Principles of Finance with Excel (Основы финансов c Excel)

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PFE, Chapter 6, Weighted average cost of capital page 27

ABC

Profit after taxes 10,637,000

Add back depreciation 8,062,000

Changes in working capital

Subtract increases in current assets -1,141,000

Add increases in current liabilities 4,962,000

Subtract out capital expenditures -16,347,000

Add back after-tax interest 208,240

Free cash flow (FCF) 6,381,240 <-- =SUM(B2:B8)

COURIER CORPORATION

Calculation of FCF for 2000

Using FCFs and WACC to value Courier

In finance theory, the market value of a company’s debt and equity is the value of its free

cash flows discounted at its weighted average cost of capital:

,Value of Debt Equity PV value of future FCFs discounted at WACC+=

Suppose that you’ve performed a careful analysis of Courier Corporation and that you

think the future growth of Courier’s FCF is 8% per year. Since Courier’s WACC is 14.51%, we

can value the company as the present value of its future FCFs in the following way:

()

2000

6,381,240* 1 8% 6,381,240* 1 8%

105,849,458

14.51% 8%

1 14.51%

Courier value

Value of Equity Debt PV FCFs discounted at WACC

FCF FCF growth rate

FCF

WACC WACC

∞∞

∞

===

−

∑∑

∑

Notice that this valuation—like the Gordon dividend model of Section 6.2—makes use of the

constant-growth annuity formula developed in Chapter 1 (p000):

()

2000 2000

*1 *1

FCF FCF growth rate FCF FCF growth rate

WACC FCF growth rate

WACC

∞

−

∑

PFE, Chapter 6, Weighted average cost of capital page 28

Since the debt of Courier is worth $31,693,000, we value the equity at $104,849,458-

$31,693,000=$74,156,458. Since there are 2,938,000 shares, each share is worth

74,156,458

25.24

2,938,000

= . This compares favorably with the current share price of Courier, $21.66,

so this makes Courier (in the parlance of stock market analysts) a “buy” recommendation.

Here’s all of this in a spreadsheet:

ABC

Year 2000 FCF 6,381,240

Anticipated FCF growth 8%

WACC 14.51%

Firm value 105,849,458 <-- =B2*(1+B3)/(B4-B3)

Debt value 31,693,000

Equity value 74,156,458 <-- =B6-B7

Number of shares 2,938,000

Per-share value 25.24 <-- =B8/B10

VALUING COURIER

One further note—mid-year discounting

We introduced this topic in Chapter 4 and subsequently dropped it like a hot potato. The

idea was that because most cash flows occur throughout the year—the appropriate discounting

process should discount them as if they occur in mid-year. In terms of the computation just done

for Courier, instead of calculating:

()

(

)

()

2000 2000

2000

FCF FCF growth FCF FCF growth

Debt Equity

WACC

FCF FCF growth

WACC FCF growth

+= + +

−

…

we should be calculating the

PFE, Chapter 6, Weighted average cost of capital page 29

()

2000 2000

0.5 1.5

0.5

2000

FCF FCF growth FCF FCF growth

Debt Equity

WACC WACC

FCF FCF growth

WACC

WACC FCF growth

+= + +

⎡⎤

⎢⎥

−

⎣⎦

…

As explained in Chapter 4 (p000), mid-year discounting raises our valuation of cash

flows, since the earlier a cash flow occurs, the more it is worth. If we implement mid-year

discounting for Courier, then our valuation of Courier’s shares increases from $25.25 to $27.77:

AB C

Year 2000 FCF 6,381,240

Anticipated FCF growth 8%

WACC 14.51%

Firm value 113,269,251 <-- =(1+B4)^0.5*B2*(1+B3)/(B4-B3)

Debt value 31,693,000

Equity value 81,576,251 <-- =B6-B7

Number of shares 2,938,000

Per-share value 27.77 <-- =B8/B10

VALUING COURIER

Using mid-year discounting

Summing up

In this chapter we have calculated the firm’s weighted-average cost of capital (WACC).

The WACC is the risk-adjusted discount rate for the firm’s free cash flows. It is often used to

value projects whose riskiness is similar to the riskiness of the firm’s existing activities, and it is

also used to derive the value of the firm. Both of these uses have been illustrated in this chapter.

The WACC is defined as:

()

EDC

WACC r r T

DED

=+−

PFE, Chapter 6, Weighted average cost of capital page 30

In the table below we summarize how we derived each of the elements of this formula:

Cost of equity r

We’ve used the Gordon model to determine the cost of equity:

()

Div g

=+,

where Div

= total dividends + stock repurchases of the current year

g = anticipated growth rate of dividends+repurchases

= total equity value on current date

Cost of debt r

In principle, this should be the firm’s marginal borrowing rate, but this is

often difficult to determine. For Courier, we used a number representative

of the firm’s cost of borrowing. An alternative is to use the firm’s average

borrowing cost over the previous year:

nterest paid in current year

Average debt this year and last

Market value of

equity E

Current number of shares * current market price per share

Market value of

debt D

The market value of a firm’s debt is difficult to calculate. We almost

always substitute the book value of the firm’s debt for this number. In the

Courier example we showed how to determine this book value from the

firm’s balance sheets.

Firm’s tax rate T

ought to be the firm’s marginal tax rate. In practice we usually use

either:

a) The firm’s average tax rate, measured by:

33.04%

Taxes from Profit and Loss Statement

average tax rate

Profit before taxes

b) The firm’s statutory tax rates. Courier’s statutory Federal tax rate is

34%. State taxes are another 2.98% of its income. Another estimate of its

tax rates might thus be 36.98% .

A final warning

Cost of capital calculations are critical for valuations and controversial. They involve a

mixture of theory and judgment. Almost every number in the WACC calculation above can be

determined in several ways. In many cases professionals do extensive sensitivity analysis on the

WACC and the FCF growth to establish a price range—the range of valuations which appears to

be reasonable, given the variation in plausible assumptions.

PFE, Chapter 6, Weighted average cost of capital page 31

The most important modification you might want to make to the WACC calculation

above involves the cost of equity r

. An important competing model to the Gordon model is the

capital asset pricing model (CAPM). In Chapter 14 we will show you how to use this model to

calculate the cost of equity.

Exercises

1. Compute the weighted average cost of capital (WACC) for a company having:

Market value of debt $200,000

Market value of equity $300,000

Cost of debt, r

7.5%

Cost of debt, r

13%

Tax rate, T

40%

2. Calculate the cost of equity r

for a company having:

Market value of debt $2,500,000

Market value of equity $1,000,000

Cost of debt, r

Tax rate, T

25%

Weighted average cost of capital, WACC 10%

3. Aboudy Corporation’s stock price is currently $22.00 per share. The company has just paid a

dividend of $0.55 per share, and shareholders anticipate that this dividend will grow in the future

at a rate of 6% per year. Use the Gordon model to calculate the company’s cost of equity r

PFE, Chapter 6, Weighted average cost of capital page 32

4. Gradcom’s anticipated next-year dividend is $1.20. Analysts anticipate that this dividend will

grow at a 4% annual rate.

4.a. If the stock’s current share price is $30, what is its cost of equity r

according to the

Gordon Model?

4.b. Show in an Excel graph the cost of equity as a function of the dividend growth rate (let

the growth rate be 0%, 2%, 4%, …, 20% ).

5. Consider the following data regarding Cinema Company.

ABCDEF

Year

Dividend

per share

Total

dividends

Number of

repurchases

Payments

from share

repurchases Total

1995

0.25 ??? 0 0 ???

1996

0.25 ??? 115,000 140,000 ???

1997

0.3 ??? 0 0 ???

1998

0.31 ??? 200,000 260,000 ???

1999

0.35 ??? 120,000 180,000 ???

2000

0.37 ??? 0 0 ???

2001

0.39 ??? 0 0 ???

2002

0.42 ??? 120,000 220,000 ???

Stock price, end of 2002

1.83

Number of shares, January 1995 4,300,000

Cinema Company

5.a. Complete the ??? in the spreadsheet above (assume that the dividend payment was

before the share repurchase).

5.b. Find the cost of equity r

of Cinema using the Gordon dividend model for the total

equity payout.

5.c. What would be Cinema’s cost of equity if we consider only the dividend payments

without the share repurchases?

PFE, Chapter 6, Weighted average cost of capital page 33

6. It is 1 January 2005, and you are interested in finding the cost of equity r

of your company.

After a quick search you have found the following data:

•

The company currently has 1,600,000 shares outstanding. The current share price is $3.

•

The company’s earnings for 2004 were $2,000,000. The company policy has just paid out

$300,000 in dividends, and it intends to continue this 15% dividend payout from earnings

in the future.

•

During 2004 the company spent $600,000 on share repurchases. It is the company’s

intention to increase the amount spent on share repurchases at the same growth rate as the

amount spent on dividends.

•

Projected earnings growth is 2% per year.

Using the Gordon model for the total equity payout, what is the company’s cost of equity r

*******

You wish to estimate the share’s price of ‘softy’, your favorite underwear company. You

know that tomorrow the company will pay its annual dividend in the amount of 1.5$ per

share, a growth in the company’s cash dividends of 4% comparing to last year. As an

experienced investor, you demand a yield of 12% on your investment in the company.

What should be the company’s share price?

Your boss asked you to find the WACC of ‘Welcome to Paradise’ company. After a

quick research you have come up with the following data:

• The company has 1,600,000 shares, currently sold for 2$ per share.

• The company’s debt is 2,500,000$. The amount of interest paid last year by the

company was $300,000.

• The corporate tax rate is 40%.

• The cost of capital requested by the investors is 13%.

What is the company’s WACC?

PFE, Chapter 6, Weighted average cost of capital page 34

3. You are interested in calculating the cost of capital of ‘The lions’ Company, based on the

average WACC of its industry, which is 11%. You know that the company stock price is

$11, and it has 5,500,000 shares. The company cost of debt is 9%, its debt is $4,000,000

and the company’s tax rate is 40%. What is the company cost of capital?

You are interested in calculating the WACC of ABC Company. Its stock price is $8, and

it has a debt to equity ratio of 1. ABC’s cost of debt is 9%, its cost of capital is 12% and

the company’s tax rate is 40%. What is the company’s WACC?

Assume the following data concerning ‘ZZZ’ Company.

• The company has 2,000,000 shares, currently sold for 2.5$ per share.

• The company’s debt is 3,000,000 from the company market value. The interest rate paid

last year by the company was $250,000.

• The company paid total dividend of $600,000 last year, and its expected dividend

growth is 3%. In addition, the company repurchases 150,000 of its shares.

• The corporate tax rate is 30%.

What is the company’s WACC?

You have come up with the following data concerning ‘Zion’ Company.

• The company has 2,500,000 shares.

• The company’s debt is 90% from the company market value. The interest rate paid last

year by the company was $500,000.

• The company paid total dividend of $800,000 last year, which is 25% of its pre-tax

profit, and its expected growth next year is in $50,000 more.

• The company paid tax in the amount of 950,000.

• The cost of capital requested by the investors is 13%.

What is the company’s WACC?

You are considering a new project to your firm. This project requires investment of

$500,000 and generates cash flow of $70,000 for the next 10 years. To your judgment,

PFE, Chapter 6, Weighted average cost of capital page 35

the project has no risk. You know that your company’s WACC is 14%, and that the risk

free rate is 6%. Should you take this project?

‘The sauce’, a well-known pizza factory, have asked you to evaluate the factory free cash

flow (FCF) activity. You have estimated that the FCF of the factory is $4,500,000, its

WACC is 12.5% and its estimated growth is 5% each year. If you know that ‘The sauce’

debt is $19,000,000 and it has 6,500,000 outstanding shares, what should be the share’s

price? Repeat the question by using mid-year discounting as well.

1. XYZ Corp. has just paid a dividend of $5 per share. You think this dividend will grow at 8%

per year. If you think the correct discount rate for the dividend stream of XYZ is 25%, how

much should you be willing to pay for the stock?

2. You just bought a share of ABC Corp. for $28. The company has just paid a dividend of $2

per share, and you anticipate that this dividend will grow at a rate of 12% per year. What is your

implied cost of equity for ABC?

3. You are considering purchasing a stock of ABC Corp, which has just paid a $3 annual

dividend per share. The company does not repurchase any of its shares. You anticipate that the

company’s dividends will grow at a rate of 20% per year for the next 5 years. After this time,

you think that the growth of the annual dividends will slow to 5% per year. If your cost of equity

for ABC is 10%, what price should you be prepared to pay for the stock?

4. Suppose that a firm is financed with 70% equity and 30% debt. The interest rate on debt is

8%, and the expected return on the common stocks is 17%. The firm’s tax rate is 40%. What is

the firm’s weighted average cost of capital?

PFE, Chapter 6, Weighted average cost of capital page 36

5. You are given the following information for Twin Inc.

Long-Term Debt Outstanding: $300,000

Current Yield to Maturity (r

): 8%

Number of Shares of Common Stock: 10,000

Price per Share: $50

Book Value per Share: $25

Expected Rate of Return on Stock (r

): 15%

a) Calculate Twin Inc.’s weighted-average cost of capital (assuming that the firm

pays no taxes).

b) How would r

and the weighted-average cost of capital change if Twin Inc.’s

stock price falls to $25 due to declining profits? Assume that business risk is unchanged.