Risk And Capital Budgeting

Professor ThomsonFin 3013

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Creating Value: Choosing the Right Discount Rate

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The numerator, that is, the project cash flows, were the focus last chapter.

This chapter we focus on the discount rate.

The denominato

r should:

Reflect opportunity costs to firm’s investors

Reflect the project’s risk

Be derived from market data

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A Simple Case: Look for similar risk

Firm is financed with 100% equity

Project risk is similar to the firm’s existing asset

risk

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

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Another simple case (less likely)• The project has no systematic risk• Theory says use the risk free rate

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Carbonlite Inc. Cost of Equity

E(Rc ) = Rf + c (E(Rm) - Rf) = 5% + 1.5(11%-5%)= 14% cost of equity

Carbonlite Inc., an all-equity firm, is evaluating a proposal to build a new manufacturing

facility.

• Firm manufactures bicycle frames.• As a luxury good producer, firm is very

sensitive to economy (product demand is elastic).

• Carbonlite’s stock has a beta of 1.5 (Does it make sense for beta of this stock to be high?)

• Managers note Rf = 5%, expect the market return will be 11%.

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Leverage

• LeverOld French levier, the agent noun to lever "to raise", c. f. levant) is a rigid object that is used with an appropriate fulcrum or pivot point to multiply the mechanical force that can be applied to another object.

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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.

Beta measures sensitivity to the market

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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Carbonlite Inc Fiberspeed Corp

Sales volume 10,000 sofas 10,000 sofas

Price $1,000 $1,000

Total Revenue $10,000,000 $10,000,000

Fixed costs per year $5,000,000 $2,000,000

Variable costs this year

$4,0000,000 $7,000,000

Total cost $9,000,000 $9,000,000

EBIT $1,000,000 $1,000,000

Carbonlite Inc. ($400 Variable Cost per

frame ) vs. Fiberspeed Corp. ($700 VC per frame)

What if sales volume increases by 10% ?

10,000 frames10,000 frames

$10,000,000$10,000,000

$9,000,000$9,000,000

$1,000,000$1,000,000

The two firms are in the same industry.

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

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Carbonlite Inc Fiberspeed Corp

Sales volume 10,000 sofas 10,000 sofas

Price $1,000 $1,000

Total Revenue $10,000,000 $10,000,000

Fixed costs per year $5,000,000 $2,000,000

Variable costs this year

$4,4000,000 $7,700,000

Total cost $9,000,000 $9,000,000

EBIT $1,000,000 $1,000,000

Carbonlite Inc. ($400 Variable Cost per

frame ) vs. Fiberspeed Corp. ($700 VC per frame)

EBIT for Carbonlite is up 60%, while its up only 30% for Fiberspeed

What if sales volume decreases by 20% (from Base) ?

11,000 frames11,000 frames

$11,000,000$11,000,000

$9,700,000$9,400,000

$1,300,000$1,600,000

With 10% higher sales

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Carbonlite Inc Fiberspeed Corp

Sales volume 10,000 sofas 10,000 sofas

Price $1,000 $1,000

Total Revenue $10,000,000 $10,000,000

Fixed costs per year $5,000,000 $2,000,000

Variable costs this year

$3,200,000 $5,600,000

Total cost $9,000,000 $9,000,000

EBIT $1,000,000 $1,000,000

Carbonlite Inc. ($400 Variable Cost per

frame ) vs. Fiberspeed Corp. ($700 VC per frame)

EBIT for Carbonlite is down -120%, while its down only -60% for Fiberspeed

Conclusion: Lower operating risk leads to lower financial risk

8,000 frames8,000 frames

$8,000,000$8,000,000

$7,600,000$8,200,000

$400,000$ -200,000

With 20% Lower sales

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Operating Leverage for Carbonlite and Fiberspeed

Fiberspeed

Carbonlite 

EBIT

Sales

Other things equal, higher operating leverage means that Carbonlite’s beta will be higher

than Fiberspeed’s beta.

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The Effect of Financial Leverage on Beta

Firm NoLever Firm LeverAssets $100 million $100 millionDebt $0 $50 millionEquity $100 million $50 millionCase #1: Gross Return on Assets Equals 20 Percent (Great Year)

EBIT $20 million $20 millionInterest $0 $4 millionCash to equity $20 million $16 millionROE 20 ÷ 100 = 20% 16 ÷ 50 = 32%

Case #2: Gross Return on Assets Equals 5 Percent (Poor Year)EBIT $5 million $5 millionInterest $0 $4 millionCash to equity $5 million $1 millionROE 5 ÷ 100 = 5% 1 ÷ 50 = 2%

Financial leverage makes Firm Lever’s ROE more volatile, so its beta will be higher .

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Conclusion – Firm’s decisions determine the risk of the firm

• Firms create higher market risk (along with higher expected returns) as they employ more– Operating leverage (e.g. use fixed cost

capital rather than variable cost labor)– Financial leverage (use fixed cost debt,

rather than variable return equity)

• Either action will reveal itself in a higher beta; thus, firms in the same industry can have quite different Beta’s

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The WACC – Weighted Average Cost of Capital

• It is common for firms to use debt and preferred as well as equity to finance itself (using debt increases financial leverage).

• The firms financing can be see as a portfolio, with the overall return on a firm being the weighted average of the components

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Review: Return on a Portfolio• E(Rp) = w1E(R1) + w2E(R2) + w3E(R3)

• WACC = wErE) + wFrF + wDrD(1-Tc)

Where:wE = capital structure weight in Equity

wF = capital structure weight in PreFerred

wD = capital structure weight in Debt

rE = cost of Equity capital

rF = cost of PreFerred capital

rD = pretax cost of Debt capital

TC = marginal corporate tax rate

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Cost of Equity (market evidence)• We know from the Dividend Discount

Model (DDM, Chapter 5) that:P0 = D1/(R-g)

– Where R = the appropriate discount rate to use in discounting the firm’s future dividends

– This rate, R, varies with the systematic risk of the company

• If we know, (or can estimate) D1, g, and P0) then we can compute rE = D1/P0 + g

• The is one way to measure RE = cost of equity

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Cost of Equity (Alternate market based approach)

• We know from the CAPM (Chapter 8) that:

E(Ri) = Rf + i[E(Rm) – Rf]

• E(Ri) can also be seen as an estimate of the cost of equity (i.e. a measure of rE)

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Cost of Debt (market price)

• From Chapter 6, we learned to compute the YTM of a bond. The YTM is what the market requires for a return on that bond; therefore, if a firm issue new bonds it will have to pay this rate

• Interest paid to bond holders is a business expense and is tax deductible

• The after tax cost of bonds is the pre tax cost less the tax effect

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Cost of Debt

• Define: rD = cost of debt (which = YTM)

• The the after tax cost of debt is:= rD(1-TC)

• Where TC = corporate tax rate

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The Weighted Average Cost of Capital (WACC)

Use weighted average cost of capital (WACC) as discount rate.

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DWACC

• Lox-in-a-Box is a chain of fast food stores.• Firm has $100 million equity (E), with cost of equity re =

15%;• Also has bonds (D) worth $50 million, with rd = 9%.• Assume that the investment considered will not change

the cost structure or financial structure.

• If a firm uses financial leverage, and if the project under consideration represents the average market risk of the firm we:

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Example 10.1 WACC for Noble’s Best Doughnuts

• Noble’s Best Doughnuts has a beta of 0.7. Treasury bills are yielding 3% and the market risk premium is 7%. It has 1,000,000 shares outstanding that are trading at $35 per share. It has 20,000 outstanding bonds trading at 120% of par (7% coupon with 15 years until maturity). It also has issued 25,000 shares of preferred that have an annual dividend of $8.00, and are trading for $125. What is the WACC for Noble given its 30% tax rate?

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Rules for Selecting an Appropriate Project Discount RateCost of equity is the appropriate discount

rate for an all-equity firm undertaking projects of average systematic risk for that

firmWhen a levered firm invests in a project

similar to its existing projects, the WACC is the right discount rate. (The market beta

for the stock takes into account the leverage for the firm

When a firm invests in a project different than its existing projects, using the WACC

may lead to wrong investment choices.If Google decides to go into the Doughnut

business, it should check the WACC of Krispy Kreme for a market justified discount

rate.

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A Closer Look at RiskBreak-Even Analysis

Managers often want to assess business’ value drivers.

Finding the break-even point is often useful for assessing operating risk.

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

are covered.

Cost/unit VariablePrice/unitCosts Fixed

marginonContributiCostsFixed

BEP

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Break-Even Point for Carbonlite

$5,000,000

Total revenue

Total costs

Fixed costs

Units8,333 units

Costs &Revenues

Carbonlite has high fixed costs ($5,000,000), but also high contribution margin ($600/bike). High BEP, but once FC covered, profits grow rapidly.

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Break-Even Point for Fiberspeed

$2,000,000

Total revenue

Total costs

Fixed costs

Units6,667 units

Costs &Revenues

Fiberspeed has low fixed costs ($2,000,000), but also low contribution margin ($300/bike). Low BEP, but

profits grow slowly after FC covered.

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Sensitivity Analysis

Sensitivity analysis allows mangers to test importance of each assumption underlying a

forecast.

• Test deviations from “base case” and associated NPV

GTI has developed a new skateboard. Base case assumptions yield NPV = $236,000.

1.   The project’s life is five years.2.   The project requires an up-front

investment of $7 million.

3.   GTI will depreciate initial investment on straight line basis for five years.

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Sensitivity Analysis4.   One year from now, the skateboard industry

will sell 500,000 units.5.   Total industry unit volume will increase by

5% per year.6.   BEI expects to capture 5% 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 $200 in year one9.   Selling price will decline by 10% per year

after year one.10. Variable production costs will equal 60% of

the selling price.11. The appropriate discount rate is 14

percent.

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Sensitivity Analysis of Skateboard Project

NPV Pessimistic Assumption Optimistic NPV

-$558 $8,000,000 Initial investment $6,000,000 $1,030

-343 450,000 units

Market size in year 1 550,000 units 815

-73 2% per year Growth in market size 8% per year 563

-1,512 3% Initial market share 7% 1,984

-1,189 0% Growth in market share

2% per year 1,661

-488 $175 Initial selling price $225 960

-54 62% of sales Variable costs 58% of sales 526

-873 -20% per year

Annual price change 0% per year 1,612

-115 16% Discount rate 12% 617

Dollar values in thousands except price

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Management Science Approach• One could do a type of computer

generated sensitivity analysis where each variable of interest can be randomly chosen from a distribution, and perform the NPV with these inputs. This is called a Monte Carlo simulation

• One could do a decision tree approach– See Figure 10.3, page 438

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Real Options

• You own an oil field, where your production costs are $35 per barrel. The market price of oil is $30 per barrel.

• If we apply standard NPV analysis to this problem (i.e. static assumptions), it will have a negative NPV

• Can you conceive of anyone willing to pay a positive price to buy this from you? Why would they do this?

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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 is 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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Real Options in Capital Budgeting

Expansion options

• If a product is a hit, expand production. Add more stories to your parking garage.

Abandonmen

t options • Firm can abandon a project if not

successful.• Shareholders have valuable

option to default on debt.Follow-on

investment

options

• Similar to expansion options, but more complex (Ex: movie rights to sequel)

Flexibility options

• Ability to use multiple production inputs (Ex: dual-fuel industrial boiler) or produce multiple outputs

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An example closer to home

• If you computed the NPV of your undergraduate education, using the approach showed last chapter, you would underestimate its value. Why?

• Because the successful completion of your BBA, also buys you the option to get an MBA, if that seems to be good project, sometime in the future.

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• All-equity firms can discount their standard investment projects at cost of equity.

• Firms with debt and equity can discount their standard investment projects using WACC.

• For projects that look more like an investment some other firm would undertake, use the market data from that other firm

• A variety of tools exist to assist managers in understanding the sources of uncertainty of a project’s cash flows and to evaluate them appropriately

Risk And Capital Budgeting

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Finding WACC for Firms with Complex Capital Structures

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Pr

PDE

LTr

PDE

EWACC

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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....

S.D. WilliamsTotal value = $50 million

Has 1,000,000 common shares; price = $50/share; re = 15%.

Has 200,000 preferred shares, 8% coupon, price = $80/share, 10% rate of return, $16

million value.

Has $47.1 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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Accounting for Taxes in Finding WACC

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DWACC

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We have thus far assumed away taxes, which are often important in financing decisions.

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

Accounting for taxes doesn’t change the rules for selecting the discount rate.