The Invest and Earn Problem

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

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.

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

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?

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

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

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

What if it Doesn’t? • 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

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%

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

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

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.

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

Discounting Positive Flows Forward

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

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

Subsequent Values Forward Bucket Initial Negative Values Bucket 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/((1+i)73 ) * $21,482 Solve for i $21,482 (1+i)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%

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

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

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 • I’m certainly not going to set all my earnings in

How to Tweek Take Just Enough of Your Future Earnings to offset the future negative cash flow

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

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

Discounting Back -$3625.24

Next Step Now discount part of your positive cash flow forward into the pot at 4% to balance the red ink. -$3625.24

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

I’ll Use the Simple Approach I will sweep enough future earnings forward at an available external rate to cover the future red ink commitment.

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.

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%

Three Answers - 1 Problem • Regular IRR was over 40% • but to get it - Herby had to invest his savings at over 40% (I don’t 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%

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)

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.

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 (it’s 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

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.

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

The Invest and Earn Problem