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24 Jan 2018

As a business owner you have two business opportunities that arepresented to you. Both options will present future cash flows overa three year period. To determine what option you are going toselect a net present value analysis will be performed. One of theoptions is rather risky and the future cash flows are not certain.The other option is not that risky and future cash flows are knownand consistent. Explain the relationship between the risk of thetwo options with the future cash flows (does risk increase ordecrease NPV?) and the discount rate used to calculate NPV.

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Nestor Rutherford
Nestor RutherfordLv2
26 Jan 2018

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Real Options

The assignment is to evaluate both parts, the traditional NPVcalculation as well as the Real Options approach.

Scenario: A company must decide whether to invest $100 millionin developing and implementing a new enterprise system in the faceof considerable technological and market (demand for product andmarket share) uncertainty. The firm's cost of capital is 10%.

Part 1.


The probability of a successful project (or pilot) is now .7 andthe probability of an unsuccessful project is .3.

Good Result: The Free Cash flow perpetuity (Annual Benefits) inthe “good” case is $15 million per year

Bad Result: The system proves to be more difficult to implementand improvements in management of the supply chain are less. Inaddition, the growth in market demand for the product is lower. TheFree Cash flow perpetuity (Annual Benefits) in the "bad" case isnow $1.5 million per year, not $2 million.

Given: Year 0 (now) cash flows: $-100 million for ERP purchaseand implementation.

The cost of capital is .1. Use this to calculate the PV of the“good” perpetuity and the PV of the “bad” perpetuity. Thencalculate the “good” NPV and the “bad” NPV. Finally calculate theExpected NPV and decide if you will invest.

Part 2.


The real options alternative allows for flexibility and thedelay of the investment for 1 year. In this case, if we do a pilotproject we will be better able to evaluate ERP implementationcomplexities, achievable supply chain benefits, and the marketshare our products will achieve. However, the cost of the projectwill rise to $110 Million ($10 Million this year and $100 Millionnext year) with the one-year delay and additionally managementdecides to purchase and implement the financial module in year 1 ata cost of $10 Million (real option).

The results are slightly different:

Year 0 (now) cash flows: $10 million for the pilot project.

After year 1, if the conditions indicate a good result, the firmwill invest the $100 million for the ERP with expected benefits(cash flows) of $15 million annually (forever) beginning in year 2.Benefits in year one from the financial module are $1 million.

If a bad result is indicated, the firm makes no furtherinvestments beyond the financial module, which yield annualbenefits of $.5 million in year 1 and each year thereafter(forever).

Here the firm has flexibility and has exercised its option tomake no further investments based on better information andknowledge of expected future benefits.

Evaluate the expected NPV of this project using the describedreal option.

Consider that we have the opportunity to do a pilot program byinstalling the financial model only at a cost of $10 MM. A yearfrom now, we can decide whether to invest in the full plant or not.Analyze this case as follows: Find the good case NPV and the badcase NPV. Obviously, we won't exercise the option if we discoverthat we're in the Bad Case. So, we limit our loss to $10 MM lessthe present value of the bad case starting in Year 1.

Part 3.


What is the expected NPV in each case? Compare the

expected NPV using the traditional NPV approach with theexpected NPV using real options. What do you recommend? Why? Whatdo you conclude in each case?

If you don't know the probability of success for the pilot, isthere a value that is critical to your recommendation? Is there aprobability of success above or below which you will recommendundertaking the pilot and below or above which you will recommend ago/ no go decision on the underlying project without undertaking apilot test? 



Label your work as follows:

Part 1: NPV Analysis


1. PV of "Good" perpetuity:


2. PV of "Bad" perpetuity


3. "Good" NPV:


4. "Bad" NPV:


5. Expected NPV: 


6. Invest or don't invest:

Part 2: Real Options Approach


1. Good case NPV by installing the financial module.


2. Bad case NPV by installing the financial module.


3. Expected NPV by installing the financial module.


4. Should we go ahead with the financial module pilot project orthe full project? 


5. Should we undertake both the full project and the pilot"today"?

Part 3: Critical Probabilities


1. Probability to forget the Pilot and complete the Project. Wecan find that probability by equating the present values of thefull project and thepilot. 


2. Probability of going ahead with the Pilot. We can calculatethe critical probability for going ahead with the pilot by settingthe PV expression = 0 and solving for X.


3. If there is no real option, breakeven probability for go/nogo.


Real Options: Decision-Tree Analysis

Utah Enterprises is considering buying a vacant lot that sellsfor $1.6 million. If the property is purchased, the company's planis to spend another $6 million today (t = 0) to build a hotel onthe property. The after-tax cash flows from the hotel will dependcritically on whether the state imposes a tourism tax in thisyear's legislative session. If the tax is imposed, the hotel isexpected to produce after-tax cash inflows of $720,000 at the endof each of the next 15 years, versus $1,360,000 if the tax is notimposed. The project has a 13% cost of capital. Assume at theoutset that the company does not have the option to delay theproject. Use decision-tree analysis to answer the followingquestions.

What is the project's expected NPV if the tax is imposed? Anegative value should be entered with a negative sign. Round youranswer to the nearest cent.
$

What is the project's expected NPV if the tax is not imposed? Anegative value should be entered with a negative sign. Round youranswer to the nearest cent.
$

Given that there is a 50% chance that the tax will be imposed,what is the project's expected NPV if they proceed with it today? Anegative value should be entered with a negative sign. Round youranswer to the nearest cent.
$

Although the company does not have an option to delayconstruction, it does have the option to abandon the project 1 yearfrom now if the tax is imposed. If it abandons the project, itwould sell the complete property 1 year from now at an expectedprice of $7.6 million. Once the project is abandoned, the companywould no longer receive any cash inflows from it. If all cash flowsare discounted at 13%, would the existence of this abandonmentoption affect the company's decision to proceed with the projecttoday?
-Select: Yes OR NO

Assume that there is no option to abandon or delay the project,but that the company has an option to purchase an adjacent propertyin 1 year at a price of $1 million. If the tourism tax is imposed,then the net present value of developing this property (as of t =1) is only $400,000 (so it wouldn't make sense to purchase theproperty for $1 million). However, if the tax is not imposed, thenthe net present value of the future opportunities from developingthe property would be $4 million (as of t = 1). Thus, under thisscenario it would make sense to purchase the property for $1million. Given that cash flows are discounted at 13% and thatthere's a 50-50 chance the tax will be imposed, how much would thecompany pay today for the option to purchase this property 1 yearfrom now for $1 million? A negative value should be entered with anegative sign. Round your answer to the nearest cent.
$

Just yesterday I posted a key question as to why the statelottery might hypothetically offer you an upfront lump-sum paymentof $50 million or an ongoing annuity of a $5 million check eachyear for 20 years (totaling $100 million in checks). Remember thatthis was just my simplified hypothetical example. A few peopleattempted the answer to this further above, but here's what'sreally going on...it has to do with Net Present Value (NPV). It'sbecause future-year dollars are worth less, and the further you gointo the future, the less those dollars are worth in terms oftoday's dollars. And that is why, when financial analysts look at adecision involving multi-year cash flows, they will use discountfactors to convert all of the future-year dollars to present value(i.e., this year's dollars) and add them up to yield the NPV of allof the amounts to put a final answer in terms of today's value.Where do these discount factors come from? They're derived from thereciprocal of the famous compound interest formula, but you justneed to go and look at two tables in your textbook in Chapter 12,Appendix 12A, Table A (present value of $1 due in n periods) andTable B (present value of an annuity of $1 per period). Class, Icannot stress to you enough how widely-used this concept is, andthe importance of understanding how these discount factors areapplied to solve for net present value (NPV) and a related metric,internal rate of return (IRR). You will likely need to read, andreread, Chapter 12 and closely walk through some textbook exampleswhere each year's cash flows are multiplied by the appropriatediscount factor to convert all of that money into this year'sdollars (present value). We are surrounded by this financialanalysis methodology when faced with a decision on a lotterypayout, a retirement payout (lump sum versus annuity), and many ofour states and cities right now are dealing with issues relating tothe calculation of NPV in assessing whether they currently haveenough money in the appropriate accounts to meet the futureretirement payment obligations they've made to their publicemployees. This is an economic issue that has been on the brink ofexploding for a long time (don't take my word for it, it's beendiscussed in multiple articles in the NY Times, Wall StreetJournal, The Economist), but I'm not going to add all of that intothis discussion here. Let's learn to walk before we try to run.Would you like to see how the lottery payouts I described would bemultiplied by each year's financial discount factor? Just take alook at my attached Excel workbook, and note that there are threetabs: the first assumed a 0% cost of capital (no financialdiscounting done), the second assumed a 5% cost of capital, and thethird sheet inserted a 10% cost of capital. You'll see how thesedifferent interest rates changed the discount factor multipliersand ultimately changed the NPV of each alternative (the value ofthe lump sum or the annuity, all shown in present value). Also,this example just shows money moving one way (i.e., to the state,it's cash out of their pocket...to the lottery winner, it's cashinto their pocket). In many NPV and IRR examples, money will moveboth ways over multiple years...cash flows that are expenses orinvestments are outflows and are shown as negative, while revenuesor other incoming money are inflows and are shown as positive.Please look closely at my attached Excel workbook (all three tabs)and also walk through all of the examples in the chapter showinghow to do NPV and IRR problems. There are also examples in the textof simpler metrics including payback period and accounting rate ofreturn. It's typically very hard stuff for students to master. Now,for those of you who've looked at the chapter examples, maybeyou've figured this out already:

1. What is the key difference between Tables A and B in Chapter12, Appendix 12A, and how and when are each of them used in ananalysis?

2. What do we mean by “Year 0” in a financial analysis? Whatvalue do we use for the discount factor or multiplier for the cashflow in Year 0 of a financial analysis?

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