Chapter 9Cost of Capital and Project Risk

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© 2007 Thomson South-Western

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Choosing the Right Discount Rate

Cost of equity Weighted cost of capital (WACC) The WACC and the CAPM Asset betas and project discount rates Equity risk premium

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Choosing the Right Discount Rate

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0

The numerator focuses on project cash flows, covered in chapter 8:

The denominator is the discount rate, the focus of chapter 9.

The denominator

should:

Reflect the opportunity costs of the firm’s investors.

Reflect the project’s risk.

Be derived from market data.

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A Simple Case

Firm is financed with 100% equity.

Project is similar to the firm’s existing assets.

Project discount rate is easy to determine if we assume :

In this case, the appropriate discount rate equals the cost of equity.

Cost of equity estimated using the CAPM

))(()( FmiFi RREβRRE

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Cost of Equity

Beta plays a central role in determining whether a firm’s cost of equity is high or low.

What factors influence a firm’s beta?

Operating leverage

The mix of fixed and variable costs

Sales

Sales

EBIT

EBITLeverageOperating

Financial Leverage

The extent to which a firm finances operations by borrowing

The fixed costs of repaying debt increase a firm’s beta in the same way that

operating leverage does.

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Cost of Equity

Operating leverage measures the tendency of the volatility of operating cash flows to increase with fixed operating costs.

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Cost of Equity

If a firm invests in only one industry, we can assume all its investments are equally risky.

When calculating the NPV of any project this firm might make, managers can use the required return on equity, often called the cost of equity, as the discount rate.

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Cost of Equity

Level of systematic risk varies from one industry to another, and so too should the discount rate used in capital budgeting analysis.

Other factors affect betas, and thus project discount rates. a firm’s cost structure: its mix of fixed

and variable costs. The greater the importance of fixed

costs in a firm’s overall cost structure, the more volatile will be its cash flows and the higher will be its stock beta.

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All Leather’s Cost of Equity

E(Re ) = Rf + (E(Rm) - Rf) = 10.5% 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%, expect the market risk premium will be 5%.

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All Leather Inc. and Microfiber Corp.

All Leather Inc Microfiber Corp

Sales volume 40,000 sofas 40,000 sofas

Price $950 $950

Total Revenue $38,000,000 $38,000,000

Fixed costs per year $10,000,000 $2,000,000

Variable costs per sofa

$600 $800

Total cost $34,000,000 $34,000,000

EBIT $4,000,000 $4,000,000

What if sales volume increases by 10% ?

44,000 sofas44,000 sofas

$41,800,000$41,800,000

$37,200,000$36,400,000

$4,600,000$5,400,000

The two firms are in the same industry

All Leather’s EBIT increases faster because it has high operating leverage.

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Financial Data for Carbonlite Inc. and Fiberspeed Corp.

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Operating Leverage for Carbonlite and Fiberspeed

Other things equal, higher operating leverage means that All Leather’s beta will be higher than Microfiber’s beta.

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The Effect of Leverage on Beta:

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Weighted Average Cost of Capital

WACC is the simple weighted average of the required rates of return on debt and equity, where the weights equal the percentage of each type of financing in the firm’s overall capital structure.

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Finding WACC for Firms with Complex Capital Structures

pde rPDE

Pr

PDE

Dr

PDE

EWACC

%73.12%85.211

5.12%7

5.211

49%15

5.211

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WACC

How do we calculate WACC if firm has long-term (D) debt as well as preferred (P) and common stock (E)?

An example....

Sherwin Co.Total value = 211.5 million

Has 10,000,000 common shares; price = $15/share; re = 15%.

Has 500,000 preferred shares, 8% coupon, price = $25/share, $12.5 million value.

Has $40 million long term debt, fixed rate notes with 8% coupon rate, but 7% YTM.

Notes sell at premium and worth $49 million.

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The Link between WACC to the CAPM

)( fMdfd RRRr

WACC consistent with CAPMCan use CAPM to compute WACC for levered firm.

Calculate beta for bonds of a large corporation:

First find covariance between bonds and stock market. Plug computed debt beta (d), Rf and Rm into CAPM to find rd.

Debt beta typically quite low for healthy, low-debt firms Debt beta rises with leverage.

Any asset that generates a cash flow has a beta, and that beta determines its required return as per CAPM.

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The Link Between the CAPM and the WACC

Any asset that generates cash flows has a beta that establishes the required return on the asset through the CAPM. WACC represents the rate of return that

a company must earn on its investments to satisfy both bondholders and stockholders

The CAPM establishes a direct link between required rates of return on debt and equity and the betas of these securities

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The Link Between the CAPM and the WACC

If the firm has zero debt, the asset beta equals the equity beta.

For firms that use debt, [1 (D/E)] > 1.0, which in turn means that E > A.

Holding the asset beta—the risk of the firm’s assets—constant, the more money the firm raises by issuing debt, the greater its financial leverage, and the higher its equity beta.

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Asset Betas and Project Discount Rates

When a firm uses no leverage, its equity beta equals its asset beta.

An unlevered beta simply tells us how risky the equity of a company might be if it used no leverage at all.

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Discount Rate for Unique Projects

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.

Use project’s asset beta adjusted for desired leverage.

• An example…– Assume GE is evaluating an investment in oil

and gas industry.– GE would examine existing firms that are pure

plays (public firms operating only in oil and industry).

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Data for Berry Petroleum and Forest Oil

0.550.56Asset beta *

0.640.16D/E ratio

0.610.86Fraction Equity

0.390.14Fraction Debt

0.900.65Stock beta

Forest OilBerry Petroleum

* Assumes debt beta = 0 and no taxes

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 Oil uses debt for 39% of financing; Berry Petroleum: 14%.

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Converting Equity Betas to Asset Betas for Two Pure Play Firms

69.025.0155.01

E

DAGE

To determine correct A to use as discount rate for the 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 when taxes are zero)

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:

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Converting Equity Betas to Asset Betas for Two Pure Play Firms

%96.9%)20%(5.6%)80%(83.10

de r

ED

Dr

ED

EWACC

One more step to find the right discount rate for GE’s investment in this industry: calculate project

WACC.

Using CAPM, compute rate of return GE shareholders require for the oil and gas investment.

• Assume risk-free rate of interest is 6% and expected risk premium on the market is 7%:

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

GE’s financing is 80% equity and 20% debt. Assume investors expect 6.5% on GE’s bonds:

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Accounting for Taxes

Tax deductibility of interest payments favors use of debt. Accounting for interest tax shields yields after-tax WACC.

ed rED

ErT

ED

DWACC

)1(

After-tax formula for equity beta changes to: We are still assuming debt beta = 0.

E

DTUE )1(1

βU is the beta of an unlevered firm.

Analogous to asset beta, but not strictly equal to βA due to taxes

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Finding the Right Discount Rate

1. 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.

2. When a firm with both debt and equity invests in an asset similar to its existing assets, the WACC is the appropriate discount rate to use in NPV calculations.

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Finding the Right Discount Rate

3. In conglomerates, the WACC reflects the return that the firm must earn on average across all its assets to satisfy investors, but using the WACC to discount cash flows of a particular investment leads to mistakes.

4. When a firm invests in an asset that is different from its existing assets, it should look for pure-play firms to find the right discount rate.

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Finding the Right Discount Rate

The opportunity to deduct interest payments reduces the after-tax cost of debt and changes the relationship between asset betas and equity betas

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Measuring the Expected Risk Premium on the Market Portfolio

Earnings yield (E/P), or the reciprocal of the price-to-earnings ratios

The dividend growth modelConsensus of academic experts

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Break-even Analysis

Managers often want to assess business’ value drivers:

Useful to assessing operating risk is finding break-even point.

Break-even point is level of output where all operating costs (fixed and variable) are

covered.

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Break-even Analysis Example: Carbonlite

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Break-even Analysis Example: Fiberspeed

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Sensitivity Analysis

Firms establish a “base-case” set of assumptions for a particular project and calculate the NPV based on those assumptions.

Managers allow one variable to change while holding all others fixed, and they recalculate the NPV based on that change.

Repeating this process for all the uncertain variables in an NPV calculation, allows managers to see how sensitive the NPV is to changes in baseline assumptions.

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Sensitivity Analysis of DVD Project

NPV Pessimistic Assumption Optimistic NPV

-$448,315 $43,000,000 Initial investment $39,000,000 +2,727,745

-$1,106,574

2,800,000 un Market size in year 1 3,200,000 un +3,386,004

-$640,727 2% per year Growth in market size 8% per year +3,021,884

-$4,602,832

8% Initial market share 12% +6,882,262

-$3,841,884

Zero Growth in market share

2% per year +6,121,315

-$2,229,718

$90 Initial selling price $110 +4,509,149

-$545,002 62% of sales Variable costs 58% of sales +2,824,432

-$2,064,260

-10% per yr Annual price change 0% per year +4,688,951

-$899,413 16% Discount rate 12% +3,348,720

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!

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Scenario Analysis

A more complex variation on sensitivity analysis

Rather than adjust one assumption up or down, analysts conduct scenario analysis by calculating the project NPV when a whole set of assumptions changes in a particular way.

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Monte Carlo Simulation

A more sophisticated variation of the scenario analysis is Monte Carlo simulation.

In a Monte Carlo simulation, analysts specify a range or a distribution of potential outcomes for each of the model’s assumptions.

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Misuse of Simulation Analysis

Most common misuse involves the calculation and misinterpretation of a distribution of project NPVs using the cost of capital Plotting an entire distribution of NPVs and

looking at the mean and variance of that distribution is, in a sense, double counting risk

Better approach is to calculate NPVs using the risk-free rate

Interpreting a distribution of NPVs calculated using the risk-free rate has its own problems.

Be wary of distributions of NPVs produced by a simulation program.

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Decision Trees

Decision tree: a visual representation of the choices that managers face over time with regard to a particular investment.

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Example: Decision Tree for Odessa Investment

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Real Options

A real option is the right, but not the obligation, to take a future action that changes an investment’s value.

Does not always agree with the NPV methodNPV may understate or overstate a

project’s value

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Real Options in Capital Budgeting

Embedded options arise naturally from investment;

Called real options to distinguish from financial options.

Option pricing analysis helpful in examining multi-stage projects

Can transform negative NPV projects into positive NPV!

Value of a project equals value captured by NPV, plus option.

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Types of Real Options: Expansion Options

The risk of expanding an already successful project is much less than the risk when the project first begins.

An NPV calculation misses both of these attributes—the opportunity to expand or not depending on initial success, and the change in risk that occurs when the initial outcome is favorable.

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Types of Real Options: Abandonment Options

In an extreme case, a firm may decide to withdraw its entire commitment to a particular project and exercise its option to abandon.

If a firm cannot generate cash flow sufficient to pay back its debts, shareholders can declare bankruptcy and turn over the company’s assets to lenders and walk away.

Share value =NPV + value of default option

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Types of Real Options: Follow-on Investment Options

Follow-on option similar to an expansion option: entitles a firm to make additional investments should earlier investments prove to be successful. The difference between this and the

expansion option is that the subsequent investments are more complex than a simple expansion of the earlier ones.

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Types of Real Options: Flexibility Options

Input flexibility - ability to use multiple production inputs creates option value

Output /operating flexibility - creates value when output prices are volatile

Capacity flexibility - maintaining excess production capacity that managers can utilize quickly to meet peaks in demand. Costly to purchase and maintain, but valuable

in capital-intensive industries subject to wide swings in demand and long lead times for building new capacity

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Link between Risk and Real Option Values

Generally, valuation problem covered in this text satisfies the following statement:Holding other factors constant, an

increase in an asset’s risk decreases its price.

This relationship does not hold for options.

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Link between Risk and Real Option Values

Oil extraction example:The current price of oil is $45 per

barrel, extraction costs at the site are $50. The expected future price of oil is the same as the current price, so an NPV calculation would say that this investment is worthless. Consider two different scenarios regarding the future price of oil.

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Link between Risk and Real Option Values

Oil extraction example:Low risk scenario, the price of oil in

the future will be $49 or $41, each with probability of one-half. This means the expected price of oil is

still $45.But both an NPV and an options analysis

would conclude that bidding on the rights to this site is not a good idea because the price of oil will never be above the extraction cost.

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Link between Risk and Real Option Values

High-risk scenario: The price of oil may be $60 or $30 with equal probability, so again we have an expected price of $45. If the price turns out to be $30, extracting

the oil does not make sense. If the price turns out to be $60, extracting

oil generates a profit of $10 per barrel. Therefore, a real options analysis would

say that bidding at least a little for the right to extract the oil is a sensible decision.

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Link between Risk and Real Option Values

Why does more risk lead to higher option values?

As the payoffs on the upside increase, the higher goes the price of oil. In other words, options are characterized by asymmetric payoffs. When the price of oil is extremely volatile,

the potential benefits if prices rise are quite large.

At the same time, if oil prices fall precipitously, there is no additional cost relative to a slight decline in prices.

In either case, the payoff is zero.

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Strategy and Capital Budgeting

In a perfectly competitive market, there are many buyers and sellers trading a homogeneous product or service.

Everyone behaves as a price taker. Competition and the lack of entry or exit

barriers for sellers ensures that the product’s market price equals the marginal cost of producing it, and no firm earns pure economic profit.

In a market with zero economic profits, the NPV of any investment equals zero because every project earns just enough to recover the cost of capital: no more and no less.

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Strategy and Capital Budgeting

If we want to know whether or not an investment proposal should have a positive NPV, we must identify ways in which the project deviates from the perfectly competitive ideal.

Barrier to entryCompetitive advantage

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Strategic Thinking and Real Options

Managers must articulate strategy for a given investment

Series of “if-then” statements has intangible value in that it forces managers to think through their strategic options before they invest.

Identifying a real option is tantamount to identifying future points at which it may be possible for managers to create and sustain competitive advantages.