Dev 567Project and Program Analysis

Dr. M. Fouzul Kabir KhanProfessor of Economics and Finance

North South University

Lecture 5: Project Appraisal Under Uncertainty

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• Critique of DCF1. Project analysis under risk: Using a risk-adjusted

discount rate• The certainty equivalent method• Real options in capital projects

Lecture 5

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Expected Value Analysis It is impossible to say for certain what the future

holds; therefore, CBA must include some provision for uncertainty.

Contingencies and their probabilitiesModeling uncertainty as risks begins with the

specification of a set of contingencies that are exhaustive and mutually exclusive.

A graphical illustration Probabilities may be based solely on historically onobserved frequencies, on subjective assessment byclients, analysts, or other experts.

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Contingencies and their Probabilities

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Incorporating risk into project analysis through adjustments to the discount rate, and by the certainty equivalent factor.

Project Analysis Under Risk

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● Risk is the variation of future expectations around an expected value.

● Risk is measured as the range of variation around an expected value.

● Risk and uncertainty are interchangeable words.

Introduction: What is Risk?

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Where Does Risk Occur?

End of End of End of End of Year 0 Year 1 Year 2 Year 3

-$760 ? -$876 ? -$546 ?-$235 ? -$231 ? -$231 ?

-$1,257 $127 ? $186 ? $190 ?$489 ? $875 ? $327 ?$945 ? $984 ? $454 ?

Varying Cash FlowsForecast Estimates of

• In project analysis, risk is the variation in predicted future cash flows.

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There are several approaches to handling risk:

• Risk may be accounted for by (1) applying a discount rate commensurate with the riskiness of the cash flows, and (2), by using a certainty equivalent factor

• Risk may be accounted for by evaluating the project using sensitivity and breakeven analysis.

• Risk may be accounted for by evaluating the project under simulated cash flow and discount rate scenarios.

Handling Risk

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Using a Risk Adjusted Discount Rate

layInitialOutedraterisk adjustlowRisk ycashf

edraterisk adjustlowRisk ycashfNPV

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•The structure of the cash flow discounting mechanism for risk is:-

The $ amount used for a ‘risky cash flow’ is the expected dollar value for that time period.

A ‘risk adjusted rate’ is a discount rate calculated to include a risk premium. This rate is known as the RADR, the Risk Adjusted Discount Rate.

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Conceptually, a risk adjusted discount rate, k, has three components:-

1. A risk-free rate (r), to account for the time value of money

2. An average risk premium (u), to account for the firm’s business risk

3. An additional risk factor (a) , with a positive, zero, or negative value, to account for the risk differential between the project’s risk and the firms’ business risk.

Defining a Risk Adjusted Discount Rate

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A risky discount rate is conceptually defined as: k = r + u + a

Unfortunately, k, is not easy to estimate. Two approaches to this problem are:

1. Use the firm’s overall Weighted Average Cost of Capital, after tax, as k . The WACC is the overall rate of return required to satisfy all suppliers of capital.

2. A rate estimating (r + u) is obtained from the Capital Asset Pricing Model, and then a is added.

Calculating a Risk Adjusted Discount Rate

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Assume a firm has a capital structure of:50% common stock, 10% preferred stock, 40% long

term debt.Rates of return required by the holders of each

are :common, 10%; preferred, 8%; pre-tax debt, 7%. The firm’s income tax rate is 30%.

WACC = (0.5 x 0.10) + (0.10 x 0.08) + (0.40 x (0.07x (1-0.30))) = 7.76% pa, after tax.

Calculating the WACC

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• This model establishes the covariance between market returns and returns on a single security.

• The covariance measure can be used to establish the risky rate of return, r, for a particular security, given expected market returns and the expected risk free rate.

The Capital Asset Pricing Model

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Calculating r from the CAPM

fmf RRRrE ~

• The equation to calculate r, for a security with a calculated Beta is:

Where : is the required rate of return being calculated, is the risk free rate: is the Beta of the security, and is the expected return on the market.

rE ~fR

mR

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Beta is the Slope of an Ordinary Least Squares Regression Line

Share Returns Regressed On Market Returns

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-0.02

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0.02

0.04

0.06

0.08

0.10

0.12

-0.10 -0.05 0.00 0.05 0.10 0.15 0.20

Returns on Market, % pa

Ret

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of S

hare

, %

pa

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The Regression Process

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The value of Beta can be estimated as the regression coefficient of a simple regression model. The regression coefficient ‘a’ represents the intercept on the y-axis, and ‘b’ represents Beta, the slope of the regression line.

Where,   = rate of return on individual firm i’s shares

at time t = rate of return on market portfolio at time t = random error term (as defined in

regression analysis)mtruit

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The Certainty Equivalent Method: Adjusting the cash flows to their ‘certain’ equivalents

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rbCF

rbCFNPV

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1

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The Certainty Equivalent method adjusts the cash flows for risk, and then discounts these ‘certain’ cash flows at the risk free rate.

Where: b is the ‘certainty coefficient’ (established by management, and is between 0 and 1); and r is the risk free rate.

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• Risk is the variation in future cash flows around a central expected value.

• Risk can be accounted for by adjusting the NPV calculation discount rate: there are two methods – either the WACC, or the CAPM

• Risk can also be accommodated via the Certainty Equivalent Method.

• All methods require management judgment and experience.

Analysis Under Risk :Summary

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• Critics of the DCF criteria argue that cash flow analysis fails to account for flexibility in business decisions.

• Real option models are more focused on describing uncertainty and in particular the managerial flexibility inherent in many investments

• Real options give the firm the opportunity but not the obligation to take certain action

Appraising Projects with Real Options

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• Application of financial options theory to investment in a non-financial (real) asset

• Hence the name real options

What is Real Options?

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Financial options have an underlying asset that is traded--usually a security like a stock.

A real option has an underlying asset that is not a security--for example a project or a growth opportunity, and it isn’t traded.

(More…)

How are real options different from financial options?

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• It does not obligate its owner to take any action. It merely gives the owner the right to buy or sell an asset.

What is the single most importantcharacteristic of an option?

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Ten real options to:◦ Invest in a future capital project◦ Delay investing in a project◦ Choose the project’s initial capacity◦ Expand capacity of the project subsequent to the original

investment◦ Change the project’s technology◦ Change the use of project during its life◦ Shutdown the project with the intention of restarting it

later◦ Abandon or sell the project◦ Extend the life of the project◦ Invest in further projects contingent on investment in the

initial project

Real Options in Capital Projects

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• Real options exist when managers can influence the size and risk of a project’s cash flows by taking different actions during the project’s life in response to changing market conditions.

• Alert managers always look for real options in projects.

• Smarter managers try to create real options.

What is a real option?

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• The payoffs for financial options are specified in the contract.

• Real options are “found” or created inside of projects. Their payoffs can be varied.

How are real options different from financial options?

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• Investment timing options

• Growth options ◦ Expansion of existing product line◦ New products◦ New geographic markets

What are some types of real options?

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Abandonment options◦ Contraction◦ Temporary suspension

Flexibility options

Types of real options (Continued)

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1. DCF analysis of expected cash flows, ignoring the option.

2. Qualitative assessment of the real option’s value.

3. Decision tree analysis.4. Standard model for a corresponding financial

option.5. Financial engineering techniques.

Five Procedures for Valuing Real Options

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Initial cost = $70 million, Cost of Capital = 10%, risk-free rate = 6%, cash flows occur for 3 years.

Annual

Demand Probability Cash FlowHigh 30% $45Average 40% $30Low 30% $15

Analysis of a Real Option: Basic Project

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• E(CF) =.3($45)+.4($30)+.3($15) = $30

• PV of expected CFs = ($30/1.1) + ($30/1.12) + ($30/1.13) = $74.61 million

• Expected NPV = $74.61 - $70 = $4.61 million

Approach 1: DCF Analysis

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If we immediately proceed with the project, its expected NPV is $4.61 million.

However, the project is very risky:◦ If demand is high, NPV = $41.91 million.◦ If demand is low, NPV = -$32.70 million.

Investment Timing Option

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• If we wait one year, we will gain additional information regarding demand.

• If demand is low, we won’t implement project.

• If we wait, the up-front cost and cash flows will stay the same, except they will be shifted ahead by a year.

Investment Timing Opinion

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The value of any real option increases if:◦ the underlying project is very risky◦ there is a long time before you must exercise the

option This project is risky and has one year before

we must decide, so the option to wait is probably valuable.

Procedure 2: Qualitative Assessment

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Decision Tree Analysis(Implement only if demand is not low.)

Cost 0 Prob. 1 2 3 4 Scenarioa

-$70 $45 $45 $4530%

$0 40% -$70 $30 $30 $3030%

$0 $0 $0 $0

Future Cash Flows

Discount the cost of the project at the risk-free rate, since the cost is known. Discount the operating cash flows at the cost of capital. Example: $35.70 = -$70/1.06 + $45/1.12 + $45/1.13 + $45/1.13.

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E(NPV) = [0.3($35.70)]+[0.4($1.79)] + [0.3 ($0)] E(NPV) = $11.42

Use these scenarios, with their given probabilities, to find the project’s expected NPV if we

wait.

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Decision tree NPV is higher ($11.42 million vs. $4.61).

In other words, the option to wait is worth $11.42 million. If we implement project today, we gain $4.61 million but lose the option worth $11.42 million.

Therefore, we should wait and decide next year whether to implement project, based on demand.

Decision Tree with Option to Wait vs. Original DCF Analysis