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## Risk And Capital Budgeting

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Chapter 9: Overview

- 9.1 Choosing the Right Discount Rate
- The cost of equity
- The weighted average cost of capital (WACC)
- Connecting WACC to the CAPM
- Asset betas and project discount rates
- 9.2 A Closer Look at Risk
- Breakeven analysis
- Sensitivity analysis
- Scenario analysis and Monte Carlo simulation
- Decision trees

Chapter 9: Overview (Continued)

- 9.3 Real Options
- Why NPV doesn’t always give the right answer
- Types of real options
- Expansion options
- Abandonment options
- Follow-on investment options
- The surprising link between risk and real option values
- 9.4 Strategy and Capital Budgeting
- Competition and NPV
- Strategic thinking and real options
- 9.5 Summary

Choosing the Right Discount Rate

- To calculate an NPV, an analyst must evaluate project’s risk
- Often, the best place to look for clues is a firm’s securities
- What discount rate should managers use in cap budgeting?
- Rate should reflect opportunity cost of all firm’s investors
- Rate should also reflect the risk of the specific project
- To find discount rate, start with simplifying assumptions:
- Assume all equity financing, so only have to satisfy S/Hs
- Assume firm makes all investments in a single industry
- These allow firm to use cost of equity as discount rate
- Know from chapter 6 that cost of equity found with CAPM

(Eq 9.1)

Determining All Leather’s Cost of Equity

- All Leather Inc., an all-equity firm, is evaluating a proposal to build a new manufacturing facility
- Firm produces leather sofas
- As a luxury good producer, firm very sensitive to economy
- All Leather’s stock has a beta of 1.3
- Managers note Rf = 4%, believe market’s return will be 9%
- Can use CAPM to find All Leather’s cost of equity

E(Re ) = Rf + (E(Rm) - Rf) = 4% + 1.3 (9% - 4%) =10.5% cost of equity

- All Leather beta is 1.3 due partly to high economic sensitivity
- Higher risk must be reflected in discount rate used to evaluate new manufacturing facility
- Low beta company (food processor) would use lower rate

Finding All Leather’s Cost of Equity (Cont)

- Other factors, besides economic sensitivity, impact beta
- A firm’s cost structure & production process very important
- Mix of variable & fixed costs determines operating leverage
- OL implies CF volatility will rise with fixed cost
- Substituting fixed for variable cost increases profits more than proportionally when sales increase, but hurt if sales fall
- Define degree of operating leverage (DOL) as % in EBIT divided by % in sales
- High DOL: small change in sales large change in EBIT

(Eq 9.2)

- Table on next slide details All Leather’s & competitor’s costs & prices
- Microfiber also produces sofas, but less fixed costs

Financial Data for All Leather Inc. and Microfiber Corp.

- Suppose both firms achieve 10% rise in sales volume to 44,000 sofas
- next year, holding all other figures constant. Fixed cost don’t change.
- Both firms’ revenues go from $38,000,000 to $41,800,000; a 10% rise
- All Leather’s total costs increase by $600/sofa, or $2,400,000 total
- Microfiber’s total costs increase by $800/sofa, or $3,200,000 total
- All Leather’s EBIT increases by $350/sofa, $1,400,000 total
- Microfiber’s EBIT increases by $150/sofa, $600,000 total

Calculating Operating Leverage for All Leather and Microfiber

- Using data from previous table, can compute OL for both firms
- Note key terms: EBIT= contribution margin - fixed costs
- Contribution margin = gross profit per unit of sales
- Gross profit = price per unit - variable cost per unit

DOLAll Leather =

DOLMicrofiber =

- All Leather has a degree of operating leverage (DOL) of 3.5
- EBIT increases by 35% if sales increase by 10%
- Microfiber has lower DOL of 1.5 due to lower fixed costs
- EBIT increases by only 15% if sales increase by 10%
- But firm would weather sales decline better than All Leather

Measuring Financial Leverage and its Impact on Firm’s Stock Beta

- Operating leverage: using fixed cost assets to magnify (leverage) impact of change in sales on change in EBIT
- Increasing OL yields increasing stock beta
- Firms also use fixed cost financing (debt & PS) to magnify effect of given change in EBIT on net income
- Measured as degree of financial leverage (DFL)

- If sales and EBIT increase, FL will yield magnified rise in NI
- But also works on downside; if sales & EBIT fall, so will NI
- FL increases expected net profits, but also increases risk
- Thus use of FL also increases a firm’s stock beta

Measuring Financial Leverage (Cont.)

- Demonstrate FL with firms on next table; same except financing
- Firm 1: 100% equity, Firm 2: 60% equity, 40% debt
- Cost of Firm 2’s debt = 8.5%; assume neither firm pays tax
- Both firms have $250mn assets, identical production process
- Case #1: Assume both firms generate 25% gross return on assets, or $62.5mn EBIT, and both pay out net income to S/H
- Firm 1 pays no interest, so $62.5 mn paid to S/Hs; 25% ROE
- Firm 2 pays $8.5mn int, so $54mn paid to S/Hs; 36% ROE
- Case #2: Assume both firms generate 5% gross return on assets, $12.5mn EBIT; again both pay out net income to S/H
- Firm 1 pays no interest, so $12.5 mn paid to S/Hs; 5% ROE
- Firm 2 pays $8.5mn int, so only $4mn paid to S/Hs; 2.7% ROE
- If EBIT high, FL increases ROE; decreases ROE if EBIT low

The Weighted Average Cost of Capital (WACC)

- Cost of equity the right discount rate for all-equity firm
- But what if firm has both debt and equity?
- Problem akin to finding expected return of portfolio
- Use weighted avg cost of capital (WACC) as discount rate
- Let D and E represent market values of debt & equity
- Demonstrate using Comfy Inc’s capital structure
- Comfy Inc builds residential houses
- Firm has $150mn equity (E), with cost of equity re= 12.5%
- Also has bonds (D) worth $50mn O/S, with rd = 6.5%
- Calculate WACC = 11%

Finding the WACC (Cont)

- How can Comfy’s managers be sure WACC = 11%?
- First way: assume wealthy investor purchases all firm’s debt and equity. This is return he/she would earn
- Second way: Suppose firm invests in a project earning 11% and distributes return to investors. Will they be satisfied?
- Following table shows CF generated & distributed satisfies claims

Finding WACC for Firms with Complex Capital Structures

- How to calculate WACC if firm has long-term (LT) debt as well as preferred (P) & common stock (E)?
- Find weighted average of individual capital costs

- Assume S.N. Sherwin Co. wants to determine its WACC
- Has 10,000,000 common shares O/S; price = $15/sh; rc = 15%
- Has $40mn L-T, fixed rate notes with 8% coupon rate, but 7% YTM; notes sell at premium and worth $49mn
- Has 500,000 pref shrs, 8% coupon, $75price, $12.5mn value
- Total value = $150m E+ $49m LT+$12.5m P =$211.5m

Connecting the WACC to the CAPM

- Developed separately, but WACC consistent with CAPM
- Have so far looked only at all-equity firm
- But can use CAPM to compute WACC for levered firm
- Calculate beta for bonds of a large corporation
- First find covariance between bonds & stock market, then
- Plug computed debt beta (d),Rf & Rm into CAPM to find rd
- Debt beta typically quite low for healthy, low-debt firms
- Debt beta rises with leverage, approaches equity beta in B/R

- Example shows CAPM can be used for any security
- Any asset that generates a CF has a beta, and that beta determines its required return as per CAPM

Calculating Asset Betas and Equity Betas

- The CAPM establishes direct link between required return on D & E and betas of these securities
- Beta of firm’s assets equals weighted avg of D & E betas

(Eq 9.4)

- A firm’s asset beta thus equals the cov of firm’s CFs with RM, return on market p/f, divided by var of market’s return
- For all-equity firm, asset beta = equity beta
- For levered firm, asset beta will be less than equity beta
- If asset beta known, anddebt beta is assumed to be 0, can compute equity beta directly from A

(Eq 9.5)

Finding Equity Betas from Asset Betas, and Vice Versa

- If market values of D & E known, and any two of the three betas are known, can compute the other beta
- Usually assume debt beta known (say d = 0.15)
- Assume firm has manufacturing assets with asset beta = 1.2
- If firm unlevered, equity beta equals asset beta, E = A =1.2
- Now suppose firm decides to raise 20% of funding needs by issuing relatively safe bonds (d = 0.15) & retiring equity
- Use Eq 9.4 to find E, given A = 1.2 and d = 0.15

Finding Equity Betas from Asset Betas, and Vice Versa (Cont)

- Can only use Eq 9.5 if debt beta assumed = 0
- Since debt = 20% of capital and equity = 80%, the debt-to-equity ratio D/E = 0.2 ÷ 0.8 = 0.25
- Not surprisingly, equity beta is higher if debt beta assumed 0

- Can now state decision rule for determining discount rate to use for projects with asset betas similar to firm’s own
- For all equity firm, use cost of equity given by CAPM
- For levered firm, use WACC computed using CAPM and betas of individual capital components
- If a project’s asset beta differs from firm’s asset beta, must compute and use project betas

Finding the Discount Rate to Use for Projects Unrelated to Firm’s Industry

- What if a company has diversified investments in many industries?
- In this case, using firm’s WACC to evaluate an individual project would be inappropriate
- Instead use project’s asset beta adjusted for desired leverage
- Assume GE evaluating an investment in oil & gas industry
- Much different from any of GE’s existing businesses
- Instead GE would examine existing firms that are pure plays
- These are public firms operating only in O&G industry
- Say GE selects Berry Petroleum & Forest Oil as pure plays
- Operationally similar firms, but Berry Petroleum’s E = 0.65 and Forest Oil’s E = 0.90; why so different?
- Reason: Forest uses debt for 39% of financing; Berry: 14%
- Even if core business the same risk (A equal), E will differ

Data for Berry Petroleum and Forest Oil

- Computed using Eq 9.4 and assuming debt beta = 0
- Berry Petrol: A = (%D)d + (%E)E = (0.14)(0) + (0.86)(0.65) = 0.56
- Forest Oil: A = (%D)d + (%E)E = (0.39)(0) + (0.61)(0.90) = 0.55

Converting Equity Betas to Asset Betas for Two Pure Play Firms

- To determine correct A to use as discount rate for O&G project, GE must convert pure play E to A, then average
- Previous table lists data needed to compute unlevered equity beta
- Unlevered equity beta (same as A) strips out effect of financial leverage, so always less than or equal to equity beta
- Berry’s A = 0.56, Forest’s A = 0.55, so average A = 0.55
- GE capital structure consists of 20% debt and 80% equity (D/E ratio = 0.25). Compute relevered equity beta:

Converting Equity Betas to Asset Betas for Two Pure Play Firms (Continued)

- Assume risk-free rate of interest is 6% and expected risk premium on the market is 7%
- Using CAPM equation, compute rate of return GE shareholders require for the oil and gas investment

E(R) = 6% + 0.69(7%) = 10.83%

- One more step to find the right discount rate for GE’s investment in this industry – calculate project WACC
- GE’s financing is 80% equity and 20% debt. Assume investors expect 6.5% on GE’s bonds

Summarizing Rules for Selecting an Appropriate Project Discount Rate

- When an all equity firm invests in an asset similar to its existing assets, the cost of equity is the appropriate discount rate to use in NPV calculations.
- When a levered firm invests in an asset similar to its existing assets, the WACC is the right discount rate.
- When a firm invests in an asset that is different than its existing assets, it should look for pure play firms to find the right discount rate.
- Firms can calculate an industry asset beta by unlevering the betas of pure play firms
- Given the industry asset beta, firms can determine an appropriate discount rate using the CAPM

Accounting for Taxes in Finding WACC

- Have thus far assumed away taxes, but often important
- Tax deductibility of interest payments favors use of debt
- Accounting for interest tax shields yields after-tax WACC

(Eq 9.6)

- Can likewise present method of computing after-tax equity beta from asset beta
- Again assuming debt beta = 0, equity beta given by eq below
- Accounting for taxes doesn’t change key lessons above

(Eq 9.7)

A Closer Look at RiskBreak-Even Analysis

- Managers often want to assess business’ key value drivers
- Key to assessing operating risk is finding break-even point
- Break-even point (BEP) is level of output where all operating costs (fixed and variable) are covered
- BEP found by dividing FC by contribution margin (CM)

- Use this to find BEP for All Leather & Microfiber
- All Leather: FC = $10,000,000; Pr = $950/un; VC = $600/un
- Microfiber: FC = $2,000,000; Pr = $950/un; VC = $800/un

Break-Even Point for All Leather

Costs &

Revenues

Total revenue

Total costs

$10,000,000

Fixed costs

28,572 units

Units

All Leather has high fixed costs ($10,000,000), but also high contribution

margin ($350/sofa). High BEP, but once FC covered, profits grow rapidly.

Break-Even Point for Microfiber

Costs &

Revenues

Total revenue

Total costs

Fixed costs

$2,000,000

13,334 units

Units

Microfiber has low fixed costs ($2,000,000), but also low contribution

margin ($150/sofa). Low BEP, but profits grow slowly after FC covered.

Sensitivity Analysis

- Sensitivity analysis allows mangers to test importance of each assumption underlying a forecast
- Test deviations from “base case” and associated NPV
- Best Electronics Inc (BEI) has new DVD players project. Base case assumptions (below) yields Exp NPV = $1,139,715
- 1. The project’s life is five years.
- 2. The project requires an up-front investment of $41 million.
- 3. BEI will depreciate initial investment on S-L basis for five years
- 4. One year from now, DVD industry will sell 3,000,000 units
- 5. Total industry unit volume will increase by 5% per year.
- 6. BEI expects to capture 10% of the market in the first year
- 7. BEI expects to increase its market share one percentage point

each year after year one.

- 8. The selling price will be $100 in year one.
- 9. Selling price will decline by 5% per year after year one.
- 10. Variable production costs will equal 60% of the selling price.
- 11. The appropriate discount rate is 14 percent.

Sensitivity Analysis of DVD Project

If all optimistic scenarios play out, project’s NPV rises to $37,635,010.

If all pessimistic scenarios play out, project’s NPV falls to -$19,271,270!

Using Decision Trees to Make Multi-Step Investment Decisions

- Many real investment projects are conditional & multi-stage: will only proceed to stage 2 if stage 1 successful
- Occurs frequently with new product introductions
- Begin selling in test market; if successful, build factory for full-scale production & nationwide roll-out
- Very hard to evaluate in standard cap budgeting framework
- Decision trees allow managers to break investment analysis into distinct phases
- Forces managers to perform extended “if--then” analysis
- Assume Trinkle Foods (Canada) has invented new salt substitute, Odessa; assessing market testing in Vancouver
- Market test will cost C$5 million, but no new facilities needed
- If test successful, Trinkle will spend additional C$50mn to build factory and launch nationwide one year later

Using Decision Trees (Cont)

- If market test successful, Trinkle predicts full product launch will generate +C$12mn NCF per year for 10 years
- If test unsuccessful, expect full product launch to generate only +C$2 mn NCF per year for 10 years.
- If Trinkle’s WACC=15% should Trinkle invest? If so, in what?
- Next figure shows decision tree for investment problem
- Initially, firm can choose to spend C$5 mn on market test
- If market test executed, expect probability of success = 0.5
- Proper way to use tree: begin at end & work backwards
- Suppose in one year, Trinkle learns test is successful.
- At that point, the NPV of launching the product is:

- Clearly, Trinkle would invest if it winds up on this branch

Using Decision Trees (Cont)

- But what if the initial tests are unfavorable?
- In that case, project’s NPV equals -C$39.96 mn & firm should walk away--not fund nationwide roll-out.
- Note that C$5 mn test market cost is a sunk cost at t=1, so the NPV of doing nothing at time one is zero

- Now have set of simple “if--then” decision rules from tree
- If test successful, launch nationwide and NPV = C$10.23 mn
- If test unsuccessful, don’t invest C$50 mn for national launch

Using Decision Trees (Cont)

- Now must decide (at t=0) whether to spend C$5 mn for test
- Must realize NPVs computed at t=1 and use prob (success)

- Seems unwise to invest in market test
- But very sensitive to discounting future CF at 15% rate
- Since test results known t=1, may use lower rate afterwards

Real Options in Capital Budgeting

- Though decision trees helpful in examining multi-stage projects, most promising method is option pricing analysis
- Imbedded options arise naturally from investment
- Called real options to distinguish from financial options
- Options are valuable rights, not obligations
- Can transform negative NPV projects into positive NPV
- Value of a project equals value captured by NPV, plus option
- Several types of real options frequently encountered:

1. Expansion options: If a product is a hit, expand production

2. Abandonment options: Can abandon a project if not successful; S/Hs have valuable option to default on debt

3. Follow-on investment options: Similar to expansion options, but more complex (Ex: movie rights to sequel)

4. Flexibility options: Ability to use multiple production inputs (Ex: dual-fuel industrial boiler) or produce multiple ouputs

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