Risk, Return and Capital Budgeting

For 9.220, Term 1, 2002/0302_Lecture15.pptStudent Version

Outline

1. Introduction2. Project Beta and Firm Beta3. Cost of Capital – No tax case4. What influences Beta?5. Cost of Capital in the Real World

a) Weighted Average Cost of Capital (WACC)

b) Adjusted WACC

6. Summary and Conclusions

Introduction In doing an NPV, IRR, or PI analysis, we need to have the

relevant discount rate for our project. Now that we have a better understanding of the relation

between expected return and risk, we can use this to develop an appropriate discount rate (cost of capital or opportunity cost of capital) for our analysis.

The implicit comparison we then make when doing capital budgeting analysis is … should we fund the project or would we be better off if we place the funds in similar risk financial securities (that are expected to make the return predicted by our risk/return model) – the forgone returns from the financial securities represent our opportunity cost.

We will explore how to determine the firm’s risk and the project’s risk – and thus the opportunity cost of capital.

A complication we consider is incorporating taxes into the cost of capital derivation.

Project and Firm Beta If we know the risk of a project, we can determine the

opportunity cost of capital related to the project. In most cases it is not possible to directly observe the β of a

project. If our project is the same risk as our own firm, then we can

jump ahead and use the Weighted Average Cost of Capital (WACC) for our firm. If not, we must try to find similar risk comparable companies that have publicly traded equity outstanding.

Then we can use regression analysis to estimate our comparable companies’ equity β’s .

Since, even with identical assets, companies’ equity β’s will differ as the level of debt financing (financial leverage) differs, we must first make the β’s comparable. We do this by converting each equity β into an asset or firm β.

Equity β and Asset (or firm) β from comparable companies

Consider holding a portfolio that consists of all the equity of a firm plus all the debt of a firm. What does this portfolio own?

Recall the accounting identity…

Now determine the β of this portfolioβassets = xequity●βequity + xdebt●βdebt

(Since βdebt is usually very low, for simplicity, it often assumed to be zero.)

Use the data on the next slide to calculate the asset beta for an oil exploration project – use comparable companies to estimate the βasset for the project.

Comparable Companies with SIC=1311

Company Name EquityBeta

D/E D/(D+E) E/(D+E) AssetBeta

DENBURY RESOURCES INC 0.89 92.06 47.93% 52.07% 0.46

CANADIAN NATURAL RESOURCES 0.80 76.81 43.44% 56.56% 0.45

PANAFRICAN ENERGY 0.45 - 0.00% 100.00% 0.45

TETHYS ENERGY INC 0.75 65.37 39.53% 60.47% 0.45

CANADIAN 88 ENERGY CORP 0.74 64.29 39.13% 60.87% 0.45

Column Average 0.73 59.71 34.01% 65.99% 0.46

Determining the project’s βequity from its βassets

Our firm will have its own unique amount of financial leverage (debt) in its financing mix (capital structure). Thus, we can use the βassets from the comparable firms for our project’s overall β. But we need to determine our project’s βequity so we have the relevant cost of equity capital related to the project. Use the comparable firms’ βassets and our firm’s specific D/E ratio to do this:

Βequity = βassets●(1 + D/E) (assumes βdebt =0)

Suppose our firm had a D/E ratio of 1.5, then what is the βequity for our firm?

βequity =

Cost of equity – return to the CAPM

If we know the βequity, then we can use the CAPM to determine the E[Requity].

E[Requity] =Rf+βequity●(E[RM]-Rf) Suppose Rf = .035 and E[RM]=.095

Then E[Requity] =

Cost of Debt We know from our D/E ratio of 1.5 that the

target financing for our firm includes a lot of debt. Thus we have to include the relevant proportion of debt financing when determining the overall cost of capital for our project.

Suppose each of our company’s bonds has face value of $1,000, a coupon rate of 5%, 20 years until maturity, and a current market price of $1,219.35.

What is the cost of debt (express as an effective annual rate)?

Overall Cost of Capital for the Project Given the cost of equity financing for the project and the

cost of debt financing for the project, we can calculate the overall cost of financing for the project as follows:

This is known as the weighted average cost of capital. The above equation is calculated ignoring tax effects or assuming there are no taxes.

Later we will look at WACC for the firm as a whole; note, in our analysis here we are determining the WACC for the project because we are using a cost of equity for the project that is adjusted for the project’s risk – so, as calculated here, this is not the WACC for the firm!

ED REED

ERE

ED

DWACC

A quick check in the no-tax case

With risk-free debt and no taxes, we can also calculate the project’s WACC directly from the asset β of the project and the CAPM.

E[Rproject] =Rf+βproject●(E[RM]-Rf)

=

What affects the asset β?

Cyclicality of Revenues The more a firm’s revenues move

with market conditions (i.e., are cyclical), then the more its cash flows will be correlated with the market. This correlation causes the asset β to be positive.

Next consider costs …

Operating leverage and the effect on asset β Operating leverage is the degree of fixed costs in a firm’s

cost structure and is formally defined as follows:

The higher the degree of fixed costs relative to variable costs, the more EBIT will change as revenues change; therefore the higher will be a firm’s asset β.

ΔSales

Sales

EBIT

ΔEBIT

Salesin Δ %

EBITin Δ % Leverage Operating

Operating Leverage Example

Company L Company H

Normal Market

High Market

Normal Market

High Market

Units Sold 100 210 100 210

Total Sales $ $1,000 $2,100 $1,000 $2,100

Variable Costs $800 $1,680 $200 $420

Fixed Costs $150 $150 $750 $750

EBIT $50 $270 $50 $930

From asset β to equity β We have already seen that the amount of

financial leverage (or proportion of debt financing) causes there to be a difference between the firm’s asset β and its equity β. Given risky cash flows produced by the firm’s

assets, a higher debt level makes the cash flows left for equity holders even more risky.

Thus higher financial leverage increases the equity β relative to the asset β.

Reconsider Company H with low and high debt levels.

Financial Leverage Example

H: Low Debt H: High Debt

Normal Market

High Market

Normal Market

High Market

Units Sold 100 210 100 210

Total Sales $ $1,000 $2,100 $1,000 $2,100

Variable Costs $200 $420 $200 $420

Fixed Costs $750 $750 $750 $750

EBIT $50 $930 $50 $930

Interest $10 $10 $200 $200

EBT $40 $920 -$150 $730

Notation: EBT = Earnings Before Tax

Financial leverage and equity β: conclusions from the example Suppose total assets are $8,000 in both cases. Also suppose that in the low-debt case the debt is $250.

Then equity in the low-debt case must be $7,750. In this example, the high debt case has 20 times as much

debt in the capital structure (compare the interest charges). This implies that in the high-debt case, debt must be $5,000

and therefore equity is only $3,000. Ignoring taxes, look at the standard deviation of ROE in the

two cases. Low-debt case: σROE = .08029 High-debt case: σROE = .20742 So high financial leverage (higher D/E) implies more variable

returns to equity holders. Given some correlation between revenues and the market and a positive asset β, the higher variation in ROE due to higher financial leverage implies a higher equity β.

Conclusions on factors that affect β

The three factors that affect an equity β are as follows Cyclicality of Revenues Operating Leverage Financial Leverage

WACC and Corporate Taxes When the real-world consideration of tax is brought into

the analysis, it is more difficult to convert between asset and equity β’s and thus it is more difficult to use comparable firms’ data to determine the overall cost of capital for a specific project.

The reason is that debt interest payments reduce taxes; thus, holding fixed the risk of the before-tax cash flows, more debt makes total after-tax cash flows to security holders greater and of less overall risk. More debt results in more cash saved from paying tax,

therefore there is more cash in total to be paid to debt and equity holders. In addition, tax savings are usually lower risk cash flows. Thus with tax savings added back into the after-tax cash flows, there is a lower overall risk of the total after-tax cash flows to debt and equity holders.

What is the solution with taxes? We could solve for an after-tax adjusted asset β or we

could derive a new method for converting between asset and equity β’s in the context of taxes, however, these tasks are beyond the scope of this course.

Instead, we can look to the after-tax WACC for our firm as a whole because we can usually observe our own firm’s securities and their risk characteristics. With corporate taxes, the only change in the firm’s

cost of capital is that the after-tax cost of debt is lower. The after tax cost of debt is This can now be used in the WACC equation.

WACC revised for taxes

Redo the WACC with our original data E[RE]=10.4%

(assume this is the firm’s cost of equity capital)

E[RD]=3.5% D/E = 1.5

And now, assume TC=40%

ECD REED

ETRE

ED

DWACC

1

WACC Example 1 – Self Study Determine the firm’s WACC given the

following data. Debt financing = 160,000 bonds currently priced

at $1,250 each Equity financing = 10,000,000 shares currently

priced at $30 per share Equity β = 1.8 Debt β = 0.2 Rf = 4% E[RM] = 10% TC = 45%

D=E=Use CAPM to get E[RD]=Use CAPM to get E[RE]=WACC=

=.10024=10.024%

WACC Example 2 – Self Study Determine the firm’s WACC given the

following data. D/E = 0.6 Current equity price = $50/share. Next constant

annual dividend occurs in one year and is $6. Bonds are currently priced @ $926.60, coupon rate is

4% (semiannual coupons), face value is $1,000, and maturity is in 10 years.

TC = 45% Set E = 1, solve for D =Solve for E[RD]=Solve for E[RE]=WACC=

=.0853124=8.53124%

Project risk ≠ Firm Risk Unfortunately, in the tax case we have limited

ourselves to calculating the WACC from the observed debt and equity securities (and their returns) of the firm – not for individual projects.

Thus, if we are to use WACC in the tax case, we must ensure our project’s systematic risk is identical to our firm’s overall systematic risk level.

If the project’s market risk is different from the firm’s market risk, then applying the WACC as the discount rate will produce an incorrect NPV.

Project risk ≠ Firm Risk:Errors that result if WACC is used as the discount rate

Adjusted WACC when Project Risk ≠ Firm Risk

We would need to adjust the WACC to reflect the different risk of the project’s cash flows. an upward adjustment to WACC to get the discount rate for more

risky projects. a downward adjustment to WACC to get the discount rate for less

risky projects. Similarly, a project may have various cash flows with different

risk levels. For example, CCA tax shields are generally thought to have a lower systematic risk than revenues. Thus we should have a downward adjustment to WACC to get the discount rate for CCA tax shields. If some revenues had a higher systematic risk than the corporation, then we should have an upward adjustment to the WACC to get the discount rate for these revenues.

For this course, we will not do the adjustment, but you should be aware of this important issue and the direction and impact of such adjustments.

Summary and Conclusions In a no-tax world, if we know about a project’s risk, then we

can use the CAPM (or other risk/return models) to determine the discount rate for the project.

A project or firm’s asset risk, as measured by βassets, is influenced by the cyclicality of revenues and the degree of operating leverage. Financial leverage magnifies the asset β into the equity β.

In the real-world situation that includes taxes, we can use the firm’s securities to calculate the WACC. Here, the after-tax cost of debt is used. The WACC can then be used as the discount rate for the

analysis of projects as long as the projects have the same market risk as the firm.

If project risk is different, then WACC cannot be used as shown. WACC must be adjusted up or down to get the correct discount rates for higher or lower risk projects and for higher or lower risk cash flows.