Real Option Valuation

MODEL SELECTION MENU Modified Black-Scholes Models Option to Delay a Project Valuing the option to delay an already valued investment is a commonly applicable and worthwhile exercise. As expected cash flows and discount rates that drive traditional valuation techniques change over time, so does the net present value. Therefore, while a project may have a small or negative present value today, it may have a significantly positive present value in the future.

Option to Expand a Project Investments in projects made today in order to take on projects or enter markets in the future, are essentially options to expand. A negative present value may be accepted on the initial investment, because of the possibility of high postive net present values on future projects.

Option to Abandon a Project Not all projects are successful and when cash flows are lower than expected, it is useful to evaluate the option to abandon the project. While estimation of the liquidation (abandonment) value limits the usefulness of the resulting valuation, understanding the sensitivites can be a worthwhile exercise.

Advanced Applications Binomial Option Pricing The binomial option pricing model is suitable for complex situations where options exist on options in a 'tree' like manner. Furthermore, while outcomes can be approximated to the normal distribution, this assumption required by the Black-Scholes model can be relaxed with the binomial model.

Game Theory Analysis This model utilises real option theory to calculate the value of expected strategy for each of two firms in a competitive environment. Essentially the model determines the level of cash flows required for each of the following and leading firm to enter the market with the proposed product. This model is useful for evaluating the proposed investment under a competitive environment.

The Option to Delay New plant $100 $150 5 9.0% 16.0% 20.0%

INPUTS: Can be adjusted to alter the results.

The PV of expected net cash flows from initiating New plant now (not including up-front investment). The PV of set-up & development costs to required undertake the project. The project lifetime, or period during which the project can be undertaken. The equivalent risk-free rate for the project life. The variance or 'riskiness' of the project's expected cashflows (standard deviation squared). The annual cash yield lost each year the project is delayed.

OUTPUTS: d1 N(d1) d2 N(d2)

-0.6210 0.2673 -1.5155 0.0648

VALUE

$3.6

The PV of taking on the project now (-50) is less than the option to delay (4), therefore the project should NOT be undertaken now. There is a 6.5% to 26.7% likelihood that this project will become viable before expiration (as indicated by Nd1 and Nd2).

The value of the option to delay New plant.

PARTIALS: Delta Gamma Theta Vega Rho

0.267 0.004 -3.500 73.561 31.002

Linear exposure to changes in the project cash flows. Parabolic exposure to changes in the project cash flows. Linear exposure to changes in the project's time to expiration Linear exposure to changes in the project's volatility or 'risk'. Linear exposure to changes in the risk-free rate.

Highlight a cell labelled "Valuation" to Create or Delete a Binomial branch.

Valuation Option to Invest 211.8 Underlying Asset 234.0

24891954.xls [Binomial]

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Variables

Values

Description

K a

900.00 2%

q D1 D2 r

30% 1 0.75 5%

Xf

133.86

Level of annual market cash flow for Follower to enter market.

X

120.00

Current expected annual level of cash flow in market.

F(X)

2,106.75

Follower's Payoff Value

L(X) L(X) - K

3,039.42 2,139.42

Value of Leader's future profit flow Leader's Payoff Value

S(X) S(X) - K

3,000.00 2,100.00

Value if both firms exercise immediately and Simultaneously. Simultaneous Payoff Value

Xl

78.44

Sensitivity

Market Cash Flow /Yr (X)

Exercise

Leader

Follower

Simultaneous

Expected Payoff

120.00 41.49 59.96 78.44 96.91 115.39 133.86 152.34 170.81

82.87% 0.00% 0.00% 0.00% 44.75% 76.36% 100.00% 100.00% 100.00%

14.63% 0.00% 0.00% 0.00% 35.59% 19.12% 0.00% 0.00% 0.00%

14.63% 100.00% 100.00% 100.00% 35.59% 19.12% 0.00% 0.00% 0.00%

70.75% 0.00% 0.00% 0.00% 28.83% 61.76% 100.00% 100.00% 100.00%

2,106.75 492.81 815.61 1,177.71 1,572.83 1,996.81 2,446.61 2,908.49 3,370.37

Investment required or 'Exercise Price'. Annual Growth Rate of Potential Market Cash Flow Annual Standard Deviation of Cash Flow in Target Market. Inverse demand function for 1 firm in market. Inverse demand function for 2 firms in market. Risk-free rate.

Annual market cash flow where value of Leading equals Following. P(X)

Table Expected <= Xl Xl Xl < X < Xf Xf Xf <= X

P(L)

P(F)

P(S)

Probability for each firm

Results Summary - for the expected level of annual market cash flows (120.0): Since the annual expected cash flow (X = 120.0) is between the level of cash flow where the value of Leading equals Following (Xl = 78.4), and the level of cash flow where the Follower will enter the market (Xf = 133.9), there is an equilibrium set of mixed strategies that each firm will enter the market with probability of 82.9%.

The probability that each firm will enter the market is 82.9%. In equilibrium, each firm has the probability of either Leading or Following of 14.6%, and the remaining 70.7% probability that each firm will enter the market Simultaneously. With respective expected payoff's of: Leading (L(X)-K) = 2139.4; Following F(X) = 2106.8; and acting Simultaneously (S(X)-K) = 2100.0, the weighted average expected payoff for each firm is 2106.8. Note that the expected payoff from the game, in equilibrium, is equal to the value of being a Follower.

Industry/Group Name 54.7% Advertising - Advertising 53.0% Aerospace/Defense - Aerospace/Defense 57.4% Air Transport - Air Transport 48.1% Apparel - Apparel 43.7% Auto-&Auto Truck & Truck 51.8% Auto-Parts Auto Parts 23.3% Bank- Bank 16.3% Bank- (Canadian) Bank (Canadian) 33.4% Bank- (Foreign) Bank (Foreign) 20.4% Bank- (Midwest) Bank (Midwest) 30.1% Beverage - Beverage (Alcoholic) (Alcoholic) 30.9% Beverage - Beverage (Soft Drink) (Soft Drink) 71.9% Biotechnology - Biotechnology 46.2% Building - Building Materials Materials 84.0% Cable - Cable TV TV 26.4% Canadian - Canadian EnergyEnergy 32.8% Cement - Cement & Aggregates & Aggregates 37.4% Chemical - Chemical (Basic)(Basic) 39.2% Chemical - Chemical (Diversified) (Diversified) 44.1% Chemical - Chemical (Specialty) (Specialty) 45.1% Coal- Coal 77.5% Computer - Computer Software/Svcs Software/Svcs 81.6% Computers/Peripherals - Computers/Peripherals 37.8% Diversified - Diversified Co. Co. 77.1% Drug- Drug 78.1% E-Commerce - E-Commerce 59.0% Educational - Educational Services Services 27.2% Electric - Electric Util. (Central) Util. (Central) 22.6% Electric - Electric Utility Utility (East)(East) 28.6% Electric - Electric Utility Utility (West)(West) 60.3% Electrical - Electrical Equipment Equipment 64.1% Electronics - Electronics 47.7% Entertainment - Entertainment 66.9% Entertainment - Entertainment Tech Tech 61.7% Environmental - Environmental 45.9% Financial - Financial Svcs. Svcs. (Div.) (Div.) 37.8% Food- Processing Food Processing 41.0% Food- Wholesalers Food Wholesalers 29.7% Foreign - Foreign Electronics Electronics 47.9% Foreign - Foreign Telecom. Telecom. 42.3% Furn/Home - Furn/Home Furnishings Furnishings 36.4% Grocery - Grocery 63.5% Healthcare - Healthcare Information Information 32.7% Home - Home Appliance Appliance 34.8% Homebuilding - Homebuilding 40.4% Hotel/Gaming - Hotel/Gaming 33.4% Household - Household Products Products 50.9% Human - Human Resources Resources 57.8% Industrial - Industrial Services Services 28.3% Information - Information Services Services 29.0% Insurance - Insurance (Life) (Life) 33.2% Insurance - Insurance (Prop/Cas.) (Prop/Cas.) 95.0% Internet - Internet 23.5% Investment - Investment Co. Co. 26.5% Investment - Investment Co.(Foreign) Co.(Foreign) 46.5% Machinery - Machinery 55.7% Manuf. - Manuf. Housing/RV Housing/RV 40.4% Maritime - Maritime 61.0% Medical - Medical Services Services

Average Standard Deviation 54.7% 53.0% 57.4% 48.1% 43.7% 51.8% 23.3% 16.3% 33.4% 20.4% 30.1% 30.9% 71.9% 46.2% 84.0% 26.4% 32.8% 37.4% 39.2% 44.1% 45.1% 77.5% 81.6% 37.8% 77.1% 78.1% 59.0% 27.2% 22.6% 28.6% 60.3% 64.1% 47.7% 66.9% 61.7% 45.9% 37.8% 41.0% 29.7% 47.9% 42.3% 36.4% 63.5% 32.7% 34.8% 40.4% 33.4% 50.9% 57.8% 28.3% 29.0% 33.2% 95.0% 23.5% 26.5% 46.5% 55.7% 40.4% 61.0%

58.3% Medical - Medical Supplies Supplies 46.5% Metal- Metal Fabricating Fabricating 55.0% Metals - Metals & Mining & Mining (Div.) (Div.) 23.1% Natural - Natural Gas (Distrib.) Gas (Distrib.) 42.6% Natural - Natural Gas (Div.) Gas (Div.) 22.2% Newspaper - Newspaper 42.2% Office - Office Equip/Supplies Equip/Supplies 41.6% Oilfield - Oilfield Svcs/Equip. Svcs/Equip. 797.0% Packaging - Packaging & Container & Container 38.6% Paper/Forest - Paper/Forest Products Products 37.6% Petroleum - Petroleum (Integrated) (Integrated) 47.6% Petroleum - Petroleum (Producing) (Producing) 40.6% Pharmacy - Pharmacy Services Services 71.1% Power - Power 63.8% Precious - Precious MetalsMetals 61.6% Precision - Precision Instrument Instrument 39.7% Publishing - Publishing 23.3% R.E.I.T. - R.E.I.T. 27.6% Railroad - Railroad 51.2% Recreation - Recreation 41.6% Restaurant - Restaurant 56.2% Retail- Retail (Special (Special Lines)Lines) 39.7% Retail- Retail Automotive Automotive 32.0% Retail- Retail Building Building SupplySupply 43.4% Retail- Retail Store Store 31.0% Securities - Securities Brokerage Brokerage 77.0% Semiconductor - Semiconductor 66.2% Semiconductor - Semiconductor Equip Equip 40.8% Shoe- Shoe 46.5% Steel- (General) Steel (General) 49.6% Steel- (Integrated) Steel (Integrated) 108.5% Telecom. - Telecom. Equipment Equipment 74.1% Telecom. - Telecom. Services Services 23.2% Thrift- Thrift 35.9% Tire & - Tire Rubber & Rubber 28.0% Tobacco - Tobacco 47.0% Toiletries/Cosmetics - Toiletries/Cosmetics 39.6% Trucking - Trucking 28.5% Utility- Utility (Foreign) (Foreign) 20.5% Water - Water Utility Utility 88.9% Wireless - Wireless Networking Networking

58.3% 46.5% 55.0% 23.1% 42.6% 22.2% 42.2% 41.6% 797.0% 38.6% 37.6% 47.6% 40.6% 71.1% 63.8% 61.6% 39.7% 23.3% 27.6% 51.2% 41.6% 56.2% 39.7% 32.0% 43.4% 31.0% 77.0% 66.2% 40.8% 46.5% 49.6% 108.5% 74.1% 23.2% 35.9% 28.0% 47.0% 39.6% 28.5% 20.5% 88.9%