Corporate Financial Strategy Lecture 4: Current Practice in Capital Budgeting and Real Options Module Leader: Professor Jon Tucker Selected slides by McGraw Hill

Lecture Objectives Company & Project Costs of Capital Measuring the Cost of Equity Analyzing Project Risk Certainty Equivalents The Capital Investment Process Sensitivity Analysis Real Options & Decision Trees Real Options Example Reader: Operating leverage; Monte Carlo Simulation; Timing Options

Company & Project Costs of Capital Company cost of capital Company cost of capital: Expected return on a portfolio of all the company’s existing securities Opportunity cost of capital for investment in the firm’s assets, and therefore the appropriate discount rate for the firm’s average risk projects If firm has no debt, then cost of capital = expected rate of return on its stock BUT company cost of capital is NOT the correct discount rate if new projects are more or less risky than the firm’s existing business

Company & Project Costs of Capital A firm’s value can be stated as the sum of the value of its various assets As projects A and B can have different risks, then this should be reflected in different discount rates for the two projects THUS the true cost of capital depends on the use to which that capital is put

Company & Project Costs of Capital A company’s cost of capital can be compared to CAPM required return For Johnson & Johnson: r = rf + β (rm - rf) = 2 + 0.5(7) = 5.5% Required return Project beta 0.5 Company cost of capital 5.5 0.2 SML The company cost of capital is not the appropriate discount rate for all its projects. If you consider each project as a mini-firm, the value of that mini-firm depends on its beta. The discount rate depends on the project’s discount rate. The required rate of return depends on the project and not on the company that is undertaking it.

Company & Project Costs of Capital Project cost of capital  Johnson & Johnson should accept any project lying above the upward-sloping SML Company cost of capital  Accept any project, regardless of risk, that offers a higher return than the company’s cost of capital It makes little sense that companies should use the same rate of return from a very safe project as from a very risky one: Though some companies use only one cost of capital

Company & Project Costs of Capital Debt and the company cost of capital Company cost of capital = expected return on a portfolio of all the company’s existing securities THUS it is a blend of: Cost of debt (interest rate) Cost of equity (expected rate of return on common stock) Company cost of capital = rassets = rportfolio

Company & Project Costs of Capital Example Firm’s market-value balance sheet: Asset value 100 Debt value (D) 30 Equity value (E) 70 Asset value 100 Firm value (V) 100 If investors expect 7.5% return on debt and 15% on equity, and the corporation tax rate = 35%: Weighted average cost of capital (WACC)

Measuring the Cost of Equity Estimating beta To calculate the WACC, you need to estimate the cost of equity calculated from CAPM: But how do we estimate beta?  Use past returns versus market returns to estimate beta (e.g. over 104 weeks)  Slope gives beta  but note how betas change through time  R-squared measures the proportion of the total variance in the stock’s returns that can be explained by market movements  If R2 is low then total variance is more explained by unique risk rather than market risk

Measuring the Cost of Equity Citigroup Returns 2010-2011 Weekly Data 2010-2011   beta = 1.83 alpha = -0.31 R-squared = 0.64 Correlation = 0.80 Annualized std dev of market = 19.52 Annualized std dev of stock = 44.55 Variance of stock = 1984.83 Std error of beta 0.14

Measuring the Cost of Equity Citigroup Returns 2008-2009 Weekly Data 2008-2009   beta = 3.32 alpha = 0.24 R-squared = 0.49 Correlation = 0.70 Annualized std dev of market = 30.11 Annualized std dev of stock = 142.95 Variance of stock = 20436.08 Std error of beta 0.34

Measuring the Cost of Equity Estimating beta Standard error of the estimated beta shows extent of possible mismeasurement Confidence interval can be computed of +2/-2 standard errors (gives range within which beta will occur 95% of the time) BUT estimation errors tend to cancel out when you estimate betas of portfolios: Beta Standard Error Canadian Pacific 1.27 .10 CSX 1.41 .08 Kansas City Southern 1.68 .12 Genesee & Wyoming 1.25 Norfolk Southern 1.42 .09 Rail America 1.15 .14 Union Pacific 1.21 .07 Industry portfolio 1.34 .06 Managers often turn to industry betas

Measuring the Cost of Equity Expected return on Union Pacific Corporation’s common stock If we wanted to estimate company cost of capital for Union Pacific, we could use 1.21 as its beta or industry average of 1.34 What is the risk free rate? If long term bonds yield = 2.7% and risk premium for holding long term bonds rather than Treasury bills = 1.4%, then we could use 2.7%-1.4% or roughly 1.2% as the expected long-term return from T-bills (higher than 0.02% 3 month T-bill rate in 2012) If market risk premium = 7%: Cost of equity = expected return = rf + β (rm – rf) = 1.2 + (1.21 x 7.0) = 9.7% With cost of debt = 4.8%, and corporation tax rate of 35%, and debt to value of 14.3%, then WACC = WACC = (1 – Tc) rD D/V + rE E/V = (1 – 0.35) x 4.8 x 0.143 + 9.7 x 0.857 = 8.8%

Measuring the Cost of Equity Asset Betas Company cost of capital (COC) is based on the average beta of the assets, taxes and financing The average beta of the assets is based on the % of funds in each asset For Union-Pacific, βE = 1.21 and we assume βD = 0.30 D/V = 0.143 and E/V = 0.857 Thus: Asset beta = estimate of average risk of firm’s railroad business

Analyzing Project Risk What happens when you do not have a project beta? If you want to set a cost of capital for a particular line of business, look for pure-play companies (that specialize in one activity) in that line of business and estimate their average asset beta or cost of capital Company cost of capital is useless for conglomerates which instead have to consider industry-specific costs of capital OR the manager has to exercise judgement

Analyzing Project Risk Advice for managers when a stock is not listed or the new project is very different from the firm’s usual investment: 1. Think about determinants of asset betas Observe characteristics of high- and low-beta assets 2. Don’t be fooled by diversifiable risk 3. Avoid fudge factors Do not add fudge factors to the discount rate Better to adjust the cash flow forecasts

Analyzing Project Risk What determines asset betas? 1. Cyclicality What is important is the relationship between the firm’s earnings and the aggregate earnings on all real assets i.e. earnings beta or cash flow beta Cyclical firms (whose revenues and earnings are strongly dependent on the business cycle) tend to be high beta firms THUS investors demand higher rates of return from investment whose performance is strongly tied to the performance of the economy e.g. airlines, construction, steel, etc.

Analyzing Project Risk What determines asset betas? 2. Operating leverage High operating leverage (high risk)  when a production facility has high fixed costs relative to variable costs Cash flow = (revenue – fixed cost – variable cost) PV (asset) = PV (revenue) – PV (fixed cost) – PV (variable cost) OR PV (revenue) = PV (fixed cost) + PV (variable cost) + PV (asset)

Analyzing Project Risk What determines asset betas? 2. Operating leverage fixed cost = 0; revenue and variable cost should be the same

Analyzing Project Risk What determines asset betas? 2. Operating leverage THUS higher ratio of fixed costs to project value = higher operating leverage  higher project beta

Analyzing Project Risk What determines asset betas? 3. Other factors A project’s value is equal to the expected cash flows discounted at the risk-adjusted discount rate, which will change if: Risk-free rate changes Market risk premium changes If either of these changes, then the discount rate changes and the project’s value changes The longer the project’s cash flows, the more it is exposed to shifts in the discount rate  thus long-term project will have a high beta even though it does not have high operating leverage or high cyclicality

Analyzing Project Risk Allowing for possible bad outcomes Managers often add “fudge factors” to offset worries about bad outcomes in projects, but: Bad outcomes do not affect the expected rate of return demanded by investors Better to adjust cash flows themselves and not discount rates Better to compute unbiased forecast (expected outcome taking into account probabilities)

Analyzing Project Risk Allowing for possible bad outcomes Example Project Z will produce one cash flow, forecasted at $1 million at year 1 It is regarded as average risk, suitable for discounting at 10% company COC:

Analyzing Project Risk Allowing for possible bad outcomes Example BUT company’s engineers are behind schedule developing technology for project. There is a small chance that it will not work. Most likely outcome still $1 million, but some chance that project Z will generate zero cash flow next year Without zero cash flow probability:

Analyzing Project Risk Allowing for possible bad outcomes Example If technological uncertainty introduces a 10% chance of zero cash flow, unbiased forecast could drop to $900,000 – with zero cash flow probability:

Analyzing Project Risk Best approach then: Make unbiased forecast of project’s cash flows (includes diversifiable and market risks) Consider whether diversified investors would regard the project as more or less risky than average project (only market risks relevant)

Certainty Equivalents Valuation with certainty equivalents Example – office development construction project Office building to be sold for $800,000 in one year Cash flow is uncertain, same risk as market, so  = 1 rf = 7%;  risk adjusted discount rate = 7+(1x5) = 12% THUS PV = 800,000 / 1.12 = $714,286 If potential customer offered to fix the price at which it will buy in a year, you would accept a lower payment than $800,000: PV = Certain cash flow / 1.07 = $714,286 THUS certain cash flow = $764,286

Certainty Equivalents Certainty equivalents to adjust for risk i.e. certain cash flow of $764,286 has same PV as expected but uncertain cash flow of $800,000 This cash flow of $764,286 is called the certainty-equivalent cash flow To compensate for delayed payoff and uncertainty in real estate prices, you need a return of $85,714: Compensation for time value of money Mark-down (haircut) to compensate for risk ($35,714)

Certainty Equivalents Certainty equivalents to adjust for risk

Certainty Equivalents For PV of cash flow at period 1: OR for cash flows two, three, or t years away:

Certainty Equivalents When to use a single risk-adjusted discount rate for long-lived assets Example Project A is expected to produce CF = $100m for each of three years. Given a risk free rate of 6%, a market risk premium of 8%, and project beta of 0.75, what is the PV of the project?

Certainty Equivalents Example Project A is expected to produce CF = $100m for each of three years. Given a risk free rate of 6%, a market risk premium of 8%, and beta of 0.75, what is the PV of the project?

Certainty Equivalents Example Project A is expected to produce CF = $100 m for each of three years. Given a risk free rate of 6%, a market premium of 8%, and beta of 0.75, what is the PV of the project? Compare with project B which has lower cash flows, but they are RISK FREE. What is the new PV?

Certainty Equivalents Example Project A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market premium of 8%, and beta of 0.75, what is the PV of the project? Compare with project B which has lower cash flows, but they are RISK FREE. What is the new PV? Since the 94.6 is risk free, we call it a Certainty Equivalent of the 100.

Certainty Equivalents The difference between the cash flow and the certainty equivalent cash flow is a deduction for risk: The difference between the 100 and the certainty equivalent (94.6) is 5.4 / 94.6 = 5.71% can be considered the annual premium on a risky cash flow

The Capital Investment Process Capital budget List of investment projects planned for the coming year Starting point for future investment outlays Project proposals can be bottom-up from plants to divisions to senior managers OR top-down, coming from senior management Need to establish consensus forecasts of economic indicators at outset Preparation of the capital budget is a process of negotiation, but final budget must reflect firm’s strategic planning

The Capital Investment Process Project authorizations and biased forecasts Once a capital budget has been approved by top management and the board, it becomes official plan BUT it is not the final sign-off for projects Most companies also require appropriation requests – detailed forecasts, discounted cash flow analyses, supporting information Companies set ceilings for authorising projects Many project forecasts are biased  people tend to be over-optimistic and understate project risks Increasing the project hurdle rate does not improve things: BMA law: The proportion of proposed projects having positive NPVs at the corporate hurdle rate is independent of the hurdle rate!

The Capital Investment Process Post-audits Conducted shortly after projects have begun to operate They: Identify problems that need fixing Check the accuracy of forecasts Suggest questions that should have been asked before the project was undertaken Their real use is helping managers to do a better job in the next round of investments

Sensitivity Analysis Sensitivity Analysis Analysis of the effects of individual changes in sales, costs, etc. on a project Scenario Analysis Project analysis given a particular combination of assumptions Simulation Analysis Estimation of the probabilities of different possible outcomes Break Even Analysis Analysis of the level of sales (or other variable) at which the company breaks even 6 39

Sensitivity Analysis Example Otobai Company is considering introducing an electrically powered motor scooter Cash flow forecasts are as follows with a 10% cost of capital:

Sensitivity Analysis At 10% opportunity cost of capital  go ahead with investment: Assumptions Marketing department has estimated revenue as follows: Unit sales = new product’s share of market x size of scooter market = 0.1 x 1 million = 100,000 scooters Revenue = unit sales x price per unit = 100,000 x 375,000 = ¥37.5 billion

Sensitivity Analysis Assumptions (cont.) Production department estimates that variable costs per unit = ¥300,000 Projected volume is 100,000 per year, thus total variable cost = ¥300,000 x 100,000 = ¥30 billion Fixed costs are ¥3 billion per year Initial investment can be depreciated on a straight line basis over 10 years Profits are taxed at 50% Sensitivity analysis Sensitivity analysis then conducted with respect to market size market share, etc. Ask marketing and production staff for optimistic and pessimistic estimates for key variables

Sensitivity Analysis Sensitivity analysis What happens to NPV if the variables are set one at a time to their optimistic and pessimistic values? Most dangerous variables: Market share Unit variable cost

Sensitivity Analysis Value of information Can you resolve some of the uncertainty before your company invests? Pessimistic value for UVC  production department is worried that a machine will not work as designed and the operation will have to be performed by more costly methods (extra cost of ¥20,000 per unit)  chance of this is 10% After-tax cash flow would be reduced in this event by: Unit sales x additional unit cost x (1 – tax rate) = 100,000 x 20,000 x 0.50 = ¥1 billion

Sensitivity Analysis Value of information NPV would be reduced by: Thus NPV of project = +3.43 – 6.14 = - ¥2.71 billion Perhaps a small design change could eliminate the need for the new machine OR a ¥10 million machine pre-test will reveal whether the machine will be ok (and enable resolution of problem): Invest ¥10 million to avoid 10% probability of ¥6.14 billion fall in NPV i.e. you are better off by -10 + (0.10 x 6,140) = +¥604 million!

Sensitivity Analysis Limits to sensitivity analysis 1. It always gives somewhat ambiguous results e.g. what does optimistic or pessimistic mean? We could be more precise: Only 10% chance of actual value being better than optimistic value Only 10% chance of actual value being worse than pessimistic value 2. Underlying values are likely to be inter-related e.g. if market size is bigger than expected: Demand will be stronger than expected Unit prices will be higher

Sensitivity Analysis Scenario analysis It might be useful to consider some alternative scenarios This allows us to look at different but consistent combinations of variables e.g. if possibility of sharp rise (20%) in oil prices:  Rise in demand for electric scooters THUS: market share by 3%  BUT also prompts worldwide recession and inflation THUS: Market size to 0.8 million scooters Prices and costs by 15% On balance, this helps the project  NPV increases to ¥6.4 billion

Sensitivity Analysis Scenario analysis

Sensitivity Analysis Break-even analysis How bad can sales get before the project begins to lose money? We can plot the PV of inflows and outflows for different sales Lines cross when project has a zero NPV  85,000 scooters In terms of accounting profits, break-even at 60,000 scooters:

Sensitivity Analysis Break-even analysis Point at which NPV=0 is break-even point Otobai Motors has a break-even point of 85,000 units sold

Sensitivity Analysis Break-even analysis When we deduct depreciation, revenues can cover the ¥15bn but are not enough to repay the opportunity cost of capital of the ¥15bn Break-even in accounting terms  negative NPV!

Real Options & Decision Trees Real options = options to modify projects: If things go well  expand project If things go badly  cut-back or abandon project Option to Expand In 2006 FedEx airfreight secured options to buy 15 aircraft at a predetermined price for delivery 2009-2011 “Decision Tree” Square = action or decision Circle = outcome revealed PVGO = “value of firm’s options to invest and expand”

Real Options & Decision Trees Option to Abandon Once a project is no longer profitable, company will cut losses and exercise option to abandon project Some assets are easier to bail out than others, particularly where there is a second-hand market BUT with some assets you have to pay to abandon them Example – outboard motors production Technology A – produces motors using specialist equipment, but worthless if abandoned Technology B – produces motors using standard equipment, worth $17 million if abandoned

Real Options & Decision Trees Option to Abandon Choose A if you have to continue regardless of outcomes BUT B provides an insurance policy Total value of project using technology B is its DCF value: Assuming that the company continues PLUS value of abandonment option

Option to Abandon

Real Options & Decision Trees Option to Abandon For technology B, the decisions are obvious: Continue if buoyant Abandon otherwise Payoffs to technology B: Buoyant  continue  payoff of $22.5m Sluggish  abandon  payoff of 1.5 + 17 = $18.5m

Real Options & Decision Trees Decision Trees - Diagram of sequential decisions and possible outcomes Decision trees help companies determine their options by showing the various choices and outcomes The option to avoid a loss or produce extra profit has value The ability to create an option thus has value that can be bought or sold 19 57

Real Options & Decision Trees   Production options

Real Options & Decision Trees Magna Charter example Plane charter company 40% chance that demand will be low in first year  THEN 60% chance it will remain low thereafter 60% chance that demand will be high in first year  THEN 80% chance it will remain high thereafter What kind of plane should company buy? 1. Turboprop (costs $550,000) Depreciates slowly 2. Piston-engine plane (costs $250,000) But less capacity, less customer appeal Rapid depreciation – could buy another (second hand) in a year for $150,000 Company’s plan: Start out with one piston plane and buy another if demand is still high

Magna Charter example Cash flows converted into certainty equivalent flows

Real Options & Decision Trees How do we work out the NPV of the two plane options? We need to start at RHS and work back: Next year, company needs to decide whether to expand if purchase of piston-engine is succeeded by high demand If company expands: it invests $150,000 and receives a payoff of $800,000 if demand is high and $100,000 if demand is low Expected payoff is: (Probability high demand x payoff with high demand) + (probability low demand x payoff with low demand) = (0.8 x 800) + (0.2 x 100) = $660,000 If discount rate is 10%: NPV = -150 + 660 / 1.10 = $450,000

Real Options & Decision Trees If company does not expand: Expected payoff is: (Probability high demand x payoff with high demand) + (probability low demand x payoff with low demand) = (0.8 x 410) + (0.2 x 180) = $364,000 If discount rate is 10%: NPV = 0 + 364 / 1.10 = $331,000

Real Options & Decision Trees When faced with expansion decision, we can then roll back to today’s decision If first piston-engine plane is bought, company can expect to receive $550,000 in year 1 if demand is high and $185,000 if it is low: High demand (0.6) $550,000 Invest $250,000 Low demand (0.4) $185,000 $100,000 cash flow plus $450,000 NPV $50,000 cash flow plus NPV of (0.4 x 220) + (0.6 x 100) -------------------------------- 1.10 =$135,000

Real Options & Decision Trees NPV of investment in piston-engine plane is therefore $117,000: NPV = -250 + (0.6 (550) +0.4 (185)) / 1.10 = $117,000 If company invests in the turboprop, no need to roll back: THUS piston-engine plane has NPV of £117,000 which is better!

READER Read the following sections in your own time: Operating leverage and break-even points Monte Carlo simulation Timing Options

Operating Leverage  

Monte Carlo Simulation Monte Carlo simulation = tool for considering all possible combinations Example – the electric scooter project: 1. Modelling the project Give computer precise model of project (equations of inter-relationships) 2. Specifying probabilities Determine expected value and forecast error 3. Simulate the cash flows Compute samples from distribution of forecast errors and calculate cash flows for each period 4. Calculate present value Distribution of project cash flows should enable you to calculate expected cash flows more accurately

Monte Carlo Simulation Simulation of cash flows for year 10 of the electric scooter project

Timing Options Timing options Example You own a timber forest To access it, you need to invest $75,000 in roads The investment’s value increases but at a decreasing rate:

Timing Options Timing options Work out NPV at each date at 10% cost of capital: Best time to harvest will be year 4  After year 4, growth in value < cost of capital In real world of uncertainty, it may be worth waiting to see if marginally positive NPV projects become more attractive