Dr. M. Fouzul Kabir Khan Professor of Economics and Finance North South University Lecture 5: Project Appraisal Under Uncertainty

Critique of DCF 1. Project analysis under risk: Using a risk-adjusted discount rate The certainty equivalent method Real options in capital projects 2

3  It is impossible to say for certain what the future holds; therefore, CBA must include some provision for uncertainty.  Contingencies and their probabilities Modeling 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 on observed frequencies, on subjective assessment by clients, analysts, or other experts.

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Incorporating risk into project analysis through adjustments to the discount rate, and by the certainty equivalent factor. 5

● 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. 6

In project analysis, risk is the variation in predicted future cash flows. 7

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. 8

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. 9

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. 10

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. 11

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. 12

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. 13

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. 14

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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) u it 16

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. 17

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. 18

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 19

Application of financial options theory to investment in a non-financial (real) asset Hence the name real options 20

 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…) 21

It does not obligate its owner to take any action. It merely gives the owner the right to buy or sell an asset. 22

 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 23

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. 24

The payoffs for financial options are specified in the contract. Real options are “found” or created inside of projects. Their payoffs can be varied. 25

Investment timing options Growth options ◦ Expansion of existing product line ◦ New products ◦ New geographic markets 26

 Abandonment options ◦ Contraction ◦ Temporary suspension  Flexibility options 27

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. 28

 Initial cost = $70 million, Cost of Capital = 10%, risk-free rate = 6%, cash flows occur for 3 years. Annual Demand Probability Cash Flow High30%$45 Average40%$30 Low30%$15 29

E(CF)=.3($45)+.4($30)+.3($15) = $30 PV of expected CFs = ($30/1.1) + ($30/1.1 2 ) + ($30/1.1 3 ) = $74.61 million Expected NPV = $ $70 = $4.61 million 30

 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. 31

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. 32

 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. 33

Cost 0Prob Scenario a -$70$45 30% $040%-$70$30 30% $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/ $45/ $45/ $45/

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

 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. 36