull Repellent. Randy’s marketers assure him Repellent. Randy’s marketers assure him that he will clear $125,000 a month.that he will clear $125,000 a month.

Randy will get his money at the beginning Randy will get his money at the beginning of each year from a group of Venture of each year from a group of Venture Capitalists who demand a 20% Real Rate Capitalists who demand a 20% Real Rate of Return (annual basis - annual of Return (annual basis - annual compounding)compounding)

The QuestionThe Question

Will Randy Ruppert’s Seagull Repellent Will Randy Ruppert’s Seagull Repellent Factory fly? Factory fly?

General ObservationsGeneral Observations

I believe that somewhere in the middle of all I believe that somewhere in the middle of all the horse pucky in that story is a cash flow.the horse pucky in that story is a cash flow.

Lets first decide who’s perspective we will Lets first decide who’s perspective we will useuse Randy has a bunch of suppliers that will come and go - Nope not Randy has a bunch of suppliers that will come and go - Nope not

themthem There’s Randy - he has a dream, but no money - I don’t think so 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)(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 There’s the Venture Capitalists that Randy will have to sell the idea

to - here’s my perspectiveto - here’s my perspective

Time to start building a Time to start building a cash flowcash flow

I note that Randy will be getting all the I note that Randy will be getting all the money he needs for the year at the money he needs for the year at the beginning of the year.beginning of the year. Thus all this stuff with money at the middle of the year Thus all this stuff with money at the middle of the year

will simplifywill simplify I just need to know how much money Randy needs at I just need to know how much money Randy needs at

the beginning of each yearthe beginning of each year (Frequently you will find all sorts of expenses at weird (Frequently you will find all sorts of expenses at weird

times, but if you remember when the people your times, but if you remember when the people your selling to fork over cash a lot of things will simplify)selling to fork over cash a lot of things will simplify)

Money Randy needs to Money Randy needs to Finance his First YearFinance his First Year

Randy needs to buy the building $80,000Randy needs to buy the building $80,000 Randy needs to change the zoning $1,200Randy needs to change the zoning $1,200 Randy needs half the renovation moneyRandy needs half the renovation money

$60,000$60,000

Randy needs to pay patent attorneys 12 Randy needs to pay patent attorneys 12 times that year ($2000 a month)times that year ($2000 a month) $24,000$24,000 Note that this looked a lot like an annuity but the payments didn’t Note that this looked a lot like an annuity but the payments didn’t

correspond to compounding periods.correspond to compounding periods.

Randy Needs $165,200 Randy Needs $165,200 now for his first years now for his first years expenseexpense

0

$165,200

Randy Needs Money at the One Randy Needs Money at the One Year Mark to Pay for the Next Year Mark to Pay for the Next YearYear

Randy needs to finish paying off the Randy needs to finish paying off the contractor $60,000contractor $60,000

As soon as the construction is done Randy As soon as the construction is done Randy will order equipment (month 12) $45,000 will order equipment (month 12) $45,000 (10% down at order)(10% down at order)

The drawings will be approved and ready to The drawings will be approved and ready to start equipment assembly at month 15. start equipment assembly at month 15. Randy needs another 25% $112,500Randy needs another 25% $112,500

Randy’s Second Year Randy’s Second Year MoneyMoney

The equipment will be assembled at The equipment will be assembled at month 23 - Randy will need 50% more month 23 - Randy will need 50% more $225,000$225,000

Get Randy’s total money needs for the Get Randy’s total money needs for the yearyear $60,000 + $45,000 + $112,500 + $225,000 =$60,000 + $45,000 + $112,500 + $225,000 = $442,5000$442,5000

Building Our Cash FlowBuilding Our Cash Flow

0

$165,200

$442,500

1

Randy Needs Money for his 3rd Randy Needs Money for his 3rd Year Operations StartYear Operations Start

Needs to pay off equipment delivered in Needs to pay off equipment delivered in month 26 (last 15%) $77,500month 26 (last 15%) $77,500

Needs to pay Trixie to install equipmentNeeds to pay Trixie to install equipment $150,000$150,000

Needs to begin hiring and training workersNeeds to begin hiring and training workers $300,000$300,000

He needs working capital $120,000He needs working capital $120,000 Total for year Total for year $647,500$647,500

Back to Our Cash FlowBack to Our Cash Flow

0

$165,200

$442,500

1

$647,500

2

Randy Starts Making MoneyRandy Starts Making Money

At Beginning of Year 3, Randy makes his At Beginning of Year 3, Randy makes his first $125,000 to offer investorsfirst $125,000 to offer investors

During that year he will make $125,000, 12 During that year he will make $125,000, 12 timestimes Since his investors are in the year end business Since his investors are in the year end business

he will report that at the beginning of year 4.he will report that at the beginning of year 4. Most publically traded companies do quarterly Most publically traded companies do quarterly

earnings.earnings.

The pattern continues for the life of the The pattern continues for the life of the businessbusiness

The Cash FlowThe Cash Flow

0 1 2

3 4 5 6 7 8 9 10 ….

$165,200

$442,500

$647,500

$125,000

$1,500,000 ………………………………………………...

ObservationObservation

A very ugly sounding problem in fact A very ugly sounding problem in fact doesn’t look all that bad when reduced to doesn’t look all that bad when reduced to a cash flowa cash flow

Back to the Problem of Where Do I Put Back to the Problem of Where Do I Put the Pot?the Pot? It’s a point of decision for the person who’s It’s a point of decision for the person who’s

perspective is taken in the cash flowperspective is taken in the cash flow Usually money will move at that pointUsually money will move at that point

Where Does It HappenWhere 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 ………………………………………………...

Its Sweeping TimeIts 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 Numberdo I need to use tosweep this flow into thepot?

No Number - its already ready to dropinto the pot

More SweepingMore Sweeping

0 1 2

3 4 5 6 7 8 9 10 ….

$165,200$647,500

$125,000

$1,500,000 ………………………………………………...What Number forthese two investments?

$442,500

Looking at Our Investors Looking at Our Investors InvestmentInvestment

165,200165,200 442,500 * P/F (because 442,500 is in the future 442,500 * P/F (because 442,500 is in the future

and is being swept back to the left to our pot)and is being swept back to the left to our pot) How many compounding Periods? 1How many compounding Periods? 1

n=1n=1

What interest rate?What interest rate? Our investors want 20% real ROR that means no inflationOur investors want 20% real ROR that means no inflation Is our analysis no inflation?Is our analysis no inflation? Is our compounding period the same as the time listed for the Is our compounding period the same as the time listed for the

interest rate?interest rate? i = 0.2i = 0.2

The Investors Strike The Investors Strike AgainAgain

$165,200$165,200 $442,500 * 0.83333 = $368,750$442,500 * 0.83333 = $368,750 $647,500 * P/F$647,500 * P/F0.2, n0.2, n

What is nWhat is n P/F = 0.69444P/F = 0.69444 $647,500 * 0.69444 = $449,653$647,500 * 0.69444 = $449,653

Total Investor CommitmentTotal Investor Commitment $165,200 + $368,750 + $449,653 = $983,603 $165,200 + $368,750 + $449,653 = $983,603

The Mystery of the The Mystery of the Missing MoneyMissing Money

We just said our investors were committing We just said our investors were committing $983,603 to the project$983,603 to the project

In fact the total amount of money they came In fact the total amount of money they came up with is $1,255,200up with is $1,255,200 What Happened?What Happened?

Our investors have opportunities to invest their money at Our investors have opportunities to invest their money at 20% Real ROR. They can make a commitment to Randy 20% Real ROR. They can make a commitment to Randy without turning over all the money now. That means they without turning over all the money now. That means they can get some gratification elsewhere before turning over can get some gratification elsewhere before turning over the money.the money.

Time to Sweep some Time to Sweep some Positive Doe inPositive Doe in

0 1 2

3 4 5 6 7 8 9 10 ….

$442,500

$125,000

$1,500,000 ………………………………………………...

Investors have $983,603in the pot

How Much PositiveDoe will it take to makeour investors happy?

What magic number should I use to sweepthat first $125,000 into the pot

P/F0.2,3

I Smell An Annuity!I Smell An Annuity!

0 1 2

3 4 5 6 7 8 9 10 ….

$1,500,000 ………………………………………………...

Investors have $983,603in the pot

$125,000*.5787 = $72,338

$1,500,000 * A/P

Lets Cancel

Wait a minute - We Can’tCancel Things Like That!

My Problem TodayMy Problem Today I know the Annuity - I need to get a present I know the Annuity - I need to get a present

value.value. The wrong symbol is on topThe wrong symbol is on top

Last time I had this problem I just flipped itLast time I had this problem I just flipped it Lets do it againLets do it again

Our new hero - P/AOur new hero - P/A As before the formula is just flippedAs before the formula is just flipped

Called Present Value of an Annuity or Series Present Called Present Value of an Annuity or Series Present WorthWorth

APiii

n

n

/1

)1(*)1(

What Does P/A Do?What Does P/A Do?

It takes an annuity and converts a whole It takes an annuity and converts a whole bunch of repeating values into a single bunch of repeating values into a single present valuepresent value

To Use It Take One Payment from the To Use It Take One Payment from the Annuity to get the amountAnnuity to get the amount P = P/A*(one annuity payment)P = P/A*(one annuity payment)

Do Not! Add up all the money in the Do Not! Add up all the money in the annuity and then use P/A to multiply that annuity and then use P/A to multiply that total.total.

How Might the FE Test Your How Might the FE Test Your Understanding of P/A?Understanding of P/A?

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

What to RecognizeWhat to Recognize

$300,000 * P/A$300,000 * P/A9%,10 years9%,10 years = Answer = Answer

(Obviously we will not invest more than (Obviously we will not invest more than what the future revenue is worth right what the future revenue is worth right now)now)

We Could Get P/A from the We Could Get P/A from the Formula but I’m just Going Formula but I’m just Going to Show the Table this time.to Show the Table this time.

$300,000 * 6.418 = $1,925,000

Picking Off the AnswerPicking Off the Answer

A- $3,000,000A- $3,000,000 B- $3,270,000B- $3,270,000 C- $1,925,000C- $1,925,000 D- $4,558,000D- $4,558,000

Our Calculations say $1,925,000Our Calculations say $1,925,000 Pick CPick C

And we are one step closer to our FEAnd we are one step closer to our FE

Now Back to Our Seagull Now Back to Our Seagull RepellentRepellent

0 1 2

3 4 5 6 7 8 9 10 ….

$1,500,000 ………………………………………………...

Investors have $983,603in the pot

$72,338

$1,500,000 * P/A

Wait a minute - Whatsthe test for an annuity?

Characteristics of an Characteristics of an AnnuityAnnuity

Series of equal payments or cash flowsSeries of equal payments or cash flows CheckCheck

The cash flows occur at the end of the The cash flows occur at the end of the compounding periodscompounding periods Check (or at least because we lumped up the Check (or at least because we lumped up the

monthly cash flows to year end pay backs)monthly cash flows to year end pay backs)

The first cash flow occurs one The first cash flow occurs one compounding period in the future.compounding period in the future. We’reWe’re

Oh What Ever Shall We Oh What Ever Shall We Do?Do?

0 1 2

3 4 5 6 7 8 9 10 ….

$1,500,000 ………………………………………………...

Investors have $983,603in the pot

$72,338

1 2 3 4

Remember - I told you the pot is USUALLYplaced at the point of decision so the investorcan stick his nose in it to count the money

This would be a good This would be a good time to break the ruletime to break the rule

0 1 2

3 4 5 6 7 8 9 10 ….

$1,500,000 ………………………………………………...

Investors have $983,603in the pot

$72,338I’m going to put a fake bucket right here.

Now that cash flow is an annuity!

Lets Get Our Magic Lets Get Our Magic NumberNumber

P/AP/Ai,ni,n

The interest rate is 20%The interest rate is 20% i = 0.2i = 0.2

n is the number of compounding periods n is the number of compounding periods and paymentsand payments So n = So n =

The ##@!! Problem The ##@!! Problem Forgot to Tell me How Forgot to Tell me How Long the Factory will RunLong the Factory will Run

Not an uncommon problemNot an uncommon problem Most people planning for a successful Most people planning for a successful

business don’t try to figure out when it will failbusiness don’t try to figure out when it will fail

We could look at life of equipment, but We could look at life of equipment, but that may just be a replacement timethat may just be a replacement time would work nice if we were evaluating a piece would work nice if we were evaluating a piece

of equipment for the factory or even building a of equipment for the factory or even building a bridge or section of interstatebridge or section of interstate

The Perpetual Annuity The Perpetual Annuity TrickTrick

P/AP/Ai,n=i,n=∞∞≈1/i≈1/i

P= 1,500,000/0.2 = $7,500,000P= 1,500,000/0.2 = $7,500,000

Application TimeApplication Time

0 1 2

3 4 5 6 7 8 9 10 ….

$1,500,000 ………………………………………………...

Investors have $983,603in the pot

$72,338

$1,500,000 * 5

Now there is just one Now there is just one little problemlittle problem

0 1 2

3 4 5 6 7 8 9 10 ….Investors have $983,603in the pot

$72,338

$7,500,000

I’ve got a big chuck of my moneyin a pot in the wrong place

What magic number should I useto sweep the little pot of money intothe big pot?

P/F0.2, 3 = 0.5787

$7,500,000 * 0.5787

Investors Check Out the Investors Check Out the PotPot

Investors have $983,603in the pot

Value of Future Earnings$4,412,588

Our Gut Feeling is thatthis investment is lookingreal good

A Couple Of Classy Check A Couple Of Classy Check Out the Pot ToolsOut the Pot Tools

Tool #1Tool #1 Add up everything - both positive and Add up everything - both positive and

negativenegative Total comes out at $3,428,985Total comes out at $3,428,985

The sweep it all into one pot and check The sweep it all into one pot and check out the total technique is called Net out the total technique is called Net Present ValuePresent Value NPVNPV Book Calls it NPW for Net Present WorthBook Calls it NPW for Net Present Worth

The NPV ToolThe NPV Tool

With NPV we set our required ROR and With NPV we set our required ROR and use that value for i in all the magic use that value for i in all the magic numbers we use to sweep the money numbers we use to sweep the money into our pot.into our pot.

If the total is zero that means that the If the total is zero that means that the positive earnings were worth as much as positive earnings were worth as much as our investmentour investment we are happy and buy the projectwe are happy and buy the project

Evaluating NPVEvaluating NPV If the total is positive that means the If the total is positive that means the

earnings are worth more than we hoped earnings are worth more than we hoped for. for. We slobber all over everything and buy the We slobber all over everything and buy the

project.project.

If the total is negative that means the If the total is negative that means the earnings didn’t justify our investmentearnings didn’t justify our investment We have ways of dealing with such a potWe have ways of dealing with such a pot

Next ToolNext Tool

Present Value RatioPresent Value Ratio Take all the investments (negative flows) Take all the investments (negative flows)

and sweep them back into the pot as red inkand sweep them back into the pot as red ink Take all the positive earnings and sweep Take all the positive earnings and sweep

them back into the pot as earningsthem back into the pot as earnings Divide the Positive earnings by the Divide the Positive earnings by the

Investment (red ink)Investment (red ink) The resulting number is a present value ratioThe resulting number is a present value ratio Book calls it (Benefit-Cost Ratio)Book calls it (Benefit-Cost Ratio)

Evaluating Present Value RatioEvaluating Present Value Ratio

If the project made as much money as the If the project made as much money as the investment - the value will be 1investment - the value will be 1

If the project made more money than the If the project made more money than the investment - the value will be more than 1investment - the value will be more than 1 For our Seagull Repellent Factory the value For our Seagull Repellent Factory the value

is 4.486 (Which means we made ungodly is 4.486 (Which means we made ungodly globs of money)globs of money)

If the numerator is smaller than the If the numerator is smaller than the denominator our investment didn’t get denominator our investment didn’t get paid backpaid back

Money Pot at Future TimeMoney Pot at Future Time

We encountered this with Fursee We encountered this with Fursee ForsightForsight We used F/P numbers to move all her We used F/P numbers to move all her

borrowed money forward in time to borrowed money forward in time to graduationgraduation

Act of creating a sum in the future is Act of creating a sum in the future is called a Net Future Valuecalled a Net Future Value

Differences with NFVDifferences with NFV

Unlike NPV and PVR there is no fixed Unlike NPV and PVR there is no fixed criteriacriteria

NFV is usually compared against some NFV is usually compared against some problem specific target amount to see if problem specific target amount to see if we got enoughwe got enough Can also be used to compare several Can also be used to compare several

courses of actioncourses of action (More on that latter)(More on that latter)

Using Class Assistant to Using Class Assistant to Help Randy RuppertHelp Randy Ruppert

Cash Flow Analyzer

Enter Your Annual Interest Rate as a %, but do not use the % key during data entry 20Enter the number of compounding periods in one year 1Period interest rate 0.2 (in decimal form)

Cash Flow Evaluation Index Values(Warning IRR and Payback may not function properly on unconventional cash flows)NPV 3318501IRR 57.2567%PVR 4.383109Payback Period 4 (this value is reported to an integer # of compounding periods)

Enter # of compounding periods into future at which to take NFV 23NFV 2.2E+08 (cash flows beyond the NFV time are discounted back to the NFV time)

Enter Your Cash Flow in the Column Below (Remember to use minus signs for money flowing out of your pocket)Time zero is the current instant of time, values 1, 2 etc represent compounging period in the future

Time Cash Flow P/F Present Value Cum Cash Pback Mark Pos PV Neg PV F/P Future Value

0 -162500 1 -162500 -162500 0 0 -162500 66.24737 -107651981 -442500 0.833333 -368750 -605000 0 0 -368750 55.20614 -244287192 -647500 0.694444 -449652.7778 -1252500 0 0 -449652.8 46.00512 -297883153 125000 0.578704 72337.96296 -1127500 0 72337.96 0 38.3376 47922004 1500000 0.482253 723379.6296 372500 1 723379.6 0 31.948 479220005 1500000 0.401878 602816.358 1872500 0 602816.4 0 26.62333 39935000

We enter the interestrate

We enter the number ofCompounding periods/year

We enter ourCash flow

Out comes ouranswer

But Class Assistant Can’t But Class Assistant Can’t do an infinite cash flowdo an infinite cash flow

Engineers often don’t try to get the right Engineers often don’t try to get the right answer - just close enough to make it workanswer - just close enough to make it work

P/F tells us how much future earnings are P/F tells us how much future earnings are worth to usworth to us at 20% interestat 20% interest

P/F is 0.40187 for cash 5 years in the futureP/F is 0.40187 for cash 5 years in the future P/F is 0.16151 for cash 10 years in the futureP/F is 0.16151 for cash 10 years in the future P/F is 0.02608 for cash 20 years in the futureP/F is 0.02608 for cash 20 years in the future

Cash more than 20 years in the future is worth less than Cash more than 20 years in the future is worth less than 2 cents on the dollar2 cents on the dollar

The Mineral Inventory The Mineral Inventory EffectEffect

Experts publish papers about world Experts publish papers about world running out of resources in 20 yearsrunning out of resources in 20 years

Read a very convincing paperRead a very convincing paper Of course it was from 1926Of course it was from 1926

About every 20 years panicAbout every 20 years panic End of WWIIEnd of WWII 1970s1970s

Whats HappeningWhats Happening

Costs money now to find oil or mineralsCosts money now to find oil or minerals What you find becomes part of your What you find becomes part of your

reservesreserves

What happens when it costs more to find What happens when it costs more to find reserves than the NPV of the reserves reserves than the NPV of the reserves you find?you find?

Reserves are following economic Reserves are following economic considerationsconsiderations

Cutting Off Long Cash Cutting Off Long Cash Flows Before we PukeFlows Before we Puke

Generally about the first 20 or so years of Generally about the first 20 or so years of a cash flow will determine what its wortha cash flow will determine what its worth (At least to engineering accuracy)(At least to engineering accuracy)

Our solution is to just make up a point to Our solution is to just make up a point to cut-off the annuity that’s long enough to cut-off the annuity that’s long enough to not make any differencenot make any difference I’ll make n=20I’ll make n=20

So You Won’t Feel Left So You Won’t Feel Left OutOut

Do Homework #5Do Homework #5 Problem gives you two cash flows and has you Problem gives you two cash flows and has you

calculate the NPVscalculate the NPVs

Being able to do NPVs will be a basic Being able to do NPVs will be a basic calculation for Engineering Econ going calculation for Engineering Econ going forwardforward