8-1
Capital Structure and Valuation
8-2
Example
Current
Proposed
$8,000
$8,000
$0
$4,000
$8,000
$4,000
10%
10%
Share Price
$20
$20
Outstanding
400
200
Assets
Debt
Equity
Interest
Capital Structure
Current
8-3
ROA
Earnings
ROE
EPS
Recession
5%
$400
5%
$1.00
Expected
15%
$1,200
15%
$3.00
Expansion
25%
$2,000
25%
$5.00
ROA
EBI
Interest
Earnings
ROE
EPS
5%
$400
400
$0
0%
$0
15%
$1,200
400
$800
20%
$4.00
25%
$2,500
400
$1,600
40%
$8.00
Proposed
Miller and Modigliani: Proposition I
8-4
Strategy A: Buy 100 shares of levered equity
Recession
Expected
Earnings
$0
$400
Initial Cost: 100 x $20 = $2,000
Expansion
$800
Strategy B: Buy 200 shares of unlevered equity
using $2,000 in borrowing (Homemade Leverage)
Earnings
$200
$600
Interest
$200
$200
Net Earnings
$0
$400
Initial Cost: 200 x $20 -$2,000 = $2,000
$1,000
$200
$800
Proposition I (no taxes): Value of the unlevered firm is equal to the value of the levered firm
Miller and Modigliani: Proposition II
(no taxes)
8-5
 Remember: rWACC = D/A × rD + E/A × rE
 MM(I) implies rWACC is independent of leverage
 Define r0 is cost of capital for all-equity firm
 r0 = unlevered earnings / unlevered equity =15%
 Result: r0=rWACC if there are no taxes
 Result: MM(II) (no taxes): rE = r0 + D/E × (r0 – rD)
Cost of Capital and MM(2)
Cost of
Capital (%)
rE
r
0
rWACC
rD
D/E
8-6
Taxes
 Present value of the tax shield

Interest = rD × D

Tax reduction = Tc × rD × D

Under normal circumstances we can assume:
cash flow from tax reduction has same risk as debt
cash flows are perpetual

PV(Tax Shield) = (Tc × rD × D) / rD = Tc × D
 MM(I): VL = VU + Tc × D
 VU = (EBIT × (1 – Tc)) / r0
8-7
MM(2): rE = r0 + D/E × (1-Tc) (r0 – rD)
Cost of
Capital (%)
r
0
8-8
rE
A declining rWACC is a direct
result from MM(I), i.e, the value
of the firm rises in leverage
rWACC
rD
D/E
Example
8-9
 Blue Inc. has no debt and is expected to generate $4
million in EBIT in perpetuity. Tc=30%. All after-tax earnings
are paid as dividends.The firm is considering a
restructuring, allowing $10 million in debt at an interest
rate of 8%. The unlevered cost of equity, r0, is 18%.
 What is the current value of Blue?

VU=EBIT × (1–Tc) / r0 = ($4 million × 0.7) / 0.18 = $15.56 million
 What will the new value be after the restructuring?

VL = VU + Tc × D = $15.56 + 0.3 × $10 = $18.56 million
 What will the new required return on equity be?

rE = 0.18 + (10/8.56) × 0.7 × (0.18 – 0.08) = 26.18%

Check with: Elevered = ((4 – 0.8) × 0.7) / 0.2618 = $8.56 million
How about using rWACC?
8-10
 rWACC = (10/18.56) × 0.7 × 0.08 + (8.56/18.56) × 0.2618 = 15.08%
 Hence, Blue has decreased its WACC from 18% to 15.08%
 VL = (4 × 0.7) / 0.1508 = $18.56 million
Downside of Debt
Financial Distress and Agency Costs
8-11
 Financial Distress costs decrease the size of
the firm and hence decrease the distribution to
shareholders and bondholders.
 Costs

Direct costs of financial distress

Indirect costs of financial distress

Agency costs (of debt)
 Asset substitution and risk shifting
 Underinvestment
 Milking the company
8-12
Static trade-off theory of debt
Firm Value
Maximum
Firm Value
Actual Firm Value
Debt
Optimal amount of Debt
More on Agency Costs
Benefits of debt
8-13
 Agency cost of Equity (motive)

Shirking is less likely when issuing debt

Perquisites are less likely with debt

Over-investment is less likely with debt
 Agency cost of Free Cash Flow (opportunity)

Retained earnings versus dividends?

Growth and investment opportunities
 Debt serves as a monitoring device,
decreasing managerial discretion
The Pecking-Order Theory
 Internal Financing
 External Financing

Debt Financing

Equity Financing (last resort)
 Asymmetric information and Signaling
 Dynamic decision, rather than static
8-14
Valuation
 Weighted Average Cost of Capital

All Cash Flows discounted by discount rate that takes
into account leverage
 Adjusted Present Value

Separate cash flows from project and cash flows from
financing
 Flow-to-Equity Approach

Cash flows to equity holders discounted by the cost
of equity
8-15
Example
8-16
 You are considering a project with the following
characteristics:

Perpetual cash inflows starting in year 1 of $25,000 per year

Yearly operating expenses of 12% of revenues

Initial investment outlay of $125,000

Tc=34% and r0=14%, rD=8%
 Calculate the NPV for an all-equity firm
 Calculate the NPV for a firm with a target capital structure
of 65% debt and 35% equity

Use WACC method

Use APV method

Use FTE method
Answers
 Unlevered firm valuation
To the
shareholders
Cash Inflows
$25,000
Operating Expenses
$ 3,000
Operating Income
$22,000
Tax
$ 7,480
Unlevered Cash Flow (UCF) $14,520
NPV = –$125,000 + ($14,520 / 0.14) = –$21,286
8-17
Answer
 WACC
rWACC = (D/V) × (1–Tc) × rD + (E/V) × rE
rWACC = (0.65) × (1– 0.34) × 0.08 + (0.35) × rE
rE = r0 + (D/E) × (1 – Tc) × (r0 – rD)
rE = 0.14 + (65/35) × (1 – 0.34) × (0.06) = 0.2135 = 21.35%
rWACC = (0.65) × (1– 0.34) × 0.08 + (0.35) × 0.2135 = 10.906%
NPV = –$125,000 + ($14,520 / 0.10906) = $8,138
8-18
Answer
 APV
8-19
NPV of Financing Side Effects
APV = NPV + NPVF
NPVF = Tc × D
APV = –$21,286 + (0.34 × 0.65 × (APV + $125,000))
0.779 × APV = $6,339
APV = $8,138
Verify the target capital structure:
Firm borrows 0.65 × ($125,000 + $8,138)
Firm borrows 0.65 × $133,137 = $86,539.52
Firm uses $125,000 – $86,539.52 = $38,460.48 in equity
Answer
8-20
VL = VU + Tc × D
VL = 125,000 – 21,286 + 0.34 × 0.65 × VL
VL = 133,138  D = 0.65 × 133,138
 FTE method
To the
shareholders
Cash Inflows
Operating Expenses
Operating Income
Interest (8% of $86,539.52)
Income after interest
Tax
Levered Cash Flow (LCF)
$25,000
$ 3,000
$22,000
$ 6,923
$15,077
$ 5,126
$ 9,951
From before, rE = 21.35% and PV = $9,951 / 0.2135 = $46,609
NPV = – $38,460 + $46,598 = $8,138
Evaluation
8-21
 Valuation for all-equity firm is easy
 Valuation for levered firm is complex

tax shields

bankruptcy, agency, and other costs
 WACC, APV, and FTE method

constant risk over life of project (constant r0)

constant debt/value ratio over life of project (constant rE and rWACC)

FTE and WACC work well under this scenario

if debt/value ratio is changing use APV (based on the level of debt)

APV works well for LBO’s and cases with interest subsidies and
flotation costs (see example in Appendix 17A).
Beta revisited
 Remember the following:

Levered Equity = L = Unlevered Assets × (1 + (D/E))

Assumes Debt = 0 and no corporate taxes
 With corporate taxes (assume Debt = 0):

L = U × [1 + (1–Tc) × (D/E)]

Unlevered Firm < Levered Equity
Remember: RE > R0 > RD
8-22
What if Beta of debt  0?
 L = U + [(1–Tc) × (U – D) × (D/E)]
L = levered equity
U = unlevered equity (100% equity firm)
D = debt
E = equity
8-23