Project Interactions

Applying the models

So far we have discussed simple projects that are mutually exclusive and made some assumptions

Competing projects have the same livesWe know the future cash flows with certaintyManagement does not have the ability to make decisions that change the cash flows after the project is started.

This chapter expands on the basic decision variables (NPV, IRR etc) in cases where projects with different lives are compared, cash flows are uncertain, and we discuss the value & impact of management.

Capital Rationing

Choosing among projects when limited by the amount of resources available. Previously we assumed that the firm could undertake any positive NPV project, however it may be limited by available resources.

Spending Limits

Assume that the company has a limit on the amount of funds that it believes it can raise.Example: 3 projects Spending limit of 12MProject Investment NPV A 12,000,000 18,000,000 B 7,000,000 14,000,000 C 5,000,000 10,000,000

Which project(s) should it undertake?

Using Profitability Index

Given the spending limits, the firm should also look at the return per dollar invested.Project Investment NPV PI A 12,000,000 18,000,000

1.5 B 7,000,000 14,000,000 2.0 C 5,000,000 10,000,000 2.0

While B & C have a lower NPV individually they both have a higher profitability index.

Problems

Profitability index can be misleading if looked at alone.Project Investment NPV PI A 10,000,000 14,000,000 1.4 B 5,000,000 6,000,000 1.2 C 5,000,00010,000,000 2.0

The firm should still look at the total amount of NPV!

Problems with Profitability Index

If more than one constraint is to be rationed then PI can be misleading. For example, if one project depends upon another. Also PI ignores the amount of wealth created.

Comparing Projects with Unequal Lives

Replacement Chain ApproachRepeat projects until they have the same life span.Compare a two year project with a four year project by repeating the two year project

Comparing Projects with Unequal Lives

Equivalent Annual Annuity (finding an annualized NPV)To Find EA

find the NPV of the ProjectUse the NPV as the PV of an annuity and solve for paymentChoose the project with the highest EAA

Abandonment Decisions

Often one question is when to stop a project. By quitting at different points in time the NPV and EAA will vary due to the changes in salvage value.Use EAA and treat each abandonment time as a separate project.

Uncertain Cash Flows

So far we have assumed that we can estimate the cash flows from the project with certainty.However, it is difficult to correctly forecast future cash flows – how can the risks associated with changes in the economic environment and the difficulties with forecasting cash flows be accounted for?

Three Types of Risk

Stand Alone RiskViews project in isolationWith-in firm (Corporate Risk)Looks at the firms portfolio of projects and how they interactMarket RiskRisk from the view of a well diversified investor.

Definitions

RiskExposure to a chance of injury or lossProbabilityThe likelihood an event occursRisk vs. UncertaintyRisk – the probability of the outcome is knownUncertainty – includes judgment concerning

the probability

Definitions and Terms Continued

Objective Prob –can measure prob. preciselySubjective Prob. – Includes judgment or opinionVariation Risk – We want to look at a range of possible outcomes

Issues in Risk Measurement

1. Stand Alone Risk is the easiest to measure2. Market Risk is the most important to the

shareholder3. To evaluate risk you need three things

i. Standard deviation of the projects forecasted returns

ii. Correlation of the projects forecasted returns with the firms other assets

iii. Correlation of the projects forecasted returns with the market

Issues in Risk Management con’t

4. Using the numbers in 3) you can find the corporate beta and market beta coefficient (equal to ((

5. ost projects have a + correlation with other projects and a coefficient < 1

6. Most projects are positively correlated with the market with coefficient < 1

7. Corporate risk should also be examined1. More important to small business2. Investors may look at things other than market risk3. Firm Stability is important to creditors, suppliers etc

Stand Alone Risk (Review)

The easiest approach to measuring stand alone risk is to use the standard deviation of the projects returns.Just like security analysis you need to be careful looking at only standard deviation – don’t forget coefficient of variation

Measuring Stand Alone RiskQuick Review

Sensitivity Analysis

Scenario Analysis

Monte Carlo Simulation

Applying Sensitivity and Scenario Analysis

In our examples we simplified the problem by changing the aggregate cash flows.When evaluating the project, any assumptions about inputs can change – impacting the incremental cash flows.A few of many possible examples:

Changes in variable input costsChanges in salesChanges in tax laws

Probability Review

Mutually exclusive eventsIf A occurs then B cannot. Example considering building a new sports arena. There are two sites North and South. Prob North = .5 Prob South = .25This implies the prob that the stadium is built is .5 + .25 = .75

Probability Review 2

Independent EventsExample Exxon is considering two drilling sites, gulf coast and AlaskaP(A) = New oil from gulf coast = .7P(B) = Prob of oil in Alaska = .4

Event B No Event B(.4) (.6)

Event A (.7) .28 .42

No event A (.3) .12 .18

Probability Review 3

Dependent Events Prob of one event depends upon the otherNorth Side is voting on bonds for the new arena, 80% chance of the bond passing If passed there is a 60% chance the stadium gets built in North. If the bonds fail there is a 30% chance that the stadium gets built in North

Prob Review 3 con’t

North North Selected RejectedBond (.8)(.6) (.8)(.4) Passes (.8) =.48 =.32

Bond (.2)(.3) (.2)(.7)Fails (.2) =.06 =.14

Decision Trees

So far our decision making has ignored the role of management.We know that things change as a project progresses and decision trees attempt to account for this.

Project Example

Peripherals Inc. is considering making a new copier/printer.Stage 1: Conduct a market study to investigate potential

sales, cost = $500,000Stage 2: If sizable market exists at time t=1 spend

1,000,000 to build prototype (80% prob)Stage 3: If it passes all test spend $10,000,000 at time t=2

60% probStage 4: Year t = 3 to t = 6 High demand (20% prob) $12M in CF each yr Avg Demand (60% prob) $5M in CF each yr Low Demand (20% prob) –$2M in CF each yr

Building the decision tree

t = 0 t = 1 -1,000,000 80%-500,000 20% 0

Stage 1 and Stage 2 represented on the tree

Building the decision tree

t = 1 t = 2 -10,000,000 60%-1,000,000 40%

0

Stage 2 and Stage 3 represented on the tree

Stage 1 to 3

t=0 t=1 t=2 -10,000,000 60% -1,000,000 80%-500,000 40% 0 20%

0

Decision Tree

Continue to Build the tree (on the board in class)When finished find the NPV of each branch and multiply it times the probability for each branch to find the expected NPV.

Real Options

Opportunities arise that present the management with the ability to make a choice. The decision points in the above decision tree represent this.

For example: At time t=2, if we realize that the project is going to produce only

-$2,000,000 each year we would not proceed with the project. There is an option to abandon the project.

Real Options

Three main components

1. Determining the value of a real option.2. Identifying the optimal response to

changing conditions.3. Structuring projects to create real

options.

Valuing a Real Option Using the Decision Tree

In the earlier decision tree. Assume we can abandon the project if we find out that it is going to result in –2,000,000 CF each year.We would need to recalculate the NPV of that branch without the –2,000,000 CF’sNPV = -9,364,795.92

instead of –14,207,508.52The total NPV is then 1,235,339.21 instead of

770,438.80 an increase of 464,900.41

Other Benefits

If the reduction in uncertainty decreases the risk the firm can lower the WACC increasing the NPV even further.The key is building the decision points into the capital budgeting process from the beginning

Real Options and Financial Management

Flexibility Option -- Switch inputs during the production process.Capacity options – Ability to manage capacity in response to changing economic conditions.New Product Options – May accept initial negative NPV if it allows rights to future goods.Timing Options – Allow you to postpone or increase production.

Value of Real Options

In each case the option can add value to the project.You would want to compare the added value of the option to the cost of implementing the option.

Example – it costs an extra 10Million to build a plant that could allow inputs to be switched. Given the volatility in the price of the inputs – you estimate the real option to switch inputs is worth $20 Million

Characteristics of Real Options

Real options often increase the value of a projectThe value of most real options increases:

As the longer the amount of time that exists before the option needs to be exercised increasesThe source of risk becomes more volatileIf interest rates increase.

Options

Call Option – the right to buy an asset at some point in the future for a designated price. Put Option – the right to sell an asset at some point in the future at a given price

Call Option Profit

Call option – as the price of the asset increases the option is more profitable. Once the price is above the exercise price (strike price) the option will be exercisedIf the price of the underlying asset is below the exercise price it won’t be exercised – you only loose the cost of the option.The Profit earned is equal to the gain or loss on the option minus the initial cost.

Profit Diagram Call Option

Profit

Spot Cost Price

S

S-X-C

X

Call Option Intrinsic Value

The intrinsic value of a call option is equal to the current value of the underlying asset minus the exercise price if exercised or 0 if not exercised. In other words, it is the payoff to the investor at that point in time (ignoring the initial cost)

the intrinsic value is equal tomax(0, S-X)

Payoff Diagram Call Option

Payoff

Spot Price

S

S-X

XX

Put Option Profits

Put option – as the price of the asset decreases the option is more profitable. Once the price is below the exercise price (strike price) the option will be exercisedIf the price of the underlying asset is above the exercise price it won’t be exercised – you only loose the cost of the option.

Profit Diagram Put Option

Profit

Spot Price

Cost X

S

X-S-C

Put Option Intrinsic Value

The intrinsic value of a put option is equal to exercise price minus the current value of the underlying asset if exercised or 0 if not exercised. In other words, it is the payoff to the investor at that point in time (ignoring the initial cost)

the intrinsic value is equal tomax(X-S, 0)

Payoff Diagram Put Option

Profit

Spot Price

Cost

XS

X-S

Pricing an Option

Black Scholes Option Pricing ModelBased on a European Option with no dividendsAssumes that the prices in the equation are lognormal.

Inputs you will need

S = Current value of underlying assetX = Exercise pricet = life until expiration of optionr = riskless rate2 = variance

PV and FV in continuous time

e = 2.71828 y = lnx x = ey

FV = PV (1+k)n for yearly compoundingFV = PV(1+k/m)nm for m compounding

periods per yearAs m increases this becomesFV = PVern =PVert let t =n rearranging for PV PV = FVe-rt

Black Scholes

Value of Call Option = SN(d1)-Xe-rtN(d2) S = Current value of underlying asset

X = Exercise pricet = life until expiration of optionr = riskless rate2 = varianceN(d ) = the cumulative normal

distribution (the probability that a variable with a standard normal distribution will be less than d)

Black Scholes (Intuition)

Value of Call Option

SN(d1) - Xe-rt N(d2)The expected PV of cost Risk NeutralValue of S of investment Probability

ofif S > X S > X

Black Scholes

Value of Call Option = SN(d1)-Xe-

rtN(d2)

Where:

t

trXS

d

)2()ln(2

1

tdd 12

Application to Real Options

Investment Option Real OptionStock Price PV of projects Cash FlowsExercise Price Expenditure required to

acquire projects assets

Time to Expire Length of time the decision can be deferred

Variance Riskiness of projects assets

Example

Disney – Can spend 100M to create a Spanish version of the Disney channelPV of future CF’s = $80M Initial investment = $100M

The resulting NPV of the project is80M – 100M = -$20 Million

A Real Option

Assume the expansion will provide political connections resulting in an advantage if they expand into South America. Assume the expansion would cost $150M and could be taken at any time over the next ten years The firm believes that the NPV of expanding is 100M.S = 100M X = 150M r = .065 Variance = .40

Plugging into the Black Scholes Model

Value of Call Option = SN(d1)-Xe-rtN(d2)

= 100(.8648) – 150e(-.065)(10)(.435) = 52.3 Million

Original NPV = 80M – 100M = - 20MAdd the value of the option = Total Value of Project

-20M+52.3 = 32.3M

Put Option

The black scholes value is similar for a put optionValue of put option = Xe-rtN(-d2)-SN(-d1)

Option to Abandon

An example of a real option that corresponds to a put option would be an option to abandon a project in the future.

Developing Prob Estimates

History – What happened last year…

Experiments – Test programs, market surveys etc…

Judgment – Subjective adjustment

Structuring Project Cash Flows to Help Manage Risk

Variable and Fixed Costs

Pricing Strategy

Sequential Investment

Financial Leverage

Measuring Corporate and Market Risk

Corporate and Market beta’s