Principles of Finance with Excel (Основы финансов c Excel)

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PFE Chapter 15, Using SML and WACC page 22

ABC

Equity beta 0.89 <-- Yahoo

Shares outstanding (million) 369.3 <-- Yahoo

Market value per share 11.32 <-- Yahoo

Market value of equity ($ million), E 4,180 <-- =B5*B4

Book value of equity per share 4.83 <-- Yahoo

Total book value of equity 1,784 <-- =B8*B4

Debt/Equity ratio 3.03 <-- Yahoo

Book value of debt 5,405 <-- =B10*B9

Cash on hand 53

Net debt ($ million), D 5,352 <-- =B11-B12

Risk-free rate, r

1.60%

Expected market return, E(r

)

7.15%

Computation of WACC

Percentage of equity, E/(E+D) 0.4386 <-- =B6/(B6+B13)

Percentage of debt, D/(E+D) 0.5614 <-- =1-B19

Cost of equity, r

6.54% <-- =B15+B2*(B16-B15)

Cost of debt, r

6.81%

Tax rate, T

41.25%

WACC 5.11% <-- =B19*B21+(1-B23)*B20*B22

HILTON HOTELS CORPORATION (HLT)

using Yahoo for much of the information

15.4. Computing the WACC using an asset

Asset

A somewhat different approach to computing the weighted average cost of capital

(WACC) is to use the

asset beta approach. In this approach we need both the equity beta

and

the

for Hilton. The asset beta is defined as the weighted average

of the debt and equity

betas:

PFE Chapter 15, Using SML and WACC page 23

()

**1*

proportion proportion

equity of equity debt corporate of debt

**1*

beta in firm beta tax rate in firm

value value

Asset E D C

ED ED

ββ β

=+−

⎛⎞ ⎛⎞

⎜⎟ ⎜⎟

⎛⎞ ⎛⎞⎛ ⎞

⎜⎟ ⎜⎟

=+−

⎜⎟ ⎜⎟⎜ ⎟

⎜⎟ ⎜⎟

⎝⎠ ⎝⎠⎝ ⎠

⎜⎟ ⎜⎟

⎝⎠ ⎝⎠

Having computed the beta

Asset

, we now compute the WACC by using the SML:

(

)

Asset M f

WACC r E r r

⎡

⎤

=+ −

⎣

⎦

In order to illustrate this approach for Hilton, we note that all the necessary calculations

have been done in the previous section—with the exception of the computation of the debt beta

. We compute this

by assuming that the SML holds for debt as well as equity:

(

)

()

This is the

beta of

Hilton's debt

fD Mf

cost of debt r r E r r

Er r

↑

⎡

⎤

==+ −

⎣

⎦

−

⇒=

−

In the spreadsheet below you can see that Hilton’s debt

is 0.938 (cell B8). This means

that its asset beta is 0.70 (cell B15), which gives the WACC as 5.49% (cell B17).

PFE Chapter 15, Using SML and WACC page 24

ABC

Equity beta,

0.89 <-- Yahoo

Risk-free rate, r

1.60%

Expected market return, E(r

)

7.15%

Cost of debt 6.81%

Debt beta,

0.938 <-- =(B7-B4)/(B5-B4)

Corporate tax rate 41.25%

Percentage of equity, E/(E+D) 0.4386

Percentage of debt, D/(E+D) 0.5614

Asset beta, β

Asset

0.70 <-- =B2*B12+(1-B10)*B13*B8

WACC 5.49% <-- =B4+B15*(B5-B4)

HILTON HOTELS CORPORATION (HLT)

computing the WACC with the asset beta

PFE Chapter 15, Using SML and WACC page 25

Why is the debt

so high?

Hilton’s

is higher than as its equity beta,

. This may seem surprising. Before we

start, in this box, with reasons why this might be so, note that the asset beta,

Asset

, is based on

the after-tax debt beta, (1-T

)

, which is of course much lower than the equity beta

Here are several other possible reasons for the size of Hilton’s debt beta:

•

The debt is risky because Hilton has a low credit rating. Risky debt would, of course,

have a higher beta.

•

The debt is risky because it has a relatively long term, and so is more sensitive to

fluctuations in interest rates.

•

We’ve overestimated the cost of the debt. In reality, r

should be the expected cost of

Hilton’s debt. If Hilton’s debt is risky, then investors in the debt expected a lower return

than the promised return. So if the promised return is 6.81%, it could be that the

expected return is 5%, allowing for the possibility of financial distress. This means that

the debt beta

is lower than what we’ve calculated. [The actual adjustment of a debt

for financial distress is quite complicated—see my book Financial Modeling.]

15.5. Don’t read this section!

A final question that may have occurred to you: Why is it that we get a different cost of

capital using the traditional WACC approach and using the asset beta (

Asset

) approach? We’re

PFE Chapter 15, Using SML and WACC page 26

going to answer this question in this section, but we warn you that reading the section may be

bad for your health.

Still here? The answer is that for cost of capital purposes, you should adjust the SML for

corporate taxes. In addition, there are two SMLs—one for equity and one for debt. Here are the

appropriate formulas:

(

)

(

)

(

)

() ( )

Equity SML: * 1 * * 1

Debt SML: * * 1

Ef C E M f C

Df D M f C

rr T Er r T

rr Er r T

⎡

⎤

=−+ −−

⎣

⎦

⎡⎤

=+ − −

⎣⎦

Note that the two SMLs have the same tax-adjusted market risk premium

()

(

)

Mf C

Er r T

⎡⎤

−−

⎣⎦

but have different intercepts—the equity SML has intercept

(

)

rT−

, whereas the debt SML

has intercept r

If we apply this approach to Hilton, and if we assume that the cost of debt is r

= 6.81%,

then we get the debt

as:

() ( )

6.81% 1.60%

0.8387

* 1 7.15% 1.60%

Mf C

Er r T

−

===

−− −

Now, as you can see in the spreadsheet below, the WACC is the same, whether you

compute it with the traditional method or with the asset

Asset

And—in all honesty—the difference between the two calculations in the previous part of the chapter is not big

enough to make much of a difference.

The two-SML model is fully explained in Corporate Finance: A Valuation Approach by Simon Benninga and

Oded Sarig (McGraw-Hill, 1997).

PFE Chapter 15, Using SML and WACC page 27

ABC

Risk-free rate, r

1.60%

Expected market return, E(r

)

7.15%

Corporate tax rate 41.25%

WACC using traditional method

Equity beta 0.89 <-- Yahoo

Cost of equity 6.47% <-- =B2*(1-B4)+B7*(B3-B2*(1-B4))

Cost of debt 6.81%

Percentage of equity, E/(E+D) 0.4386

Percentage of debt, D/(E+D) 0.5614

WACC 5.08% <-- =B11*B8+B12*(1-B4)*B9

WACC using the asset beta and the two-SML model

Equity beta,



0.8900

Debt beta,



0.8387 <-- =(B9-B2)/(B3-B2*(1-B4))

Asset beta,



Asset

0.6669 <-- =B11*B17+B18*(1-B4)*B12

WACC 5.08% <-- =B2*(1-B4)+B19*(B3-B2*(1-B4))

HILTON HOTELS CORPORATION (HLT)

using the two-SML model

15.6. Some background information on equity betas

It helps to have information on equity betas for various industries. Here, from an article

published in 1997, here are the stock betas (“equity betas”) for 66 U.S. industries:

PFE Chapter 15, Using SML and WACC page 28

ABCDEF

Industry

Equity

beta Industry

Equity

beta

Agricultural Production—Crops

1.63

Transportation by Ai

1.61

Agricultural Services

0.49

Measuring Instruments

1.34

Livestock and Animal Specialties

1.41

Leather and Leather Products

0.83

Amusement and Recreation Services

2.12

Industrial and Computer Equipment

1.49

Auto Repair, Services, Parking

1.54

General Merchandise Stores

1.02

Depository Institutions

1.61

Metal Mining

0.94

Contractors and Builders

0.64

Mining and Quarrying

1.28

Building Materials, Hardware

2.65

Miscellaneous Manufacturing

0.78

Printing and Publishing

1.21

Miscellaneous Retail

1.26

Business Services

1.38

Miscellaneous Repair Services

1.69

Auto Dealers and Gasoline Stations

0.71

Motion Pictures

0.94

Chemicals and Allied Products

1.30

Wholesale Nondurable Goods

0.95

Apparel

1.00

Petroleum Refining

0.63

Apparel and Accessory Stores

1.10

Oil and Gas Extraction

0.80

Coal Mining

-1.16

Paper and Allied Products

1.17

Nondepository Credit Institutions

1.95

Personnel Services

1.24

Wholesale Trade—Durable Goods

1.38

Pipelines Except Natural Gas

0.70

Educational Services

1.84

Railroad Transportation

1.24

Electronic and Electrical Equipment

1.75

Eating and Drinking Places

1.34

Engineering andAccounting Services

2.00

Real Estate

1.37

Fabricated Metal Products

1.89

Rubber and Plastics products

1.03

Security Brokers and Dealers

2.23

Hotels and Lodging

1.72

Food and Kindred Products

0.66

Tobacco Products

2.21

Motor Freight and Warehousing

0.69

Stone, Clay, Glass, and Concrete

1.76

Furniture and Fixtures

1.04

Communications

0.95

Home Furniture

1.12

Textiles

1.02

Food Stores

1.02

Special Trade Contractors

1.26

Health Services

1.54

Transportation Equipment

1.44

Heavy Construction

2.07

Transportation Services

0.79

Holding and Other Investment Offices

0.96

Electric, Gas, and Sanitary Service

0.47

Insurance Carriers

1.21

Water Transportation

1.18

Insurance Agents and Brokers

1.35

Lumber and Wood Products

1.60

Number of industries 64 <-- =COUNT(B3:B35,E3:E35)

Lowest beta -1.16 <-- Coal

Highest beta 2.65 <-- Building materials

Average beta 1.26 <-- =AVERAGE(B3:B35,E3:E35)

Note

: We would expect the weighted average equity beta

to be 1; however, the

average beta

given above is not weighted.

How many betas < 0? 1 <-- =COUNTIF(B3:E35,"<0")

How many betas > 2? 5 <-- =COUNTIF(B3:E35,">2")

How many 0 < beta < 1 18 <-- =COUNTIF(B3:E35,"<1")

How many 0.9 < beta < 1.1 11 <-- =COUNTIF(B3:E35,"<1.1")-COUNTIF(B3:E35,"<0.9")

How many betas > 1 45 <-- =COUNTIF(B3:E35,">1")

EQUITY BETAS BY INDUSTRY

Source: "Full-information Industry Betas," by Paul D. Kaplan and James D. Peterson

Published in Financial Management, Summer 1998, pp. 85-93.

Data is for 1996

PFE Chapter 15, Using SML and WACC page 29

Note that the coal industry has a negative beta, indicating that the returns from holding

coal stocks increase when the market goes down and decrease when the market goes up. To

judge by its beta, therefore, the coal industry is countercyclical.

Here’s the frequency distribution of the betas:

Frequency Distribution of Equity Betas

-1.1--1.0

-1.0--0.9

-0.9--0.7

-0.7--0.6

-0.6--0.4

-0.4--0.3

-0.3--0.1

-0.1-0.1

0.1-0.2

0.2-0.4

0.4-0.5

0.5-0.7

0.7-0.8

0.8-1.0

1.0-1.1

1.1-1.3

1.3-1.4

1.4-1.6

1.6-1.7

1.7-1.9

1.9-2.0

2.0-2.2

2.2-2.3

2.3-2.5

2.5-2.6

2.6-2.8

2.8-0.0

Summary

The computation of the weighted average cost of capital (WACC) is critical for corporate

valuation. In this book we have already seen the importance of the WACC in Chapter 6.

The WACC depends critically on our estimate of the cost of equity r

. There are only

two practical approaches for computing the cost of equity—the Gordon dividend model,

discussed in Chapter 6, and the SML. This chapter has dealt in great detail with using the SML

to compute the cost of equity and the resulting WACC. We’ve illustrated the use of the equity

The issue of stock valuation is discussed in somewhat more detail in Chapter 18, which sums up the various

approaches to this important topic.

PFE Chapter 15, Using SML and WACC page 30

for computing the cost of equity r

. We have also shown how you can use a combination of

the equity beta

, the debt

, and the asset

Asset

to compute the WACC.

Through the use of a detailed example for Hilton Hotels, we have shown where to get the

data required to make all these calculations.

Exercises (unfinished)

** The current riskfree rate is 4% and the expected rate of return on the market portfolio is 10%.

The Brandywine Corporation has two divisions of equal market value. The bond to stock ratio

(B/S) is 3/7. The company’s bond can be assumed to present no risk of default. For the last few

years, the Brandy division has been using a discount rate of 12% in capital budgeting decisions

and the Wine division a discount rate of 10%. You have been asked by their managers to report

on whether these discount rates are properly adjusted for the risk of the projects in the two

divisions.

•

What are the betas of typical projects implicit in the discount rates used by the two

divisions?

•

You estimate that the stock beta of Brandywine is 1.6. Is this consistent with the stock

beta implicit in the discount rates used by the two divisions?

•

You estimate that the stock beta of the Korbell Brandy Corp. is 1.8. This company is

purely in the brandy business, its bond to stock ratio is 2/3 and its bond beta is 0.2. Based

on this information (and on your estimate of Brandywine’s stock beta), what discount rate

PFE Chapter 15, Using SML and WACC page 31

would you recommend for projects in the Brandy and in the Wine divisions of

Brandywine?

** Sun Inc. has an equity beta of 0.5. Its capital structure consists of equal amounts of equity and

risk-free debt. The debt has a pre-tax yield of 6% and the expected rate of return on the market

index is 18%. Sun Inc. is considering expanding into Snow Inc. business. This new business is

expected to generate an after-tax internal rate of return of 25%. Vacation Inc. is already in this

new business, and its equity beta is 2.0 and it uses a blend of 10% (risk-free) debt and 90%

equity in its capital structure. If the new project is to be funded with 50% debt, should Sun Inc.

enter the Snow Inc. business? Assume that both companies have a marginal tax rate of 50%, and

that the business risk of Vacation Inc. is comparable to the risk of Sun Inc.’s venture.

** A company is deciding whether to issue stock to raise money for an investment project which

has the same risk as the market and an expected return of 15%. If the risk-free rate is 5%, and the

expected return on the market is 12%, the company should go ahead:

a. This is false. The company should not take this project.

b. Regardless of the company’s beta.

c. Unless the company’s beta is greater than 1.25.

d. Unless the company’s beta is less than 1.25.

** A project has the following forecasted cash flows (in thousands of dollars):

C0 C1 C2 C3

-100 60 50 40

The estimated project beta (beta of assets) is 1.6. The market return is 15% and the risk-free

rate is 7%. Estimate the opportunity cost of capital and the project’s present value (using the

same rate to discount each cash flow.)

b) A share of a stock with a beta of 0.75 now sells for $50. Investors expect the stock to pay a

year-end dividend of $3. The T-Bill rate is 4%, and the market risk premium is perceived to

be 8%. What is the investors’ expectation of the price of the stock at the end of the year?

c) Reconsider the stock in question (b). Suppose investors actually believe the stock will sell for

$54 at year-end. Is the stock a good or bad buy? What will investors do? At what point will