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Chapter 9. Risk And Capital Budgeting. Professor John Zietlow MBA 621. 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

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slide1

Chapter 9

Risk And Capital Budgeting

Professor John ZietlowMBA 621

chapter 9 overview
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
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
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
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
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
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
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
operating leverage for all leather and microfiber
Operating Leverage for All Leather and Microfiber

EBIT

All Leather

Microfiber

Sales

measuring financial leverage and its impact on firm s stock beta
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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 risk break even analysis
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
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
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
  • 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
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
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
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 cont34
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 cont35
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
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