VALUATION AND CAPITAL BUDGETING FOR THE LEVERED FIRM
The goal of this topic is to value a project or the firm its, when leverage is
employeed
There are three standard approaches to valuation under leverage : (all
three approaches provide the same value estimate)
1. The adjusted present value (APV) method,
2. The flow-to –equity (FTE) method,
3. The weighted-average-cost-of-capital (WACC) method.
1. The adjusted present value (APV) method
APV = NPV + NPVF
APV : The value of the project to a levered firm
NPV : The value of the project to an unlevered firm
NPVF : The net present value of the financing side effects
There are four side effects :
a. The Tax Subsidy To Debt (TCB)
b. The Cost Of Issuing New Securities
c. The Cost Of Financial Distress
d. Subsidies To Debt Financing
1
Example (considers the tax subsidy), but not the other three side effects.
Assume, a Project of the P.B. Singer Co, with characteristics :
Cash inflows : $500,000 per year for the indefinite future
Cash costs : 72% of sales ; Initial investment : $475,000
TC : 34% ; rO : 20% (the cost of capital for all-equity firm)
If both the project and the firm are financed with only equity, the project’s
cash flow is
Cash inflows
$500,000
Cash costs
-360,000
Operating income
140,000
Corporate tax (0,34 tax rate)
-47,600
Unlevered cash flow (UCF)
$92,400
Given a discount rate or 20%, the PV of the project is
$92,400/0.20 = $462,000
2
The NPV of the project, that is, the value of the project to an all-equity
firm, is
$462,000 - $475,000 = -$13,000 (The project would be rejected
by an all-equity firm)
Assume, the firm finances the project with exactly $126,229.50 in debt,
so that remaining investment of $348,770.50 ($475,000 - $126,229.50)
is financed with equity.
APV = NPV + TCxB
$29,918 = -$13,000 + 0,34 x $126,229.50 (accepted project)
2. Flow-To-Equity Approach (FTE) approach is an alternative capitalbudgeting approach.
FTE = Cash flow from project to equityholders of the levered
rs (cost of equity capital)
3
There are three steps to the FTE approach.
Step 1 : Calculating Levered Cash Flow (LCF)
Assuming an interest rate of 10%, the perpetual cash flow to
equityholders in our example is
Cash inflows
Cash costs
Interest (10% x $126,229.50)
Income after interest
Corporate tax (0.34 tax rate)
Levered cash flow (LCF)
$500,000.00
-360,000.00
-12,622.95
127,377.05
-43,308.20
$84,068.85
UCF – LCF = (1 - TC) rBB
UCF- (1 - TC ) rBB = LCF
$92,400 – (1 -0.34)x 0.10 x $126,229.50 = $84,068.85
4
Step 2. Calculating rs
Assume, ro =20% ; debt to value ratio of ¼ implies a target debtto-equity ratio of 1/3. The formula for rs is
rs = ro +
B (1- T ) ( r - r )
C
o
B
S
rs = 0.20 + 1/3. (0.66) (0.20 – 0.10) = 0.222
Step 3. Valuation
The present value of the project’s LCF is
LCF $84,068,85

 $378,688.50
rs
0.222
The NPV of the project is simply the difference between the PV of the
project’s LCF and the investment not borrowed. So, NPV is
$378,688.50 – ($475,000 - $126,229.50) = $29,918
5
3. Weighted-Average-Cost-Of-Capital Method
The WACC approach begins with the insight that projects of levered
firms are simultaneously with both debt and equity.
The formula rWACC is
rW ACC 
S
B
rS 
rB 1 - TC 
SB
SB
The NPV of the project can be written is



  UCFt / 1  rW ACC  - Initial investment
t 1
t
If the project is a perpetuity, the NPV is
[UCF / rWACC ] – Initial investment
rWACC = ¾ x 0.22 + ¼ x 0.10 (0.66) = 0.183
The NPV of the project is
[$92,400/0.183] - $475,000 = $29,918
6
# A COMPARISON OF THE APV, FTE, AND WACC APPROACHES
− The APV approaches first values the project on an all-equity basis.
− The FTE approaches discounts the after-tax cash flow from a project
going to the equityholders of a levered firm (LCF)
− The WACC calculates the project’s after-tax cash flows assuming allequity financing (UCF).
− All three approaches perform the same task : valuation in the
presence of debt financing.
− APV & WACC display the greatest similarity.
− The FTE approach, the future cash flows to the levered
equityholders (LCF) are valued.
7
THE THREE METHODS OF CAPITAL BUDGETING WITH LEVERAGE
1. Adjusted-Present-Value (APV) Method

UCF
 1  r 
t 1
t
 Additional effects of debt Initial investment
0
UCFt = The project’s cash flow at date t to the equityholders of an unlevered firm
r0
= Cost of capital for project in an unlevered firm
2. Flow-to-Equity (FTE) Method

LCF
 1  r 
t 1
t
- (Initial investment - Amount borrowed)
S
LCFt = The project’s cash flow at date t to the equityholders of a levered firm
rs
= Cost of equity capital with leverage
3. Weighted-Average-Cost-Of-Capital (WACC) Method
UCF
 1  r  - Initial investment

t
t 1
t
WACC
rWACC = Weighted average cost of capital
Notes :
1. The middle term in the APV formula implies that the value of a project with leverage is greater than value of the project
without leverage. Since rWACC < r0 the WACC formula implies that the value of a project with leverage is greater than the
value of the project without leverage.
2. In the FTE method, cash flow after interest (LCF) is used. Initial investment is reduced by amount borrowed as well.
Guidelines :
1. Use WACC or FTE if the firm’s target debt-to-value ratio applies to the project over its life.
2. Use APV if the project’s lebel of debt is known over the life of the project.
8
# CAPITAL BUDGETING WHEN THE DISCOUNT RATE MUST BE
ESTIMATED
Example : WWE is a large conglomerate thinking of entering the widget
business, where it plans to finance projects with a debt-to-value ratio of
25% (a debt-to-equity-ratio of 1/3). There is currently one firm in the
widget industry, (AW). This firm is financed with 40% debt & 60% equity.
The beta of AW’s equity is 1.5. AW has a borrowing rate of 12%, &
WWE expects to borrow for its widget venture at 10%. TC is 40%, the
market risk premium is 8.5%, and Rf is 8%. What is the appropriate
discount rate ( ro, rs, & WACC) for WWE to use for its widget venture?
The four step procedure will allow us to calculate all three discount
rates.
1. Determining AW’s Cost of Equity Capital (using the SML)
AW’s cost of Equity Capital :
rs = RF + (RM – RF)
20.75%= 8% + 1.5 x 8.5%
9
2. Determining AW’s Hypothetical All-Equity Cost of Capital
AW’s cost of capital if All-Equity : (MM Proposition II under taxes)
rS = rO + B (1 - TC ) (rO – rB )
S
20.75% = ro + (0.4/0.6) (0.60) (rO – 12%)
rO = 0.1825
3. Determining rs for WWE’s Widget Venture. Using the FTE, where the
discount rate for levered equity is determined from :
Cost of Equity Capital for WWE’s Widget Venture:
rS  rO 
B
(1  TC )( rO  rB )
S
rs = 18.25% + 1/3(0.60) (18.25% - 10%) = 19.9% < cost of
equity capital for AW, 0.2075
4. Determining rWACC for WWE’sWidget Venture:
rW ACC 
S
B
rS 
rS 1 - TC 
SB
SB
rWACC = (3/4) 19.9% + (1/4) (10%) (0.60) = 16.425%
10
# APV EXAMPLE
Bicksler Enterprises is considering a $10 million project that will last five years, implying
straight-line depreciation per year of $2 million. The cash revenues less cash expenses
per year are $3,500,000. TC is 34%, Rf is 10%, & the cost of unlevered equity is 20%.
C0
Initial outlay
C1
C2
C3
C4
C5
-$10,000,000
Depreciation tax shield
0.34 X $2,000,000
= $680,000
$680,000
$680,000
$680,000
$680,000
Revenue less expenses
(1-0.34) X 3,500,000
= $2,310,000
$2,310,000
$2,310,000
$2,310,000
$2,310,000
We stated before that the APV of a project is the sum of its all-equity value plus the
additional effects of debt. We examine each in turn.
All-Equity Effects Value
Assuming the project is financed with all equity, the value of the project is
 $10,000,000 
Initial cost
$680,000   1   $2,310,000   1  
x 1 - 
 1  
5 
5   $513,951
0.10
1.10
0
.
20
1
.
20



 



Depreciation tax shield
Presentvalue of (Cash revenues – Cash expenses)
11
Additional Effects of Debt
Bicksler enterprises can obtain a five-year, nonamortizing loan for
$7,500,000 after flotation costs at the risk-free of 10 percent. Flotation costs
are fees paid when stock or debt is issued.
Flotation Costs Given that flotation costs are 1 percent of the gross
proceeds,we have
$7,500,000 = (1 – 0.01) x Gross proceeds = 0.99 x Gross proceeds
Thus, the gross proceeds are
$7,500,000 $7,500,000

 $7,575,758
1 - 0.01
0.99
This implies flotation costs of $75,758 (1% x $7,575,758). To check the
calculation, note that net proceeds are $7,500,000 ($7,575,758 - $75,758).
Date 0
Flotation cost
Date 1
Date 3
Date 4
Date 5
$15,152
$15,152
$15,152
$15,152
$5,152
$5,152
$5,152
$5,152
-$75,758
Deduction
$15,152 = $75,758
5
Tax shield from
0.34 x $15,152
Flotation costs
Date 2
= $5,152
12
The relevant cash flows from flotation costs are in boldface. When
discounting at 10 percent, the tax shield has a net present value of
$5,152 x A50.05 = $19,530
This implies a net cost of flotation of
-$75,758 + $19,530 = -$56,228
The net present value of the project after the flotation costs of debt but
before the benefits of debt is
-$513,951 - $56,228 = $570,179
Interest cost after tax is $500.000 [$757.576 x (1 – 0.34)]. Because the
loan is nonamortizing, the entire debt of $7,575,758 is repaid at date 5.
These terms are indicated below:
13
Date 0
Loan (gross
Date 1
Date 2
Date 3
Date 4
Date 5
$7,575,758
proceeds)
Interest paid
10% x $7,575,758
$757,576
$757,576
$757,576
$757,576
$500,000
$500,000
$500,000
$500,000
= $757,576
Interest cost
(1-0.34) x $757,576
after tax
= $500,000
Repayment of debt
NPV (Loan) = +
$7,575,758
Present value
Amount
borrowed - of after-tax
interest
payments
Present
- value of loan
repayments
The calculation for this example are
5
$500,000   1   $7,575,758
$976.415   $7,575,758 x 1 - 
 .010
1.10
 
1.105
 
14
The NPV (Loan) is positive, reflecting the interest tax shield.
The adjusted present value of the project with this financing is
APV
$406,236
= All-equity value – flotation costs of debt + NPV (Loan)
=
-$513,951 $56,228
+ $976,415
Though we previously saw that an all-equity firm would reject the project, a
firm would accept the project if a $7,500,000 (net) loan could be obtained.
Non-Market-Rate Financing
A number of companies are fortunate
enough to obtain subsidized financing from a governmental authority.
Suppose that the project of Bicksler Enterprises is deemed socially
beneficial and the state of New Jersey.
Grants the firm a $7,500,000 loan at 8-percent interest. In addition, all
flotation costs are absorbed by the state. Clearly, the company will
choose this loan over the one we previously calculate. The cash flows
from the loan are
15
Date 0
Loan received
Taxrest paid
Date 1
Date 2
Date 3
Date 4
Date 5
$7,500,000
8% x $7,500,000
$600,000
$600,000
$600,000
$ 600,000
$396,000
$396,000
$396,000
$ 396,000
= $600,000
After-tax interest
(1- 0.34) x $600,000
= $396,000
Repayment of debt
$7,500,000
The relevant cash flows are listed in boldface in the preceeding table.
Using equation (17.1), the NPV (Loan) is
5
$396,000   1   $7,500,000
$1,341,939   $7,500,000 x 1 - 
 0.10
(1.10) 5
  1.10  
APV = All-equity value – Floatation costs of debt + NPV (Loan)
+$827,988 = -$513,951 0
+ $1.341,939
16
# BETA AND LEVERAGE
The No-Tax Case (The relationship between the beta of the
common stock and leverage of the firm in a world without taxes :
Assumption that the beta of debt is zero.
Equity = Asset (1 + Debt/Equity)
The corporate-Tax Case: (The relationship between the beta
of the unlevered firm and beta of the leverage equity) is
Equity = (1 + (1- TC )Debt/Equity)Unlevered firm
17
EXAMPLE
C.F. Lee Incorporated is considering a scale-enhancing project. The market value of
the firm’s equity is $200 million. The debt is considered riskless. The corporate tax rate
is 34 percent. Regression analysis indicates that the beta of the firm’s equity is 2. the
risk-free rate is 10 percent, and the expected market premium is 8.5 percent. What
would the project’s discount rate be in the hypothetical case that C.F. Lee, Inc., is allequity?
We can answer this question in two steps.
1. Determining Beta of Hypothetical All-Equity Firm. Rearranging
equation (17.4), we have
Unlevered Beta
Equity
x  Equity   Unlevered firm
Equity  1 - TC  x Debt
$200 Million
x 2  1.50
$200 Million  (1 - 0.34) x $100 Million
18
2. Determining Discount Rate. We calculate the discount rate from the
security market line (SML) as
Discount Rate:
rS  RF   RM - R F 
EXAMPLE
The J. Lowes Corporation, which currently manufactures staples, is considering
a $1 million investment in a project in the aircraft adhesives industry. The
corporation estimates unlevered after-tax cash flows (UCF) of $300,000 per year
into per-perpetuity from the project. The firm will finance the project with a debtto-value ratio of (or, equivalently a debt-to-equity ratio of 1:1).
The three competitors in this new industry are currently unlevered,
with betas of 1.2, 1.3, and 1.4. Assuming a risk-free rate of 5 percent, a marketrisk premium of 9 percent, and a corporate tax rate of 34 percent, what is the net
present value of the project?
19
We can answer this question in five steps.
1. Calculating the Average Unlevered Beta in the Industry. The average
unlevered beta across all three existing competitors in the aircraft
adhesives industry is
1.2  1.3  1.4
 1.3
3
2. Calculating the Levered Beta for J. Lower’s New Project. Assuming the
same unlevered beta for this new project as for the existing competitors,
we have, from equation (17.4),
Levered Beta:

 Equity  1 

(1 - TC ) Debt 
β Unlevered firm
Equity

 0.66 x 1 
2.16  1 
 x 1.3
1


20
3. Calculating the Cost of Levered Equity for the New Project. We can
calculate the discount rate from the security market line (SML) as
Discount Rate:
rs  RF   R M - RF 
0.244  0.05  2.16 x 0.09
4. Calculating the WACC for the New Project. The formula for determining
the weighted average cost of capital, rWACC is
rW ACC 
B
B
rB (1 - TC) rS
V
V
1
1
0.139  x 0.05 x 0.66  x 0.244
2
2
5. Determining the Project’s Value. Because the cash flows are perpetual,
the NPV of the project is
Unlevered cash flows (UCF)
- Initial investment
rWACC
$300,000
- $1 million  $1.16 million
0.139
21
DIVIDEND POLICY
− The term dividend usually refers to a cash distribution of earnings.
− Public companies usually pay regular cash dividends four times a
year.
− The amount of the dividend is expressed as dollars per share
(dividend per share), as a percentage of the market price (dividend
yield), or as a percentage of earnings per share (dividend payout).
22
Standard Method of Cash Dividend Payment
FIGURE 18.1 Example of Procedure for Dividend Payment
Days
1.
2.
3.
4.
Thursday,
January
15
Wednesday,
January
28
Declaration
date
Ex-dividend
date
Friday,
January
30
Record
date
Monday,
February
16
Payment
date
Declaration Date: The board or directors declares a payment of dividends.
Record Date: A share of stock becomes ex-dividend on the date the seller is entitled to
keep the dividends are distributable to shareholders of record on a specific date.
Ex-dividend Date: A share of stock becomes ex-dividend on the date the seller is entitled to
keep the dividend; under NYSE rules, shares are traded ex-dividend on and after the
second business day before the record date.
Payment Date: The dividend checks are mailed to shareholders of record.
23
FIGURE 18.2
Dividend
Price Behavior around the Ex-dividend Date for a $1 Cash
Perfect-world case
Ex-date
Price = $(P+1)
-t

-2
-1
0
+1
+2

t
$1 is the ex-dividend price drop
Price = $P
The stock price will fall by the amount of the dividend on the ex-date (time 0).
If the dividend is $1 per share, the price will be equal to P on the ex-date.
Before ex-date (-1) Price = $(P + 1)
Ex-date (0)
Price = $P
24