Capital Structure
& Cost of Capital
Introduction

Capital budgeting affects the firm’s well-being
Discount rate is based on the risk of the cash flows
 Errors in capital budgeting can be serious

 Need to compensate investors for financing
 Project Expect Return
 Project Cash Flows
WACC

Weighted Average Cost of Capital





Also called the hurdle rate
D = Market Value of Debt
E = Market Value of Equity
P = Market Value of Preferred Stock
V=D+E+P
Costs of Financing

Cost of Preferred Stock


Cost of Debt


Based on preset dividend rate (r = D/P)
YTM is good estimate
Cost of Common Stock


Derived from current market data – Beta
Cost has 2 factors


Business or Asset Risk
Financing or Leverage Risk (Leverage increases common stock risk)
Cost of Equity Example

Market risk premium = 9%
Current risk-free rate = 6%
Company beta = 1.5
Last dividend = $2, dividend growth = 6%/year
Stock price = $15.65

What is our cost of equity?




Example – WACC

Equity Information






Cost of equity?


50 million shares
$80 per share
Beta = 1.15
Market risk prem. = 9%
Risk-free rate = 5%
RE =
Cost of debt?

RD =

Debt Information





$1 billion
Coupon rate = 10%
YTM = 8%
20 years to maturity
Tax rate = 40%
Example – WACC

Capital structure weights?
E = 50 million shares ($80/share) = $4 billion
 D = $1 billion face
 V = 4 + 1 = $5 billion
 wE = E/V =
 wD = D/V =


What is the WACC?

WACC =
Capital Restructuring

Capital restructuring
Adjusting leverage without changing the firm’s assets
 Increase leverage



Decrease leverage


Issue debt and repurchase outstanding shares
Issue new shares and retire outstanding debt
Choose capital structure to max stockholder wealth
Maximizing firm value
 Minimizing the WACC

Ex: Effect of Leverage
Current
Assets
Proposed
$5,000,000
$5,000,000
$0
$2,500,000
$5,000,000
$2,500,000
0
1
$10
$10
# Shares
500,000
250,000
Int. Rate
N/A
10%
Debt
Equity
D/E
Share $
EBIT $650,000

D = $0
Interest = 0, Net Income = $650,000
 EPS = $650,000/500,000 = $1.30


D = $2.5 mil
Interest =
 Net Income =
 EPS =
(D/E = 1)

/250,000 =
EBIT $300,000

D = $0
Interest = 0, Net Income = $300,000
 EPS = $300,000/500,000 = $0.60


D = $2.5 mil
(D/E = 1)
Interest = $2,500,000 * 10% = $250,000
 Net Income =
 EPS =
/250,000 =

Break-Even EBIT

EBIT where EPS is the same under both the
current and proposed capital structures

If EBIT > break-even point
then leverage is beneficial to our stockholders
If EBIT < break-even point
then leverage is detrimental to our stockholders

Ex: Break-Even EBIT
EPSAll Equity  EPSWith Debt
EBIT
EBIT  250,000

500,000
250,000
 500,000 
EBIT  250,000
EBIT  

 250,000 
EBIT  2 * EBIT  500,000
EBIT  $500,000
Cost of Equity Varies



If the level of debt increases, the riskiness of the
firm increases.
Increases the cost of debt.
However, the riskiness of the firm’s equity also
increases, resulting in a higher re.
Impact of Leverage

$200,000 in assets, all equity, 10,000 shares
Pre-tax
Taxes
Net
Demand
Prob
EBIT
Interest
Income
40%
Income
ROE
EPS
Terrible
0.05
($60,000)
$0
($60,000)
($24,000)
($36,000)
-18.00%
($3.60)
Poor
0.2
($20,000)
$0
($20,000)
($8,000)
($12,000)
-6.00%
($1.20)
Normal
0.5
$40,000
$0
$40,000
$16,000
$24,000
12.00%
$2.40
Good
0.2
$100,000
$0
$100,000
$40,000
$60,000
30.00%
$6.00
Great
0.05
$140,000
$0
$140,000
$56,000
$84,000
42.00%
$8.40
$40,000
$0
$40,000
$16,000
$24,000
12.00%
$2.40
14.82%
$2.96
E(value):
Std Dev:
Impact of Leverage

$200,000 in assets, half equity, 5,000 shares
Pre-tax
Taxes
Net
Demand
Prob
EBIT
Interest
Income
40%
Income
ROE
EPS
Terrible
0.05
($60,000)
$12,000
($72,000)
($28,800)
($43,200)
-43.20%
($8.64)
Poor
0.2
($20,000)
$12,000
($32,000)
($12,800)
($19,200)
-19.20%
($3.84)
Normal
0.5
$40,000
$12,000
$28,000
$11,200
$16,800
16.80%
$3.36
Good
0.2
$100,000
$12,000
$88,000
$35,200
$52,800
52.80%
$10.56
Great
0.05
$140,000
$12,000
$128,000
$51,200
$76,800
76.80%
$15.36
$40,000
$12,000
$28,000
$11,200
$16,800
16.80%
$3.36
29.64%
$5.93
E(value):
Std Dev:
M&M – Perfect Market

Miller and Modigliani (1958)


Fathers of capital structure theory
Proposition I
Firm value is NOT affected by the capital structure
 Since cash flows don’t change, value doesn’t change


Proposition II

Firm WACC is NOT affected by capital structure
M&M – Perfect Market


Assumes no taxes or bankruptcy costs
WACC = (E/V)RE + (D/V)RD


No taxes
RE = RA + (RA – RD)(D/E)
RA: “cost” of the firm’s business risk
 (RA – RD)(D/E): “cost” of the firm’s financial risk

Risks

Business risk:
Uncertainty in future EBIT
 Depends on business factors such as competition,
industry trends, etc.
 Level of systematic risk in cash flows


Financial risk:
Extra risk to stockholders resulting from leverage
 Depends on the amount of leverage
 NOT the same as default risk

M&M – Perfect Market
Ex: Perfect Market

RA = 16%, RD = 10%; % debt = 45%

Cost of equity?


RE = 16 + (16 - 10)(.45/.55) = 20.91%
If the cost of equity is 25%, what is D/E?
25 = 16 + (16 - 10)(D/E)
 D/E =


Then, what is the % equity in the firm?

E/V =
Capital Structure Example
Balance Sheet
Assets (A) 100

Assets

100
Debt Value (D)
Equity Value (E)
Firm Value (V)
rdebt=8% & requity=15%
WACC = rassets =(D/V)* rdebt + (E/V)* requity
WACC =
40
60
100
Capital Structure Example

New capital structure
Assets (A)
100
Assets
100

Debt Value (D)
Equity Value (E)
Firm Value (V)
Has the risk of the project changed?


Is the go-ahead decision different?

30
70
100
After Refinancing

Before


WACC = .4 (8%) + .6 (15%) = 12.2%
After
Imagine cost of debt dropped to 7.3%
 WACC = .3 (7.3%) + .7 (requity) = 12.2%
 requity =

Example

Debt/equity mix doesn’t affect the project’s inherent risk


However reducing debt level changes the required returns



Required return on the package of debt and equity is unaffected
Reduced debtholder risk (rdebt fell)
Reduced equityholder risk (requity fell)
How is it, then, that reducing firm risk did not reduce the
required rate of return?


Project risk is the same.
Weights changed.
Corporate Taxes

Interest is tax deductible



Effectively, govt subsidizes part of interest payment
Adding debt can reduce firm taxes
Reduced taxes increases the firm cash flows
Ex: Taxes
Unlevered
Levered
EBIT
Interest ($6250 @ 8%)
5000
0
5000
500
Taxable Income
5000
4500
Taxes (34%)
1700
1530
Net Income
3300
2970
Bondholders
Equityholders
Total Cash Flows
0
3300
3300
500
2970
3470
Interest Tax Shield

Annual interest tax shield
Tax rate times interest payment
 $6250 * .08 = $500 in interest expense
 Annual tax shield = .34(500) = 170


PV of annual interest tax shield
Assume perpetual debt
 PV =
 PV = D(RD)(TC) / RD = DTC =

Taxes – Firm Value

Firm value increases by value of tax shield
VL = VU + PV (interest tax shield)
 If perpetuity, VU = EBIT(1-.t) / rA
 Value of equity = Value of the firm – Value of debt


Ex: Unlevered cost of capital (rA)= 12%; t = 35%;
EBIT = 25 mil; D = $75 mil; rD = 9%;
VU =
 VL =
 E=

Taxes - WACC

WACC decreases as D/E increases
WACC = (E/V)RE + (D/V)(RD)(1-TC)
 RE = RA + (RA – RD)(D/E)(1-TC)

 rA =
12%; t = 35%; D = $75 mil; rD = 9%; VU =
$135.42 mil; VL = $161.67 mil; E = $86.67 mil

RE =

WACC=
Example: Proposition II - Taxes

Firm restructures its capital so D/E = 1
rA= 12%; t = 35%; rD = 9%

New cost of equity?



RE =
New WACC?

WACC =
Taxes + Bankruptcy

Probability of bankruptcy increases with debt



Increases the expected bankruptcy costs
Eventually, the additional value of the interest
tax shield will be offset by the increase in
expected bankruptcy cost
At this point, the value of the firm will start to
decrease and the WACC will start to increase
Cost of Debt Varies
Amount
borrowed
$ 0
D/V
ratio
0
D/E
ratio
0
Bond
rating
--
rd
--
250
0.125
0.1429
AA
8.0%
500
0.250
0.3333
A
9.0%
750
0.375
0.6000
BBB
11.5%
1,000
0.500
1.0000
BB
14.0%
Times Interest Earned
TIE = EBIT / Interest
EBIT = $400,000
t=40%
80,000 shares outstanding, with price of $25
D  $0
( EBIT - k d D )( 1 - T )
EP S
Shares outstanding
($400,000)
(0.6)

80,000
 $3.00
EPS & TIE:
D = $250,000, rd = 8%
$250,000
Shares repurchased 
 10,000
$25
( EBIT - k d D )( 1 - T )
EP S
Shares outstanding
($400,000- 0.08($250,
000))(0.6)

80,000- 10,000
 $3.26
EBIT $400,000
T IE

 20x
Int Exp $20,000
EPS & TIE
D = $500,000, rd = 9%
$500,000
Shares repurchased 
 20,000
$25
( EBIT - k d D )( 1 - T )
EPS 
Shares outstanding
($400,000 - 0.09($500,000))(0.6)

80,000 - 20,000
 $3.55
EBIT $400,000
TIE 

 8.9x
Int Exp $45,000
Bankruptcy Costs

Direct costs
Legal and administrative costs
 Additional losses for bondholder


Indirect bankruptcy or financial distress costs
Preoccupies management
 Reduces sales
 Lose valuable employees

Options of Distress

The right to go bankrupt
Valuable
 Protects creditors from further loss of assets


Creditors will renegotiate – why?
Avoid bankruptcy costs
 Voluntary debt restructuring

Tradeoff Theory

Tradeoff between the tax benefits and the
costs of distress.
 Tradeoff

determines optimal capital structure
VL = VU + tC*D - PV (cost of distress)

With higher profits, what should happen to debt?
In Practice



Tax benefit matters only if there’s a large tax liability
Risk and costs of financial distress vary
Capital structure does differ by industries



Lowest levels of debt


Increased risk of financial distress
Increased cost of financial distress
Pharma, Computers
Highest levels of debt

Steel, Department stores, Utilities
WACC Review

Capital budgeting affects the firm’s well-being
Discount rate is based on the risk of the cash flows
 Errors in capital budgeting can be serious

 Need to compensate investors for financing
 Project Expect Return > Cost of Capital
 Project Cash Flows > Return to Investors
General Electric

6 Divisions
Commercial Finance – loans, leases, insurance
 Healthcare – medical technology, drug discovery
 Industrial – appliances, lighting, equipment services
 Infrastructure – aviation, water, oil & gas technology
 Money – consumer finance (credit cards, auto loans)
 NBC Universal – entertainment and news

Project WACC
Using a general industry or company cost of capital
will lead to bad decisions.
Using Firm WACC

Only for projects that mirror the overall firm risk
Only be used if the new financing has the same
proportion of debt, preferred, and equity

Otherwise, use the project cost of capital

Pure Play


Find several publicly traded companies
exclusively in project’s business
Use pure play betas to proxy for project’s beta




May be difficult to find such companies
Note if the pure play is levered
Betas are non-stationary over time
Cross-sectional variation of betas, even within the
same industry
Leverage & Beta

Equity risk =
business risk (operating leverage)
+
financial risk (financial leverage)

L = U(1+(1-t)D/E)
 L = E = Equity beta = Levered beta
 U = A = Asset beta = Unlevered beta
 t = Company’s marginal tax rate
Capital Structure & Beta

Beta varies with capital choice


Original Capital Structure



debt = .2
equity = 1.2
(40/100)*.2 + (60/100)*1.2 = assets = .8
Debt drops to 30%



assets (U) = portfolio = (D/V) debt + (E/V) equity
Suppose the debt beta falls to .1
Then, assets(U) = .8 = (.3 * .1) + (.7 * equity) so equity = 1.1
Unlever betas, we move from an observed equity to asset
Leverage & Beta




Firm with no debt decides to issue $100 million
in bonds and retire some outstanding stock.
Historically, βL = .75
Value of the equity after $100 million is retired is
$235 million. The tax rate is 35%.
What is β after the transaction?


L = U(1+(1-t)D/E), where L = lev, U= unlev
L =
Post-Acquisition Beta

1995: Disney announced it was acquiring Capital
Cities for $120/share

At acquisition, Disney


equity (L) = 1.15
E = $31.1 bil
D = $3.186 bil
Based on $120 offer price, Capital Cities
equity(L) = 0.95
E = $18.5 bil
 Corporate tax rate was 36%

D = $615 mil
Disney/Capital Cities

Step 1


Step 2


Find unlevered betas for each company
Use market values of DIS & CC to find unlevered beta of
combined firm
Step 3

Find levered beta using leverage of combined firm
1) Unlevered Betas
 
U
L
1  (1  T ) * ( D )
E
2) Combined Beta
3) Levered Beta