Principles of Finance with Excel (Основы финансов c Excel)
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PFE Chapter 19, Capital structure and valuation page 53
we interpret this “inconsistent” behavior as evidence in favor of the argument that there is no net
tax advantage to debt—that is, that firm financial policy does not affect its market value.
Method 3: What does sophisticated finance research say?
Chapter 20 looks at the latest academic research on the capital structure question. Our
reading of this research is that the importance of debt over equity financing has been heavily
overemphasized in finance textbooks. There may be a small advantage of debt over equity, but it
is overwhelmed by the overall uncertainty of valuing a firm.
Summary and conclusion—United Widgets Corporation
United Widgets is a new company set up by John and Cindy, who are pondering the
effect of the equity/debt financing mix. The question they have in mind is—does it matter
whether the company is financed with share capital (equity) or with money borrowed from a
bank (debt)? The risk-return tradeoff between the two financing alternatives is complex:
•
The providers of equity financing are promised a share of the firm’s profits (if there are
any). If there are no profits, then shareholders will not get any dividends; although they
will surely be disappointed, they cannot use the non-payment of dividends to force the
firm into bankruptcy.
•
The providers of debt financing are promised a series of fixed payments. If United
Widgets cannot keep the commitment of making the fixed payments, then the company
may become insolvent. Bankruptcy will affect the shareholders of the company, denying
them their share in United Widgets.
PFE Chapter 19, Capital structure and valuation page 54
• Debt financing is generally cheaper than equity financing: The riskiness of the interest
payments promised by United Widgets to its lenders is less than the riskiness of the
dividend payments promised by the company to its shareholders. In addition interest is a
tax-deductible expense for United Widgets, whereas dividends have to be paid out of
after-tax income. Shareholders, being at greater risk than lenders, will therefore demand
a higher expected return than debtholders. The relative cheapness of debt versus equity
appears to make debt preferable as a financing mechanism. But:
•
Debt financing makes equity financing even more risky. The risky dividend stream
which comes from the company is endangered even further when shareholders promise
debtholders a series of future payments. The higher the amount of debt the firm has, the
more risky the equity financing becomes.
10
Realizing all these factors, John and Cindy ask themselves the following questions:
•
Does the debt/equity mix affect the amount of cash that can be extracted from United
Widgets?
•
Does the mix of equity and debt affect the discount rate that United Widgets should use
for discounting project cash flows? As we have seen in Chapters 6, 14, and 19, the
relevant discount rate is the weighted average cost of capital (WACC).
•
Does the debt/equity mix affect the cost of equity?
The next pages give schematic answers to these questions. The remainder of the chapter
explains these answers (on first reading you may want to skip this and go on to the body of the
10
John and Cindy briefly considered financing their firm with only debt. But this is impossible!
PFE Chapter 19, Capital structure and valuation page 55
chapter). Chapter 20 explores some empirical results and tries to give you a “take” on how to
apply the theoretical answers developed in this chapter.
PFE Chapter 19, Capital structure and valuation page 56
Financing United Widgets—Capital Structure and
Its Effects on Cost of Capital and Firm Valuation
John and Cindy set up a new
company--United Widgets, Inc.
They decide to buy a widget
machine because financial
analysis shows that the NPV of
the machine's cash flows is
positive.
United Widgets is financed with
equity (meaning: money put up
by John and Cindy and their
friends) and debt (money
borrowed from the bank).
Does the equity/debt
financing mix change
the discount rate used to
evaluate widget
machines?
Does the equity/debt
financing mix change
the total cash extracted
from the company?
UNITED WIDGETS
EFFECT OF DEBT/EQUITY MIX ON WEIGHTED AVERAGE COST OF
CAPITAL (WACC)
1. If there are no taxes, the debt/equity mix does not affect the widget-machine
discount rate.
2. If there are only corporate taxes and no personal taxes, then more debt
means that the widget discount rate decreases.
3. If both personal and corporate incomes are taxed, widget machine discount
rates can increase/decrease/stay same when the debt/equity mix changes.
EFFECT OF DEBT/EQUITY MIX ON TOTAL CASH EXTRACTED FROM
COMPANY
1. If there are no taxes, the debt/equity mix does not affect the total amount of
cash extracted from the company.
2. If there are only corporate taxes and no personal taxes, then more debt
means more cash extracted from the company; happens because the tax
system subsidizes debt (interest is an expense for tax purposes).
3. If both personal and corporate incomes are taxed, the cash extracted from
the company can go up or down: Companies enjoy a tax subsidy on their
interest payments (since interest is an expense for tax purposes). But
shareholders pay lower taxes on earnings from equity (because of an
advantageous capital gains tax) than on interest earnings from debt.
PFE Chapter 19, Capital structure and valuation page 57
EFFECT OF DEBT/EQUITY MIX ON COST OF COST OF EQUITY AND WACC
More debt in the debt/equity mix
always
makes equity riskier! The equity owners have to pay debt holders
before they pay themselves and this increases their risk.
The effect of capital structure on WACC depends on the mix of corporate and personal taxes:
1. If there are no taxes, WACC is unaffected by capital structure: the increase in the cost of equity as the
debt/equity mix increases exactly offsets the savings of cheaper debt.
2. If there are only corporate taxes, WACC decreases when more debt is used to finance the firm.
3. If there are both corporate and personal taxes, WACC can increase/decrease/stay same. Empirical
evidence (Chapter 21) seems to indicate that it doesn't change much.
()
()
()
1
where:
cost of equity (increases when debt/equity ratio )
cost of debt
market value of firm's equity
market value of firm's debt
corporate tax rate
EDC
E
D
C
ED
WACC r L r T
ED ED
rL
r
E
D
T
=+−
++
=
↑
=
=
=
=
Figure 20.5
PFE Chapter 19, Capital structure and valuation page 58
Exercises
1. Go back to the supermarket example from the beginning of the chapter. Assume that
the supermarket after-tax operating income is $120,000 each year. If Mortimer’s Group
took a $500,000 loan in 9% annual interest rate and its tax rate is 30%, what will be the
return on equity (ROE) for Mortimer’s group and Joanne’s group.
Profitaftertax
ROE
Equity
⎛⎞
=
⎜⎟
⎝⎠
?
Supermarket $1,000,000 Debt $500,000
Equity $500,000
Total assets $1,000,000 Total debt and equity $1,000,000
Supermarket $1,000,000 Debt $0
Equity $1,000,000
Total assets $1,000,000 Total debt and equity $1,000,000
Joanna’s Supermarket Group
Only equity (100%)
Mortimer’s Supermarket Group
Half equity (50%) and half debt (50%)
2.
2.a. Repeat Exercise 1 with the following balance sheets (assume that the debt still
bears a 9% interest rate):
Supermarket $1,200,000 Debt $600,000
Equity $600,000
Total assets $1,200,000 Total debt and equity $1,200,000
Supermarket $1,000,000 Debt $0
Equity $1,000,000
Total assets $1,000,000 Total debt and equity $1,000,000
Joanna’s Supermarket Group
Only equity (100%)
Half equity (50%) and half debt (50%)
PFE Chapter 19, Capital structure and valuation page 59
2.b. Show in a Data Table and a Excel chart the sensitivity of the ROE to the
equity/debt ratio.
3. You are interested in buying a warehouse for your firm. The warehouse costs $350,000
and using it will save the firm $50,000 annually forever. The firm can borrow any amount
of money at an 8% annual interest rate; all money borrowed is “perpetual debt”—meaning
that the firm pays only the annual interest payment and never returns the debt principal.
The firm’s tax rate is 40%.
What will be the firm’s additional annual income and its return on equity (ROE) on
the investment in the following four cases?
3.a. The firm finances the purchase with equity only.
3.b. The firm finances the purchase with 75% equity and 25% debt.
3.c. The firm finances the purchase with 50% equity and 50% debt.
3.d. The firm finances the purchase with 20% equity and 80% debt.
4.
4.a. Repeat Exercise 3 and show the total annual amounts received by the firm’s
share holders and debt-holders.
4.b Show in a
Data Table and an Excel chart the change in the total amount
received by the firm’s share holders and debt holders as a function of the equity
invested in the project.
PFE Chapter 19, Capital structure and valuation page 60
5. Eddy is the sole owner of his firm. He now wishes to purchase the company next door
for $600,000. His calculations show that the annual income before tax from the purchase
is $80,000.
He is considering two financing alternatives: The first is to ask for a personal loan
of $300,000 and pay the remaining amount from his savings. The second alternative is to
finance the purchase by having his firm take the $300,000 loan. Assuming the interest rate
on the loan is 9% (for infinite duration) and the corporate tax rate is 40%, what will be the
total amount received by the firm’s share holders and debt holders in each scenario,
assuming that only the interest paid by Eddy’s firm is an expense for tax purposes.
6. Returning to the previous exercise: What is the value of the firm Eddy wishes to buy
under the two financing alternatives?
7. Annie owns a “shell firm”—this is a firm which is incorporated but has no activity
whatsoever. Annie’s shell firm is about to buy another firm for $900,000. The firm she is
purchasing has an annual free cash flow (FCF) of $120,000 each year.
7.a. Annie’s bank is willing to give her a perpetual loan equal to half of the purchase
amount at 8% interest. Assuming Annie’s firm has no debt and its tax rate is T
C
=
30%, what will be her firm’s value after the purchase:
•
In case it will finance the purchase with equity only.
•
In case it takes the loan.
7.b. What will be the firm’s value in case the loan is repaid in 20 equal repayments?
PFE Chapter 19, Capital structure and valuation page 61
8. Section 20.3 gives two formulas for the cost of equity r
E
(L) of a levered firm for the
case when there are only corporate taxes:
()
E
Annual equity cash flow
rL
Value of equity
=
()
[]
()
1
EUUD C
D
rL r r r T
E
=+ − −
Use both these formulas to find the cost of equity r
E
(L) for the following cases:
8.a. The cost of equity r
E
(L) for the firm Eddy is buying in Exercise 5.
8.b. The cost of equity r
E
(L) of Amadeus Supermarket in Exercise 1.
8.c. The cost of Equity r
E
(L) of Annie’s firm from Exercise 7.
9. Section 20.3 gives two formulas for the weighted average cost of capital (WACC) of a
levered firm for the case when there are only corporate taxes:
() ()
1
EDC
E
D
WACC r L r T
E
DED
=+−
++
L
FCF
WACC
V
=
Use both these formulas to find the WACC for the following cases:
8.a. The WACC for the firm Eddy is buying in Exercise 5.
8.b. The WACC of Amadeus Supermarket in Exercise 1.
8.c. The WACC of Annie’s firm from Exercise 7.
10. “Sandy-Candy,” a hot new chewing gum company is for sale for $2,000,000. Henry is
interested in buying the company and is exploring various financing alternatives. He
knows that the interest rate on debt is r
D
=9%, corporate tax rate is T
C
= 36% and the cost
PFE Chapter 19, Capital structure and valuation page 62
of capital of the purchase is r
U
= 12%. Henry estimates that ‘Sandy-Candy’ has a free cash
flow (FCF) of $300,000 each year.
10.a. What will be the market value of Sandy Candy if Henry does not take a loan?
10.b. What will be the market value of Sandy Candy if Henry takes a $1,200,000
loan. Assume that the loan is paid by out of Sandy Candy’s earnings, and that the
interest is an expense for tax purposes.
10.c. What will be Sandy Candy’s cost of equity r
E
for the two cases above?
10.d. What will be the Sandy Candy’s WACC for the two cases above?
11. Debby, the owner of Oxford Corporation, has decided that it’s time to make some
changes to the firm’s capital structure. She estimates that Oxford’s FCF is $150,000 each
year and that this FCF can be expected to recur annually forever. The company has not
debt and has 30,000 shares outstanding, each of which is currently worth $50.
Debby wants Oxford to borrow $600,000 of perpetual debt and to use the proceeds
to repurchase shares. Assuming the interest rate on debt is r
D
= 6% and the corporate tax
rate is T
C
= 30%, calculate the following changes:
11.a. What is Oxford’s market value before it issued debt?
11.b. What is Oxford’s market value after it issued debt?
11.c. What will be Oxford share price after the debt issuance?
11.d. How many shares will be repurchased?
11.e. What is Oxford’s equity value after the repurchase of the shares?
11.f. What is Oxford’s cost of equity after the repurchase and dividend payment?
11.g. What is Oxford WACC after the repurchase and dividend payment?