Real Options

The Right to do Something Real

Introduction

• The classical DCF valuation method involves a comparison between the cost of an investment project and the present value of the cash flows the project will generate.

• The application of the formula is made possible by two more or less tacit assumptions or conventions:– Uncertain future cash flows can be replaced by their

expected values.– The discount rate is known and depends solely upon

the risk of the project.

DCF Limitations

• The classical approach presupposes a static approach to investment decision-making.

• The investment decision does not take into account the possibility of new information arriving during the life of a project.– No need to throw good money after bad.– Can invest more after good news.

Investment Decision

Good News

Bad News

Good News

Good News

Bad News

Bad News

Cash Flow

Cash Flow

Cash Flow

Cash Flow

Discounting with Information Flows

• The only way of accounting for interim information is by using scenarios.– But then what is the probability of each scenario

occurring?

• Even more fundamentally, the degree of managerial discretion in making future operating decisions will tend to affect the risk of the project under consideration.– A project that can be abandoned under adverse

circumstances will be less risky than one that cannot.• The WACC does not allow for this.

Example: Trigeorgis

• Trigeorgis wishes to value an opportunity to invest in research and development for a new drug. One year later:– If the research goes well sales will generate

cash flows of $180.– If the research goes poorly, sales will equal

$60.– Each scenario is equally likely.

Trigeorgis Continued

• The government, wishing to support this project, offers a guarantee (or insurance policy) to buy the entire output for $180 million if the research goes poorly.

• Without the guarantee the project’s cash flows have a risk-adjusted discount rate of r=20%.

• The risk-free rate is rf=8%.• What is the PV of this project (V) and of the

abandonment put option provided by the guarantee (P)?

Trigeorgis: Traditional DCF Solution

• Using traditional DCF techniques, the PV of the project without the guarantee is:

high lowpC +(1-p)C 0.5×180+0.5×60PV = = = 100.

1+r 1+0.20

• PV without the guarantee:

0.5×180+0.5× 60+120PV = = 150.

1+0.20

• Implies the guarantee’s put option is worth 150-100 = 50.

DCF Calculation: An Error

• The traditional DCF calculation is clearly wrong, as the flexibility to abandon the project for a guaranteed price should alter the project’s risk and its discount rate.

• The government’s guarantee makes the project riskless.

Valuing Trigeorgis with the Option

• Since the cash flows are riskless with the guarantee:

* 0.5×180+0.5× 60+120PV = = 166.

1+0.08

• The put option is thus worth 166-100=66.

Guarantee Option: Risk Neutral Probabilities

• If we price the put option using risk-neutral probabilities we obtain the same result.

• Since the PV of the project is 100 using the risk-adjusted discount rate, then:

180 60u = = 1.8, and d = = 0.6.

100 100

Option Value Continued

• Now use the formula:

f1+r -d 1+0.08-0.6q = = = 0.4.

u-d 1.8-0.6

• The put’s value is thus:

0.4×0+0.6×120P = = 66.7.

1+0.08

Comments about Trigeorgis

• This is a very stylized example, since with the abandonment option, the risk of the project completely disappear.

• In most cases, a firm has different options available that reduce the risk of the investments it makes.

• Measuring that risk, that is, adjusting the discount rate accordingly, is an almost impossible task.

• That is why we use real options.

Real Options in Real Life

• Option to build.– Firm owns a lot on which it can build an office complex.

• Option to abandon.– Firm can abandon a project that is going poorly.

• Scale option.– Firm can increase or reduce the size of a project.

• Option to switch.– Firm can alter a plant’s product mix.

• Growth options.– Need to complete on stage of a project successfully before

proceeding to the next.

Incorporating Real Options Into the Capital Budgeting Process: An Example

• Monsters Inc. proposes a phased expansion of its facilities. They plan to build a new, state-of-the-art screaming factory.

• Three years from now, though, they anticipate further investments to face new research challenges.

• The volatility of the project’s cash flow is 40%. The riskless interest rate is 8%.

MONSTERS Inc. -- INITIAL CALCULATIONS FOR A PROPOSED EXPANSION

Year 0 1 2 3 4 5 6

Operating Projections

Revenues 455 551 800 1080 1195 1255

-COGS 322.3 393.9 575 764.8 845.8 891.3

Gross Profit 132.7 157.1 225 315.2 349.2 363.7

-SG&A Expense 110.4 130 219.2 251.6 280.3 287.4

-Depreciation 19 21 21 46.3 48.1 50

Operating Profit 3.3 6.1 -15.2 17.3 20.8 26.3

Cash Flow Calculation

EBIT (1-tax rate) 2.2 4 -10 11.4 13.7 17.4

+Depreciation 19 21 21 46.3 48.1 50

-CAPEX 100 8.1 9.5 307 16 16.3 17

-Increase in WCR 25 4.1 5.5 75 7.1 8 9.7

=FCF -125 9 10 -371 34.6 37.5 40.7

+Terminal Value (perpetuity value at 5% per year) 609.9

MONSTERS Inc. -- INITIAL CALCULATIONS FOR A PROPOSED EXPANSION=FCF -125 9 10 -371 34.6 37.5 40.7

+Terminal Value (perpetuity value at 5% per year) 610.5

PV discount factor (12%) 1 0.89 0.80 0.71 0.64 0.57 0.51

=PV (by year) -125 8.04 7.97 -264.07 21.99 21.28 329.61

NPV 0.12

Monster Analysis

• Based on DCF calculations, the project’s NPV is slightly positive.

• The project incorporates an option not to invest in the third year if the NPV of the additional investment becomes negative.– Since cash flows are volatile, three years from now

the company will have more accurate information regarding the project’s profitability.

• The next exhibit separates the initial investment cash flows from those in year 3.

MONSTERS Inc. -- PROJECTIONS

REARRANGED Year 0 1 2 3 4 5 6

Phase 1

Cash Flow 0 9 10 11 11.6 12.1 12.7

+Terminal Value 190.5

-Investment -125

x discount factor (12%) 1 0.893 0.797 0.712 0.636 0.567 0.507

=PV (by year) -125 8.0 8.0 7.8 7.4 6.9 102.9

NPV 16.02

Phase 2

Cash Flow 0 23.1 25.4 28

+Terminal Value 420

-Investment -382

x discount factor (12%) 0.712 0.636 0.567 0.507

=PV (by year) -271.9 14.7 14.4 227.0

NPV -15.84

MONSTERS Inc. -- PROJECTIONS

Phase 1 + Phase 2

Cash Flow 0 9 10 11 34.6 37.5 40.7

+Terminal Value 610.5

-Investment -125 -382

x discount factor (12%) 1 0.893 0.797 0.712 0.636 0.567 0.507

=PV (by year) -125.0 8.04 7.97 -264.07 21.99 21.28 329.92

NPV 0.12

Monster Inc.: Phase 2 Value

• Cash flows from Phase 2 are also expected, and in PV terms (as of year 0) are:

4 5 6 6

23.1 25.4 28.0 420PV(Phase 2 Cash Flows) =

1.12 1.12 1.12 1.12256.1.

Monster Option

• Therefore, the company has the option to invest in a project whose expected cashflow (as of year 0) is 256.1, and whose cost is 382 (in year 3).

• This looks like an option! • Cash flows are volatile (volatility=40%), and the

company will exercise the option if in year 3, the expected cash flows are larger than the cost of the project. That is:

NPV(Expansion, Year 3) =max [PV(Cash Flows,Year 3)-382,0]

Monster Option Value

• Option value in year 0 can be calculated using standard option valuation techniques. The inputs are:– S=256.1– X=382– σ=40%– rf=8%– Time to Maturity: 3 years

• From the Black-Scholes formula: c = 55.12– This is the Phase 2 NPV.

• The project’s NPV 55.12+16.3 = 71.82– Why is it higher once we incorporate the option to expand?

Measuring the Future Asset Prices and Volatility

• The asset price in real options analysis is the present value of future cash flows associated with the assets when using passive present value analysis.

• Volatility is harder to estimate. – The reason is that it is not constant during the

life of the option. – Usually the firm’s stock volatility or a historical

standard deviation based on cash flow estimates is employed.