Risk and Managerial (Real) Options in Capital Budgeting Chapter 14 Risk and Managerial (Real) Options in Capital Budgeting

After Studying Chapter 14, you should be able to: Define the "riskiness" of a capital investment project. Understand how cash-flow riskiness for a particular period is measured, including the concepts of expected value, standard deviation, and coefficient of variation. Describe methods for assessing total project risk, including a probability approach and a simulation approach. Judge projects with respect to their contribution to total firm risk (a firm-portfolio approach). Understand how the presence of managerial (real) options enhances the worth of an investment project. List, discuss, and value different types of managerial (real) options.

Risk and Managerial Options in Capital Budgeting The Problem of Project Risk Total Project Risk Contribution to Total Firm Risk: Firm-Portfolio Approach Managerial Options

An Illustration of Total Risk (Discrete Distribution) ANNUAL CASH FLOWS: YEAR 1 PROPOSAL A State Probability Cash Flow Deep Recession 0.05 $ –3,000 Mild Recession 0.25 1,000 Normal 0.40 5,000 Minor Boom 0.25 9,000 Major Boom 0.05 13,000

Probability Distribution of Year 1 Cash Flows Proposal A 0.40 0.25 Probability 0.05 –3,000 1,000 5,000 9,000 13,000 Cash Flow ($)

Expected Value of Year 1 Cash Flows (Proposal A) CF1 P1 (CF1)(P1) $ –3,000 0.05 $ –150 1,000 0.25 250 5,000 0.40 2,000 9,000 0.25 2,250 13,000 0.05 650 S=1.00 CF1=$5,000

Variance of Year 1 Cash Flows (Proposal A) (CF1)(P1) (CF1 – CF1)2(P1) $ –150 (–3,000 – 5,000)2 (0.05) 250 ( 1,000 – 5,000)2 (0.25) 2,000 ( 5,000 – 5,000)2 (0.40) 2,250 ( 9,000 – 5,000)2 (0.25) 650 (13,000 – 5,000)2 (0.05) $5,000

Variance of Year 1 Cash Flows (Proposal A) (CF1)(P1) (CF1 – CF1)2*(P1) $ –150 3,200,000 250 4,000,000 2,000 0 2,250 4,000,000 650 3,200,000 $5,000 14,400,000

Summary of Proposal A The standard deviation = SQRT (14,400,000) = $3,795 The expected cash flow = $5,000 Coefficient of Variation (CV) = $3,795 / $5,000 = 0.759 CV is a measure of relative risk and is the ratio of standard deviation to the mean of the distribution.

An Illustration of Total Risk (Discrete Distribution) ANNUAL CASH FLOWS: YEAR 1 PROPOSAL B State Probability Cash Flow Deep Recession 0.05 $ –1,000 Mild Recession 0.25 2,000 Normal 0.40 5,000 Minor Boom 0.25 8,000 Major Boom 0.05 11,000

Probability Distribution of Year 1 Cash Flows Proposal B 0.40 0.25 Probability 0.05 –3,000 1,000 5,000 9,000 13,000 Cash Flow ($)

Expected Value of Year 1 Cash Flows (Proposal B) CF1 P1 (CF1)(P1) $ –1,000 0.05 $ –50 2,000 0.25 500 5,000 0.40 2,000 8,000 0.25 2,000 11,000 0.05 550 S=1.00 CF1=$5,000

Variance of Year 1 Cash Flows (Proposal B) (CF1)(P1) (CF1 – CF1)2(P1) $ –50 (–1,000 – 5,000)2 (0.05) 500 ( 2,000 – 5,000)2 (0.25) 2,000 ( 5,000 – 5,000)2 (0.40) 2,000 ( 8,000 – 5,000)2 (0.25) 550 (11,000 – 5,000)2 (0.05) $5,000

Variance of Year 1 Cash Flows (Proposal B) (CF1)(P1) (CF1 – CF1)2(P1) $ –50 1,800,000 500 2,250,000 2,000 0 2,000 2,250,000 550 1,800,000 $5,000 8,100,000

Summary of Proposal B The standard deviation = SQRT (8,100,000) = $2,846 The expected cash flow = $5,000 Coefficient of Variation (CV) = $2,846 / $5,000 = 0.569 The standard deviation of B < A ($2,846< $3,795), so “B” is less risky than “A”. The coefficient of variation of B < A (0.569<0.759), so “B” has less relative risk than “A”.

Projects have risk that may change from period to period. Total Project Risk Projects have risk that may change from period to period. Projects are more likely to have continuous, rather than discrete distributions. Cash Flow ($) 1 2 3 Year

Probability Tree Approach A graphic or tabular approach for organizing the possible cash-flow streams generated by an investment. The presentation resembles the branches of a tree. Each complete branch represents one possible cash-flow sequence.

Probability Tree Approach Basket Wonders is examining a project that will have an initial cost today of $900. Uncertainty surrounding the first year cash flows creates three possible cash-flow scenarios in Year 1. –$900

Probability Tree Approach Node 1: 20% chance of a $1,200 cash-flow. Node 2: 60% chance of a $450 cash-flow. Node 3: 20% chance of a –$600 cash-flow. (0.20) $1,200 1 (0.60) $450 –$900 2 (0.20) –$600 3 Year 1

Probability Tree Approach (0.10) $2,200 Each node in Year 2 represents a branch of our probability tree. The probabilities are said to be conditional probabilities. (0.20) $1,200 (0.60) $1,200 1 (0.30) $ 900 (0.35) $ 900 (0.60) $450 (0.40) $ 600 –$900 2 (0.25) $ 300 (0.10) $ 500 (0.20) –$600 (0.50) –$ 100 3 (0.40) –$ 700 Year 1 Year 2

Joint Probabilities [P(1,2)] (0.10) $2,200 0.02 Branch 1 0.12 Branch 2 0.06 Branch 3 0.21 Branch 4 0.24 Branch 5 0.15 Branch 6 0.02 Branch 7 0.10 Branch 8 0.08 Branch 9 (0.20) $1,200 (0.60) $1,200 1 (0.30) $ 900 (0.35) $ 900 (0.60) $450 (0.40) $ 600 –$900 2 (0.25) $ 300 (0.10) $ 500 (0.20) –$600 (0.50) –$ 100 3 (0.40) –$ 700 Year 1 Year 2

Project NPV Based on Probability Tree Usage z NPV = S (NPVi)(Pi) The probability tree accounts for the distribution of cash flows. Therefore, discount all cash flows at only the risk-free rate of return. i = 1 The NPV for branch i of the probability tree for two years of cash flows is CF1 CF2 NPVi = + (1 + Rf )1 (1 + Rf )2 - ICO

NPV for Each Cash-Flow Stream at 5% Risk-Free Rate (0.10) $2,200 $ 2,238.32 $ 1,331.29 $ 1,059.18 $ 344.90 $ 72.79 –$ 199.32 –$ 1,017.91 –$ 1,562.13 –$ 2,106.35 (0.20) $1,200 (0.60) $1,200 1 (0.30) $ 900 (0.35) $ 900 (0.60) $450 (0.40) $ 600 –$900 2 (0.25) $ 300 (0.10) $ 500 (0.20) –$600 (0.50) –$ 100 3 (0.40) –$ 700 Year 1 Year 2

NPV on the Calculator Remember, we can use the cash flow registry to solve these NPV problems quickly and accurately! Source: Courtesy of Texas Instruments

Actual NPV Solution Using Your Financial Calculator Solving for Branch #3: Step 1: Press CF key Step 2: Press 2nd CLR Work keys Step 3: For CF0 Press –900 Enter  keys Step 4: For C01 Press 1200 Enter  keys Step 5: For F01 Press 1 Enter  keys Step 6: For C02 Press 900 Enter  keys Step 7: For F02 Press 1 Enter  keys

Actual NPV Solution Using Your Financial Calculator Solving for Branch #3: Step 8: Press   keys Step 9: Press NPV key Step 10: For I=, Enter 5 Enter  keys Step 11: Press CPT key Result: Net Present Value = $1,059.18 You would complete this for EACH branch!

Calculating the Expected Net Present Value (NPV) Branch NPVi Branch 1 $ 2,238.32 Branch 2 $ 1,331.29 Branch 3 $ 1,059.18 Branch 4 $ 344.90 Branch 5 $ 72.79 Branch 6 –$ 199.32 Branch 7 –$ 1,017.91 Branch 8 –$ 1,562.13 Branch 9 –$ 2,106.35 P(1,2) NPVi * P(1,2) 0.02 $ 44.77 0.12 $159.75 0.06 $ 63.55 0.21 $ 72.43 0.24 $ 17.47 0.15 –$ 29.90 0.02 –$ 20.36 0.10 –$156.21 0.08 –$168.51 Expected Net Present Value = –$ 17.01

Calculating the Variance of the Net Present Value NPVi $ 2,238.32 $ 1,331.29 $ 1,059.18 $ 344.90 $ 72.79 –$ 199.32 –$ 1,017.91 –$ 1,562.13 –$ 2,106.35 P(1,2) (NPVi – NPV )2[P(1,2)] 0.02 $ 101,730.27 0.12 $ 218,149.55 0.06 $ 69,491.09 0.21 $ 27,505.56 0.24 $ 1,935.37 0.15 $ 4,985.54 0.02 $ 20,036.02 0.10 $ 238,739.58 0.08 $ 349,227.33 Variance = $1,031,800.31

Summary of the Decision Tree Analysis The standard deviation = SQRT ($1,031,800) = $1,015.78 The expected NPV = –$ 17.01

Simulation Approach An approach that allows us to test the possible results of an investment proposal before it is accepted. Testing is based on a model coupled with probabilistic information.

Simulation Approach Factors we might consider in a model: Market analysis Market size, selling price, market growth rate, and market share Investment cost analysis Investment required, useful life of facilities, and residual value Operating and fixed costs Operating costs and fixed costs

Simulation Approach Each variable is assigned an appropriate probability distribution. The distribution for the selling price of baskets created by Basket Wonders might look like: $20 $25 $30 $35 $40 $45 $50 0.02 0.08 0.22 0.36 0.22 0.08 0.02 The resulting proposal value is dependent on the distribution and interaction of EVERY variable listed on slide 14.31.

Simulation Approach Each proposal will generate an internal rate of return. The process of generating many, many simulations results in a large set of internal rates of return. The distribution might look like the following: OF OCCURRENCE PROBABILITY INTERNAL RATE OF RETURN (%)

Contribution to Total Firm Risk: Firm-Portfolio Approach Combination of Proposals A and B Proposal A Proposal B CASH FLOW TIME TIME TIME Combining projects in this manner reduces the firm risk due to diversification.

Determining the Expected NPV for a Portfolio of Projects NPVP = S ( NPVj ) NPVP is the expected portfolio NPV, NPVj is the expected NPV of the jth NPV that the firm undertakes, m is the total number of projects in the firm portfolio. j=1

Determining Portfolio Standard Deviation sP = S S sjk sjk is the covariance between possible NPVs for projects j and k, s jk = s j s k r jk . sj is the standard deviation of project j, sk is the standard deviation of project k, rjk is the correlation coefficient between projects j and k. j=1 k=1

Combinations of Risky Investments E: Existing Projects 8 Combinations E E + 1 E + 1 + 2 E + 2 E + 1 + 3 E + 3 E + 2 + 3 E + 1 + 2 + 3 A, B, and C are dominating combinations from the eight possible. C B Expected Value of NPV E A Standard Deviation

Managerial (Real) Options Management flexibility to make future decisions that affect a project’s expected cash flows, life, or future acceptance. Project Worth = NPV + Option(s) Value

Managerial (Real) Options Expand (or contract) Allows the firm to expand (contract) production if conditions become favorable (unfavorable). Abandon Allows the project to be terminated early. Postpone Allows the firm to delay undertaking a project (reduces uncertainty via new information).

Previous Example with Project Abandonment (0.10) $2,200 Assume that this project can be abandoned at the end of the first year for $200. What is the project worth? (0.20) $1,200 (0.60) $1,200 1 (0.30) $ 900 (0.35) $ 900 (0.60) $450 (0.40) $ 600 –$900 2 (0.25) $ 300 (0.10) $ 500 (0.20) –$600 (0.50)–$ 100 3 (0.40)–$ 700 Year 1 Year 2

Project Abandonment Node 3: (0.10) $2,200 Node 3: (500/1.05)(0.1)+ (–100/1.05)(0.5)+ (–700/1.05)(0.4)= ($476.19)(0.1)+ –($ 95.24)(0.5)+ –($666.67)(0.4)= –($266.67) (0.20) $1,200 (0.60) $1,200 1 (0.30) $ 900 (0.35) $ 900 (0.60) $450 (0.40) $ 600 –$900 2 (0.25) $ 300 (0.10) $ 500 (0.20) –$600 (0.50) –$ 100 3 (0.40) –$ 700 Year 1 Year 2

What is the “new” project value? Project Abandonment (0.10) $2,200 The optimal decision at the end of Year 1 is to abandon the project for $200. $200 > –($266.67) What is the “new” project value? (0.20) $1,200 (0.60) $1,200 1 (0.30) $ 900 (0.35) $ 900 (0.60) $450 (0.40) $ 600 –$900 2 (0.25) $ 300 (0.10) $ 500 (0.20) –$600 (0.50) –$ 100 3 (0.40) –$ 700 Year 1 Year 2

Project Abandonment $ 2,238.32 $ 1,331.29 $ 1,059.18 $ 344.90 $ 72.79 (0.10) $2,200 $ 2,238.32 $ 1,331.29 $ 1,059.18 $ 344.90 $ 72.79 –$ 199.32 –$ 1,280.95 (0.20) $1,200 (0.60) $1,200 1 (0.30) $ 900 (0.35) $ 900 (0.60) $450 (0.40) $ 600 –$900 2 (0.25) $ 300 (0.20) –$400* (1.0) $ 0 3 *–$600 + $200 abandonment Year 1 Year 2

Summary of the Addition of the Abandonment Option The standard deviation* = SQRT (740,326) = $857.56 The expected NPV* = $ 71.88 NPV* = Original NPV + Abandonment Option Thus, $71.88 = –$17.01 + Option Abandonment Option = $ 88.89 * For “True” Project considering abandonment option