Real Options Assignment

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

 

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

 

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

 

The Free Cash flow perpetuity in the “good” case is $15 million per year

 

The Free Cash flow perpetuity in the "bad" case is now $1.5 million per year, not $2 million.

 

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

 

 

Evaluate Using Conventional NPV Analysis

There can be a good and bad result for this investment.

 

Good Result: A good result has a probability of .7 of occurring, (in the original problem it was .5). Annual benefits under this scenario equal $15 million in after tax cash flow per year.

 

Bad Result: The system proves to be more difficult to implement and improvements in management of the supply chain are less. In addition, the growth in market demand for the product is lower. Annual benefits under this scenario are $1.5 million in after tax cash flow per year. The probability of an unsuccessful project is .3, (in the original problem it was .5).

 

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

 

Using traditional "all or nothing" NPV analysis, calculate the expected NPV of the project. Decide if you will invest.

 

There should be 6 parts to this answer:

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:

 

 

Evaluate using the Real Options Approach (all cash flows are after tax)

The real options alternative allows for flexibility and the delay of the investment for 1 year. In this case, if we do a pilot project we will be better able to evaluate ERP implementation complexities, achievable supply chain benefits, and the market share our products will achieve. However, the cost of the project will rise to $110 Million ($10 Million this year and $100 Million next year) with the one-year delay and additionally management decides to purchase and implement the financial module in year 1 at a 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 firm will 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 further investments beyond the financial module, which yield annual benefits of $.5 million in year 1 and each year thereafter (forever).

 

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

 

Evaluate the expected NPV of this project using the described real option.

 

There should be 4 parts to this answer:

1. Expected NPV by installing the financial module:

2. Expected NPV from building directly:

3. Should we go ahead with the financial module pilot project or the full project? :

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

 

 

 

Comparison: Critical Probabilities

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

 

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

 

There should be 3 parts to this answer.

1. Breakeven Probability: If we knew the probability of the full project's success to be 1.0 (i.e., a guaranteed success), we wouldn't go the pilot project route -- why waste $10 million? Therefore, there must be a breakeven probability of success that would render the pilot project irrelevant. We can find that probability by equating the present values of the full project and the pilot.

 

2. Critical Probability of Success with the Pilot: We can calculate the critical probability for going ahead with the pilot by setting the PV expression = 0 and solving for X.

 

3. Go / No Go Probability. Probability of Success without Pilot: If we have no real option, the breakeven probability for go/ no go comes from solving another similar equation. (You must find it.)

 

 

 

Please post your solution in your Assignment Folder by 11:59 PM the last day of Session 10.

 

 

Review the sample problem in the Content.

 

SAMPLE PROBLEM EXAMPLE:

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

 

Good Result: A good result has a probability of .5 of occurring. Annual benefits under this scenario equal15M in after tax cash flow per year.

Bad Result: A bad result has a probability of .5 of occurring. Annual benefits under this scenario are 2M in after tax cash flow per year.

 

1. NPV Analysis:

           

PV of Good Result = Cash Flow/COC

PV of Good Result = 15M/.1 = 150M

 

PV of Bad Result = Cash Flow/COC

PV of Bad Result = 2M/.1 = 20M

                       

Good NPV = Initial Investment + PV

Good NPV = -100M + 150M = 50M

 

Bad NPV = Initial Investment + PV

Bad NPV = -100M + 20M = -80M

 

TOTAL NPV

Good NPV x Probability + Bad NPV x Probability

(50M  x .5) + (-80M x .5) =25M - 40M = -15M

 

            or

 

Expected Annual Cash Flows: 15M x .5 + 2M x .5 = 7.5M + 1M = 8.5M

NPV of Cash Flows: Initial investment + Expected annual cash flows/COC

NPV: -100M + 85M = -15M

           

Result:

Do not do the project.

 

2. REAL OPTION ANALYSIS:

 

Now we consider that we have the opportunity to do a pilot program by installing the financial model only at a cost of10MM.

 

Good Result: After year 1, if the conditions indicate a good result, the firm will invest the 100M for the ERP with expected benefits (cash flows) of15M annually beginning in year 2. Benefits in year one from the financial module are 1M. A good result has a probability of .5 of occurring.

 

Bad Result: If a bad result is indicated, the firm makes no further investments beyond the financial module, which yield

annual benefits of .5M in year 1 and each year there after. A bad result has a probability of .5 of occurring.

 

Good Case with Module:

PV of Year 1 Cash Flows = [Initial Investment + Year 1 Benefit + Perpetuity of Benefits] / (COC + 1)

PV = [ -10M + (-100M) + 1M + 150M ] / 1.1 = 46.364M

NPV = Financial Module + PV year 1 Cash Flow

NPV = (-10M) + 46.364M = 36.364M

 

Bad Case with Module:

We won't exercise the option if we discover that we're in the Bad Case.

So, we limit our loss here to $10M less the present value of $.5MM.

PV = .5M in perpetuity = .5M/COC = .5M/.1 = 5M

NPV = Financial Module + PV of .5M in perpetuity

NPV = (-10M) + 5M = -5M

 

TOTAL NPV

NPV of the Expected Real Option with the Financial Module:

NPV = Probability of Good Case x NPV of Good Case + Probability of Bad Case x NPV of Bad Case

NPV = 36.364M x .5 + (-5M) x .5 = 18.18M - 2.5M = 15.68M

 

or

PV of cash outflows = $-10M - $100M/(1+COC) x .5 = -$55.45M (assuming the Good Result, since we will invest 10M and go forward with the project and invest 100M in year 2)

PV of cash inflows:

Good result expected value: {$1M/(1+COC) + [($15M/COC)/(1+COC)] } x .5 = $68.64M

(Year 1 benefit of 1M discounted to the present from the Financial Module + 15M benefit in perpetuity; this has .5 probability)

Bad Result expected value: {$.5M/(1+COC) + [($.5M/ COC)/(1+COC)] } x .5 = $2.50M

(Year 1 benefit of .5M discounted to the present from the Financial Module + .5M benefit in perpetuity; this has .5 probability)

NPV of expected cash inflows = $68.64M + $2.50M = $71.14M

Total NPV of the project = -$55.45M + $71.14M = $15.69M

 

Result:

NPV from building directly = -15M (from part 1)

NPV of the Real Option = 15.68M

+15.68M > -15M

 

Do the Pilot Project.

 

 

3. CRITICAL PROBABILITIES:

a. If we knew the probability of the full project's success to be 1.0 (i.e., a guaranteed success), we wouldn't go the pilot project route -- why waste $10 million? Therefore, there must be a breakeven probability of success that would render the pilot project irrelevant. We can find that probability by equating the present values of the full project and the pilot: that is the Good and Bad NPV and the Good and Bad NPV of the Real Option.

 

P = Probability of the Good Result; (1-P) is the probability of the Bad Result.

(P x 50) + (1-P) x (-80) = P x 36 + (1-P) x (-5)

= 130P - 80 = 41P - $5                                                                                              

89P = $75

P = 75/89 = 84.27%

If the probability of success of the project is more than 84.27% then we would not do the pilot.

 

b. What is the probability of going ahead with the pilot? But at 84.27% we undertake the project and don’t do the pilot.

In this case we equate the NPV of the pilot project to 0.

P x 36 + (1-P) (-5M) = 0

41P = 5

P = 5/41 = 12.2%. At this percentage we go ahead with the pilot.

But at 84.27% we undertake the project and don’t do the pilot.

 

c. If we have no real option, what is the breakeven probability?

In this case we equate the NPV of the project to 0.

(P x 50) + (1-P) x (-80) = 0

130P = 80

P = 80/130 = 61.5%