Principles of Finance with Excel (Основы финансов c Excel)

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PFE Chapter 20, Capital structure and valuation page 3

Example 1: Both groups make the same bid

Suppose that both Mortimer and Joanna’s groups bid $1 million for the supermarket. In

this case the balance sheets would look like this:

Mortimer’s Supermarket Group

Half equity (50%) and half debt (50%)

Supermarket $1,000,000 Debt $500,000

Equity $500,000

Total assets $1,000,000 Total debt and equity $1,000,000

Joanna’s Supermarket Group

Only equity (100%)

Supermarket $1,000,000 Debt $0

Equity $1,000,000

Total assets $1,000,000 Total debt and equity $1,000,000

Why would both groups make a similar bid for the supermarket? The line of reasoning

which might lead to this conclusion is the following:

A supermarket is a supermarket is a supermarket, no matter how its financed. If

Mortimer’s group think the supermarket is worth $1 million, then so will Joanna’s group

(and vice versa). The fact that one group finances with debt and equity whereas the other

group finances only with equity is irrelevant to their valuation of the supermarket.

Example 2: Mortimer’s group bids more

Is it possible that Mortimer’s group should rationally decide that—because of the group’s

greater proportion of debt financing—the supermarket is worth more than what Joanna’s group is

willing to pay? One of Mortimer’s investors thinks that their group can afford to bid more for

the supermarket than Joanna. His line of reasoning:

PFE Chapter 20, Capital structure and valuation page 4

The fact that we’re financing with debt means that it’s cheaper for us to finance

the supermarket. The interest paid on debt is an expense for tax purposes, which means

that debt is cheaper than equity. In addition, since equity is more risky than debt, equity

holders in any case want a higher return than debt holders. So our greater use of debt

means that we can afford to pay more for the supermarket.

If this logic is correct, then it’s possible that Mortimer’s group would bid $1,200,000 for

the supermarket, whereas Joanna’s group would only bid $1,000,000. In this case the two

balance sheets would look like this:

Mortimer’s Supermarket Group

Half equity (50%) and half debt (50%)

Supermarket $1,200,000 Debt $600,000

Equity $600,000

Total assets $1,200,000 Total debt and equity $1,200,000

Joanna’s Supermarket Group

Only equity (100%)

Supermarket $1,000,000 Debt $0

Equity $1,000,000

Total assets $1,000,000 Total debt and equity $1,000,000

Of course there’s no question what would happen in this case: The sellers of the

supermarket would prefer to sell to Mortimer’s group, which is offering a higher price.

Which example is more representative? Example 1 or Example 2?

As you’ll see in the chapter, both examples could be representative of how things actually

work in the world. In this chapter we frame the capital structure question (Example 1 versus

Example 2) primarily in terms of the following two questions:

PFE Chapter 20, Capital structure and valuation page 5

• Does the choice of financing affect the total cash that can be extracted from the firm? If

Mortimer’s group, with its higher proportion of debt financing, can extract more cash

from the supermarket, then it might be logical for them to be willing to pay more for the

supermarket.

• Should the choice of financing affect the discount rate the firm uses to evaluate projects?

This is where risk, the magic word in finance, comes into play.

In simple words: Is the

correct discount rate to be used for the supermarket by Mortimer’s group different from

that which should be used by Joanna’s group? Does the choice of a financing mix affect

the weighted average cost of capital (WACC)?

As you will see in this chapter, the answers to both these questions relate primarily to

taxation. It will turn out that depending on the tax system, either Example 1 or Example 2 could

be a representation of how things work.

Finance concepts in this chapter

• Debt versus equity financing

• Valuation effects of leverage

• Corporate versus personal taxation

• Modigliani-Miller model

• Miller’s “Debt and Taxes”

Recall the opening words of Chapter 10: “Risk is the magic word in finance. Whenever finance people can’t

explain something, we try to look confident and say ‘it must be the risk.’ “

It’s even possible that another variant of Example 2 would hold in which Mortimer’s group would bid less than

Joanna’s. This is pretty unlikely, as you’ll see in the remainder of the chapter.

PFE Chapter 20, Capital structure and valuation page 6

Excel functions used

• If

• NPV

20.1. Capital structure when there are corporate taxes—ABC Corp

We start our exploration of the effects of capital structure by examining the story of ABC

Corp. This well-known company is located in Lower Fantasia. Lower Fantasia has an unusual

tax code: In Lower Fantasia whereas companies are taxed on their corporate income, individuals

are not taxed on their personal income.

Our hero, Arthur ABC, is trying to figure out: a) Whether to buy ABC Corp., a well-

known company in Lower Fantasia, and b) If he buys the company, how to finance the purchase.

Buying ABC Corp. using only equity

This turns out to be fairly simple. ABC has an expected annual free cash flow (FCF) of

$1,000 per year; this FCF is anticipated to recur, year after year, at the same level. Arthur—who

has an MBA from E

astern Lower Fantasia State University (their football team is called the

“elfs”)—has computed the cost of capital for the purchase as r

= 20%. The symbol “U” as a

subscript for the discount rate r

stands for “unlevered” and is meant to remind you that in this

case r

is the discount rate appropriate for the case where Arthur buys ABC Corp. with only

equity (meaning: his own money, without borrowing).

PFE Chapter 20, Capital structure and valuation page 7

This r

= 20%. is a cost of capital that reflects only the business risks of ABC Corp. If

purchased only with equity, therefore, the company is thus worth

1,000

5,000

20%

= .

In what

follows we will use the symbol

for the “unlevered value of the firm.” V

is what a company

is worth if it is financed only with equity. In our case:

() ()

$1,000 $1,000

$5,000

20%

1 1 20%

FCF

∞∞

== ==

∑∑

Buying ABC using debt

Arthur has a wonderful source of debt financing: His mother. This wealthy old lady is in

fact his business partner, but their joint deals are structured so that she’s always the lender and

Arthur the equity owner. There’s another unusual feature to the old lady’s lending—she gives

out

perpetual debt—her loans require only an annual payment of interest, but no repayment of

principal.

The cost of debt to Arthur, denoted by r

, is the interest rate charged by his mother on

her loans to him. In this case

= 8%.

Together, Arthur and his Mom are exploring two alternative financing arrangements:

•

In Alternative A, Arthur buys ABC Corp. for cash; immediately thereafter, the company

borrows $3,000 from Mom and repays it to Arthur. (Corporate finance deals in Lower

Fantasia are a bit complicated!) In this case ABC Corp is a

levered company.

(“Leverage” in this context means that the company has debt on its balance sheets.)

The FCF is already after corporate taxes, and the discounted FCF value of the firm is thus

()

20%

120%

CF FCF

∞

∑

Throughout this chapter you’ll notice that we often assume that cash flows have infinite duration. This makes the

valuations easier, but doesn’t affect the principles.

PFE Chapter 20, Capital structure and valuation page 8

• In Alternative B, Arthur borrows $3,000 from Mom and then buys ABC Corp. for cash.

In this case, ABC Corp. is an

unlevered “all-equity” company (no debt on its balance

sheets) and Arthur is levered.

The fundamental difference between these two alternatives is that the Lower Fantasia tax

code has a corporate income tax but no personal income taxes. Under the tax code, interest paid

by corporations is an expense for tax purposes, but this is not true for interest paid by

individuals, who aren’t taxed on their personal income.

From the drawing below you can see that the

total family income produced by Alternative

A is more than that produced by Alternative B.

FINANCING ARTHUR'S PURCHASE OF ABC

Tax code: Corporate tax of 40%, but no personal taxes

Alternative A: Company borrows from Arthur's Mom Alternative B: Arthur borrows from Mom

BC Corp. -- Levered

Company has $3,000 of 8% perpetual debt from

rthur's mother

FCF = $1000

Equity income =

$1000 - 8%*3,000*(1-40%) = $856

Paid to Arthur ABC, sole owner

rthur ABC -- sole owner of all ABC's

equity. No personal tax.

nnual income = $856

rthur's mothe

. No personal

tax.

nnual afte

-tax income:

8%*$3000 = $240

Family income: Arthur + Mom

rthu

: $ 856

Mom: $ 240

Total: $ 1096

BC Corp. -- no debt

FCF = $1000

Equity income = $1000

Paid to Arthur ABC, sole owner

rthur ABC -- sole owner of all ABC's

equity. Borrowed $3000 of perpetual

debt from Mom at 8%. No personal tax,

but owes Mom interest

nnual income =

$1,000 - 8%*$3,000 = $760

Family income: Arthur + Mom

rthu

: $ 760

Mom: $ 240

Total: $ 1000

rthur's mother. No personal

tax. Gets interest from Arthur.

nnual 8%*$3000 = $240

Figure 20.1. Cash flows resulting from two methods of financing the purchase of ABC Corp.

From the family point of view, it is clear that the first alternative is better than the second.

In this alternative the family (Arthur + Mom) has an annual income of $1,096, as opposed to the

$1,000 in the second alternative. A little thought will reveal why the first alternative is

PFE Chapter 20, Capital structure and valuation page 9

preferable—ABC Corp. has a tax advantage over Arthur with respect to borrowing. It can

deduct its interest expenses from its income taxes, so that its net income taxes are only

()

8%*3000* 1 40% $144−=. This compares with Arthur’s cost for the same loan of

8%*3,000 240= .

To flesh this out a bit, let’s write out some equations:

()

Income from

Cost of debt

debt to Mom

to ABC Corp

()

**1 *

DCD

Total family income from ABC Arthur Mom

cash produced by firm FCF r Debt T r Debt

FCF r Debt T

↑

==−−+



 

   

Thus the total cash produced by the firm for its stockholders and bondholders increases with the

amount of debt the firm has. Notice that the total cash produced by the firm does not increase if

Arthur borrows the money from his mother.

20.2. Valuing ABC Corp.—taking account of leverage and corporate taxes

Recall that we stated in section 20.1 that ABC Corp’s FCFs are worth $5,000 if the

company has no leverage:

Looking at the drawing, it’s clear why this is so—when Arthur borrows from Mom, the interest is a wash: Arthur

has an interest expense of $240 and Mom has interest income of $240, for a net $0. When the company borrows

from Mom, the company has an interest expense of (1-40%)*8%*3000=$144, but Mom has interest income of

$240, for a net of $96.

PFE Chapter 20, Capital structure and valuation page 10

()

1,000 1,000

5,000

20%

1.20

V Unlevered value of ABC

PV future FCFs discounted unlevered discount rate

Annual FCF

∞

== ==

∑

So how much is the levered version of ABC Corp worth (this is the company which borrows

$3,000 from Arthur’s Mom). We use the

additivity principle explained in Chapter 16:

()

8%*3,000*40% 96

5,000 5,000

0.08

1.08

5,000 1,200 6,200

V Levered value of ABC

Unlevered value of ABC PV additional debt related CFs

∞

=+ =+

=+=

∑

The Additivity Principle in this context

The additivity principle (Chapter 17) says that the value of the sum of two cash flow

streams is the sum of their values. In the context of this problem, the two cash flow streams are:

1) The stream of FCFs which derive from the firm’s business activities, and 2) The stream of tax

shields on the interest paid by the firm.

To value these streams using the additivity principle, we discount each at its appropriate

risk-adjusted discount rate. The rate for the FCFs is r

and the rate for the tax shields—which

we assume to be riskless—is the interest rate on the debt r

ABC Corp is worth more as a levered firm than as an unlevered firm because it produces

more cash for its owners. The additional cash produced—generated by the fact that the company

can deduct the cost of its interest payments from its taxes, whereas Arthur cannot—is worth

$1,200. In symbols:

PFE Chapter 20, Capital structure and valuation page 11

()

1,000 1,000

5,000

20%

11.20

The unlevered value of the firm is

the present value of its free cash flows

discounted an an appropriate (unlevered)

cost

V V PV additional debt related CFs

FCF

∞∞

====

∑∑

() ()

of capital

8%*3,000*40% 96

1200

11.08

The tax shields created

by the debt are discounted at the interest

rate.

6,200

Interest tax

TInterest

shields

∞∞

⎧

⎪

⎨

⎪

⎩

⎧

⎛⎞

== ==

⎪

⎜⎟

⎝⎠

⎪

⎨

⎪

⎩

∑∑

The cost of equity, r

(L), and the weighted average cost of capital, WACC, with

leverage

The cost of equity is the discount rate for the cash flows accruing to shareholders. In

Chapters 9 and 16 we discussed the derivation of the cost of equity, stressing its relation to the

riskiness of the equity cash flows. In this chapter we use the symbol r

(L), with the “L” showing

that that the cost of equity is related to the leverage of the firm. As you will see, greater leverage

leads to a larger r

(L); the reason for this being that the equity cash flows are riskier when

shareholders have promised larger amounts to debtholders.

We now proceed to the computation of r

(L) for ABC Corp. The levered version of ABC

Corp. is worth $6,200, of which D = $3,000 is debt. Thus the equity of the company is worth

$3,200. We denote the market value of the equity by E. In order to calculate the firm’s cost of

equity r

(L), we first compute the cash flows that the equity owners receive:

PFE Chapter 20, Capital structure and valuation page 12

()

1,000 8%*3,000* 1 40% 856

Annualequity cash flow FCF after - tax interest

aid by ABC

−

=− −=

The discounted value of this annual equity cash flow of $856 is the value of the equity; this

defines the cost of equity r

(L) :

()

856 856

3,200

856

26.75%

3,200

equity cash flow

E Equity value

∞

⇒= =

∑

With a little mathematical flimflammery, we can show that:

()

[]

()

[]

()

r is the discount

rate for the FCFs,

When ABC borrows, it's shareholders

which represents

bear an additional . The

the firm's business

term a

risk

3,000

20% 20% 8% 1 40%

3,200

EUUD C

financial risk

rL r r r T

↑

=+ − −

=+− −

bove represents the financial risk

premium for the equity holders

26.75%=



We can now compute the WACC:

() ()

()

3,200 3,000

26.75% 8% 1 40%

3,200 3,000 3,200 3,000

16.13%

EDC

WACC r L r T

ED ED

=+−

With a little more “flimflammery” we can show that discounting the FCFs at the WACC

gives the total value of the firm:

()()

1,000 1,000

6,200

16.13%

1 1 16.13%

FCF

WACC

∞∞

===

∑∑