Principles of Finance with Excel (Основы финансов c Excel)

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PFE Chapter 15, Using SML and WACC page 12

percentage b of its earnings to its shareholders, both in the form of dividends and stock

repurchases. Then we can rewrite the formula above as:

()

(

)

1*1

where is the firm's current earnings per share

Div g b EPS g

rg g

EPS

=+= +

Manipulating this formula a bit, we get:

(

)

this is the firm's

P/E (price-earnings)

ratio

P EPS

↑

 

We now apply this logic to the market as a whole. We regard a market index such as the

S&P 500 (symbolized by M) as a stock having its own payout ratio b and growth rate of equity

payouts g. We then use the above formula to compute the expected market return

(

)

Er .

Here’s an example using data for the S&P 500 index at the end of December 2001:

ABC

S&P 500 P/E on 31dec01 46

Estimated growth of equity payout, g 6%

Payout ratio, b 50%

E(r

)

7.15% <-- =B4*(1+B3)/B2+B3

USING THE PRICE-EARNINGS

RATIO TO COMPUTE E(r

)

A sensitive reader may note that there’s some confusion of symbols here. The formula

()

P EPS

uses r

to stand for the cost of equity for a stock. Since the “cost of equity” is a synonym for the “expected return from

equity,” when we apply the formula to the market portfolio M (in this case, the S&P 500), we should by logic we

should have called this r

. Instead, we use

(

)

. Our excuse is that the symbol

(

)

is so widely used that we

cannot give it up.

PFE Chapter 15, Using SML and WACC page 13

The price-earnings ratio (P/E) for the S&P 500 is not that easy to find (see Figure 15.2 for

the source of our data). We have had to “guesstimate” the estimated growth of dividends and the

dividend payout ratio.

Figure 15.2. The price/earnings (P/E) ratio of the S&P 500 index is not that easy to find. Here

is a website which calculates the P/E ratio. The numerical example in this section uses the P/E

of 46 on 31 December 2001 to compute the expected return on the market

()

Er .

Source: http://www.bullandbearwise.com

Dividend payout is defined as the total expended by firms on both cash dividends and

repurchases of shares (we discussed this topic a bit in Chapter 6, when calculating the cost of

equity for Courier Corporation using the Gordon model). While the cash dividends are a matter

of record, the amount of repurchases is more debatable. Current estimates put the sum of

dividends and repurchases at around 50% of corporate earnings. Here, for example, is a graph

showing the relation between share repurchases and dividends for the Standard & Poors 500

PFE Chapter 15, Using SML and WACC page 14

index through 1998. Notice that by the end of the data sample, repurchases outweighed

dividends:

Figure 15.3: Share repurchases and dividends in the United States, 1982-1998. Whereas at the

beginning of the period share repurchases were relatively small compared to dividends, by the

end of the period more cash was paid out to shareholders by corporations in the form of share

repurchases than as dividends.

Source: J. Nellie Liang and Steven A. Sharpe, Share Repurchases and Employee Stock Options

and their Implications for S&P 500 Share Retirements and Expected Returns, Federal Reserve

Bank, 1999.

Dividend growth is the market anticipation of the growth of total dividends (broadly

defined as cash dividends plus repurchases) for the future. If we assume that dividends will

grow at the rate of growth of the economy, 6% is a reasonable long-term estimate.

Computing the risk-free rate r

The risk-free rate r

should be the short-term Treasury rate. This rate is available from a

variety of places, including Yahoo (see example in next section).

PFE Chapter 15, Using SML and WACC page 15

Computing the value of the firm’s debt D

In principle D should be the market value of the firm’s debt. However, in practice, this

value is usually very difficult to calculate. Standard practice is to use the book value of the

firm’s debt minus the value of its cash reserves; we refer to this concept as net debt. You should

be careful even with the book value.

Now that we’ve defined the concepts, we use the example of Hilton Hotels to compute a

firm’s weighted average cost of capital.

15.3. A fully worked-out example—Hilton Hotels

We illustrate the approach to calculating the WACC by using data for Hilton Hotels

Corp. (symbol: HLT). As discussed above, we need 8 parameters in order to calculate the

WACC for this (or any other) company:

•

E, the market value of the company’s equity today. This is simply the number of shares

times the current stock price.

•

D, the market value of the company’s debt today. We will use the book value (that is, the

accounting value) of the company’s debt as a proxy for this number.

•

, the cost of equity for the company. In this chapter we use the SML to calculate the

cost of equity. Using the SML means that the cost of equity is dependent on:

o The

of the firm’s equity. In the previous chapter we computed this

. In

practice, it is often available without computation (as in this example, read on).

o r

, the risk-free rate

o E(r

), the expected return on the market

PFE Chapter 15, Using SML and WACC page 16

• r

, the cost of debt for the company. In principle, this should be the marginal cost (the

company’s cost of obtaining new debt). In practice, we often use the company’s average

cost of existing debt.

•

the company’s tax rate. In principle, this should be the company’s marginal tax rate

(the rate on an additional dollar of earnings). In practice we often use the company’s

average tax rate.

Much of the data is available on Yahoo; Figure 15.4 shows the Yahoo screen leading to

Hilton Hotel’s “profile,” which is shown in Figure 15.5.

Figure 15.4. The Yahoo screen, indicating the Profile. This choice gives the updated financial

information for the firm used below. (Note that Yahoo’s presentation of financial materials

changes occasionally, so that you make have to look elsewhere for the financial profile.)

PFE Chapter 15, Using SML and WACC page 17

From Yahoo’s Profile, here are some data for Hilton as of 18 January 2002.

Figure 15.5. Yahoo’s profile for Hilton Hotels. Highlighted numbers are used in the

computation of Hilton’s WACC.

From this data we learn:

•

Hilton’s equity

= 0.89.

•

The market value of Hilton’s equity is E = $4.18 billion. As you’ll see in the spreadsheet

below, Yahoo has taken the number of shares times the current market value per share.

•

The book value of Hilton’s debt is D = $5.352 billion. With a bit of work, this number

can be calculated from Yahoo: According to Yahoo:

o The book value of equity per share is $4.83.

o The debt/equity ratio of Hilton is 3.03. This is the ratio of the book value of the

firm’s debt to the book value of its equity.

PFE Chapter 15, Using SML and WACC page 18

Since Hilton has 369.3 million shares outstanding, its total book value of equity is:

369.3*4.83 1,784= . This makes the total debt of the company $5,405. From this

number we subtract the $53 million in cash held by the company to arrive at net debt D =

$5,352.

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

HILTON HOTELS CORPORATION (HLT)

using Yahoo for much of the information

We still need the 2 firm-related parameters (

, T

) and 2 market parameters (r

, E(r

) ) .

For these, we’ll have to work a bit.

Hilton’s cost of debt, r

is approximately 6.81%

We compute the cost of Hilton’s debt r

by taking its interest payments and dividing by

the average debt over the year. Yahoo doesn’t have the interest-payment information, so we

have to go to Hilton’s financial statements to get these figures. Figure 15.6 shows a note from

the Hilton financial statements detailing the company’s debt. A quick calculation shows that

()

402

6.81%

6094,5716

Interest paid

Average

Cash is subtracted from the firm’s debt because Hilton could, in principle use the cash to pay off some of its debt.

PFE Chapter 15, Using SML and WACC page 19

Figure 15.6. Note from Hilton’s financial statements about the company’s debt.

Hilton’s tax rate T

is approximately 41%

Figure 15.7 shows Hilton’s income statements, with the company’s income before taxes

and taxes highlighted. The average of Hilton’s tax rate over the last 3 years is

= 41.25%:

ABCDE

Year 1998 1999 2000

Income before taxes 336 313 479

Provision for taxes 136 130 200

Tax rate 40.48% 41.53% 41.75% <-- =D4/D3

Average tax rate, T

41.25% <-- =AVERAGE(B5:D5)

HILTON'S TAX RATE T

PFE Chapter 15, Using SML and WACC page 20

Figure 15.7. Hilton’s income statements. The highlighted text allows us to compute the

company’s tax rate.

The risk-free rate in the economy r

is 1.6%

We get this number from Yahoo, as shown in Figure 15.8.

PFE Chapter 15, Using SML and WACC page 21

Figure 15.8. Yahoo screen with interest rates. The r

for use in the SML is the short-term

Treasury bond rate, 1.60%.

The expected return on the market E(r

) is approximately 7.15%

This was illustrated above in section 15.3.

So what’s Hilton’s WACC?

The weighted average cost of capital for Hilton is 5.11%: