The Invest and Earn Problem

1
The Invest and Earn Problem

• Problems of this type have one or more initial
  negative cash flows - followed by positive cash
  flows to the end of the project
• Standard Solution
• Sweep cash flow back into pot at time of decision
• Basic solution
• use NPV and required rate of return directly
• all other measurement devices are variations on
  the NPV

2
Evaluating Invest and Earn Problems

• NPV directly incorporates your required rate of
  return and allows you to decide based on whether
  0 or greater
• PVR can be used but it requires more work and not
  much better an indicator (this time you decide
  whether its 1 or greater)
• IRR is just playing with the NPV problem i value
  until the NPV is zero
• a lot of work if you already know your critical
  rate of return.

3
Variations on the Invest and Earn Problem

• The problem goes on for an indefinite length of
  time
• Response - the first 20 or 30 years pretty much
  establish the NPV / just truncate the problem
• The problem starts with a negative cash flow -
  goes positive - then goes negative at the end.
• Example - mine development problems are usually
  like this because the land must be restored when
  mining ceases

4
Negative Begin and End Variations

• This case challenges what people mean by a
  project rate of return because the project
  obligates money that will never be used in the
  profitable part of the project
• Raises havoc with the IRR because part of the
  investment will never be invested in the project
  to obtain a return from within the project
• How can a rate be internal?

5
Responses to the Negative End Challenge

• Use NPV
• many companies set a required rate of return to
  invest
• They have many opportunities to invest and only
  take those that meet the required rate
• if you have all these investment opportunities
  you just put your negative end money in another
  project and earn your required rate until you
  need it.
• If you have all these opportunities NPV answer is
  simple and hassle free

6
The IRR Bombshell

• Cash flows times magic numbers have the form of a
  polynomial
• we know from math that polynomials have as many
  roots as axis crossings
• that means there is more than 1 interest rate
  that makes the NPV zero!
• From a physical standpoint because some of the
  negative cash flow money grows inside the
  project, and some of it grows outside its just
  telling you about rates of growth inside and
  outside of the project that make NPV zero
• Of course that means the whole concept of
  internal growth is crap

7
Multiple Roots and NPV

• As long as you have plenty of opportunities to
  invest at your required rate of return NPV is not
  effected
• Who really cares whether the money grew in the
  project as long as your getting your return
• Problem comes up when money or opportunities to
  invest at the rate are not a dime a dozen
• To make answer make sense the money outside the
  project must be growing at required rate

8
What if it Doesnt?

• Situation can occur often
• Many businesses have developed specialties in one
  type of business or another - they are good at
  handling that type of risk
• They may not be able to handle risk well in other
  lines of business
• Money outside of project may not be able to be
  locked into long term commitments
• Many businesses can make 2 or 3 times more in
  their field than in the general market

9
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

10
ERR Example

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

Year 1 Year 2 Year 3
Year 4 Year 5
Year 6
Start
11
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
• Since the interest rate is unknown you have to
  just put in the formula for now

12
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
• All positive cash flows are discounted forward to
  the end of the project at 4 rate of return.

13
Discount some forward - some back
14
Discounting Positive Flows Forward
15
Later Negative Flows Also Discount Forward
Savings Discounted Forward at 4
Initial Investment
16
ERR Problem Set Up
Future Savings and Costs Discounted forward at 4
21,482
Initial Investment
-3560
17
Solving the ERR
Now discount the future pot back into the big pot
at time 0. Note this makes for a very easy IRR
problem.
Future Savings and Costs Discounted forward at 4
3560 1/((1i)73 ) 21,482
Solve for i
21,482
(1i)73 21,482/3560
Initial Investment
(1 i) 6.034(1/73)
-3560
(1 i) 1.0249
i 0.0249/month
Adapt to 1 year (1.0249)12 1.3437 or 34.37
18
Teachers Attitude Problem

• Im 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 dont 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

19
More Bad Attitude

• I dont 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

20
The Tweeked IRR

• Problem is that committing to the project means
  committing not only money now but money in the
  future
• I will have to cover that future commitment by
  taking some of my earnings and setting them aside
  to meet that expense (probably in lower earnings
  - low risk short term fluid investments)
• Its kind of like a sinking fund
• Im certainly not going to set all my earnings in

21
How to Tweek
Take Just Enough of Your Future Earnings to
offset the future negative cash flow
22
How do I do that?

• Determine what rate you can get on secure, fluid,
  short-term investments
• For Hanna and Herby it was 4
• Create a temporary pot at the beginning of the
  negative cash flow

23
Tweeking Procedures

• Discount the future negative cash flows back into
  the temporary pot at the chosen rate.

24
Discounting Back
-3625.24
25
Next Step
Now discount part of your positive cash flow
forward into the pot at 4 to balance the red ink.
-3625.24
26
How much and when?

• Part of the project earnings are to be discounted
  forward to cover the red ink
• Because the rate of return on this sort of
  sinking fund money is less than the project
  itself we want to use as little as late as
  possible
• The simple approach is to use the last so many
  savings flows to cover the red ink
• In practice one may not want to turn in zero
  earnings quarters
• They spend more for a good investor smoke screen

27
Ill Use the Simple Approach
I will sweep enough future earnings forward at an
available external rate to cover the future red
ink commitment.
28
My New Cash Flow
Now sweep the rest of the cash back into the main
pot.
Future Negative Cash Flow is cancelled by
positive cash flows swept forward.
29
The Sanitized IRR
Note that I now have a classic cash flow problem
- invest and make money there after.
I can get a regular trick free IRR on this thing.
IRR on this cash flow is 39.01
30
Three Answers - 1 Problem

• Regular IRR was over 40
• but to get it - Herby had to invest his savings
  at over 40 (I dont think so)
• ERR was 34.37
• If Herby diverts funds into a money market to
  cover the payments after he graduates he will get
  39.01

31
Summary of the Invest and Earn Problem

• Problem has a negative cash flow of initial
  investments and then positive cash flows in the
  future
• Can determine if investment is worth it using
• IRR
• NPV
• PVR (PVR is really designed for something else)

32
Sabotaged Invest and Earn Problems

• These problems have a negative cash flow at the
  end (it costs both to get in and to get out at
  the end)
• IRR becomes meaningless because some of the money
  will not grow in the project
• The numbers from the IRR may do funny things
  (with no guarantee it will be obvious)
• The IRR will be Sabotaged
• The NPV may or may not be.

33
How do I know what rates are Sabotaged?

• If doing an IRR - your sabotaged so forget it
• If doing an NPV
• Look at your required rate of return (its the i
  value you use in your magic numbers)
• How many opportunities does your company have to
  get this rate?
• Very few - Your sabotaged
• A lot - Maybe your ok

34
Continuing Exercise

• Your doing NPV and your company has many
  opportunities to get the rate of return i
• Do these opportunities provide regular and
  reliable means for your company to come up with
  the negative cash flow amounts in their
  individual projects internally?
• No - your NPV is sabatoged
• Yes - your ok - do a regular NPV problem solution
  and forget it.

35
Reasons Why You Need to Know this Stuff

• Financial planning and structure of your projects
  is always one of the biggest factors in
  determining their earnings potential