CAPITAL BUDGETING WITH
LEVERAGE
Introduction


Discuss three approaches to valuing a risky project that uses
debt and equity financing.
Initial Assumptions

The project has average risk.


The firm’s debt-equity ratio is constant.


For convenience the betas or costs of capital used will be for the
existing firm rather than being project specific.
This simplifies the application in that we don’t need to worry about
changing costs of capital and fixes the adjustment of our risk measure
for leverage.
Corporate taxes are the only imperfection.

No agency, bankruptcy or issuance costs to quantify.
The Weighted Average Cost
of Capital Method
rw acc 
E
E  D
rE 
D
E  D
rD (1   c )
 Because
the WACC incorporates the tax savings from
debt, we can compute the levered value (V for enterprise
value, L for leverage) of an investment, by discounting its
future expected free cash flow using the WACC.
V
L
0

F C F1
1  rw acc

F C F2
(1  rw acc )
2

F C F3
(1  rw acc )
3

Valuing a Project with WACC

Ralph Inc. is considering introducing a new type of
chew toy for dogs.
 Ralph
expects the toys to become obsolete after five
years when it will be discovered that chew toys only
encourage dogs to eat shoes. However, the marketing
group expects annual sales of $40 million for the first
year, increasing by $10 million per year for the
following four years.
 Manufacturing
costs and operating expenses (excluding
depreciation) are expected to be 40% of sales and $7
million, respectively, each year.
Valuing a Project with WACC
 Developing
the product will require upfront R&D and
marketing expenses of $8 million. The fixed assets
necessary to produce the product will require an
additional investment of $20 million.
 The
equipment will be obsolete once production ceases and
(for simplicity) will be depreciated via the straight-line
method over the five year period.
 Ralph
expects no incremental net working capital
requirements for the project.
 Ralph
has a target of 60% Equity financing.
 Ralph
pays a corporate tax rate of 35%.
Expected Future Free Cash Flow
"Income Statement:" Year
Sales
COGS
Gross Profit
Operating Expenses
Depreciation Exp
EBIT
Tax (35%)
Unlevered NI
Free Cash Flow:
Unlevered NI
Plus Deprecition Exp
Less Net Cap Ex
Less Changes in NWC
Free Cash Flow
0
-8.00
-2.80
-5.20
1
40.00
16.00
24.00
7.00
4.00
13.00
4.55
8.45
2
50.00
20.00
30.00
7.00
4.00
19.00
6.65
12.35
3
60.00
24.00
36.00
7.00
4.00
25.00
8.75
16.25
4
70.00
28.00
42.00
7.00
4.00
31.00
10.85
20.15
5
80.00
32.00
48.00
7.00
4.00
37.00
12.95
24.05
-5.20
0.00
20.00
0.00
-25.20
8.45
4.00
0.00
0.00
12.45
12.35
4.00
0.00
0.00
16.35
16.25
4.00
0.00
0.00
20.25
20.15
4.00
0.00
0.00
24.15
24.05
4.00
0.00
0.00
28.05
8.00
“Market Value” Balance Sheet
Assets
Excess Cash
$ 50.00
Existing Assets $ 850.00
Total Assets

$ 900.00
Liabilities
Debt
$ 390.00
Equity
$ 510.00
Total Liabilities
and Equity
$ 900.00
Cost of Capital
Debt
5%
Equity
12%
Risk Free
4%
The firm is currently at its target leverage:
 Equity
to Net Debt plus Equity ratio is:
$510.00/($510.00 + $390.00 - $50.00) = 60.0%
Valuing a Project with WACC

Ralph intends to maintain a similar (net) debt-equity
ratio for the foreseeable future, including any
financing related to the project. Thus, Ralph’s WACC
is:
rw acc 

E
E  D
510
rE 
(12% ) 
850
 8 .5%
D
E  D
340
850
rD (1   c )
(5% )(1  0.35)
Valuing a Project with WACC

The value of the project, including the tax shield
from debt, is calculated as the present value of its
future free cash flows discounted at the WACC.
V
L
0

12.45
1.0 85

16.35
1.0 85
2

20.25
1.0 85
3

24.15
1.0 85
4
28.05
+
1.085
5
 $77.30 m illion
 The
NPV (value added) of the project is $52.10 million

$77.30 million – $25.20 million = $52.10 million

It is important to remember the difference between value and
value added.
Summary of the WACC Method
1.
Determine the free cash flow of the investment.
2.
Compute the weighted average cost of capital.
3.
4.
Compute the value of the investment, including the tax
benefit of leverage, by discounting the free cash flow
of the investment using the WACC.
The WACC can be used throughout the firm as the
companywide cost of capital for new investments that
are of comparable risk to the rest of the firm and that
will not alter the firm’s debt-equity ratio.
Implementing a Constant Debt-Equity Ratio

By undertaking the project, Ralph adds new assets
to the firm with an initial market value $77.30
million.
 Therefore,
to maintain the target debt-to-value ratio,
Ralph must add $30.92 million in new debt.
 40%
× $77.30 = $30.92
 60%
× $77.30 = $46.38 (compare to $52.10)
Implementing a Constant Debt-Equity Ratio

Ralph can add (net) debt in this amount either by
reducing cash and/or by borrowing and increasing
actual debt.

Suppose Ralph decides to spend $25.20 million (cover the
negative FCF in year 0) in cash to initiate the project.

This increases net debt by $25.20 million
Assets
Excess Cash
$ 24.80
Existing Assets $ 850.00
New Project
$ 77.30
Total Assets
$ 952.10
Liabilities
Debt
$ 390.00
Equity
$ 562.10
Total Liabilities
and Equity
$ 952.10
% of Total Value
Debt
39.4%
Equity
60.6%
New Market Value Balance Sheet


We need an increase in net debt of $30.92.
Spend $25.20 million on the project and pay a
$5.72 million dividend so $30.92 million in cash
goes out (this further increases net debt and reduces
equity by the required amount).
Assets
Excess Cash
$ 19.08
Existing Assets $ 850.00
New Project
$ 77.30
Total Assets
$ 946.38
Liabilities
Debt
$ 390.00
Equity
$ 556.38
Total Liabilities
and Equity
$ 946.38
% of Total Value
Debt
40.0%
Equity
60.0%
Implementing a Constant Debt-Equity Ratio

The market value of Ralph’s equity increases by $46.38
million.


$556.38 − $510.00 = $46.38 (60% of $77.30)
Adding the dividend of $5.72 million into the mix, the
shareholders’ total gain is $52.10 million.
$46.38 + 5.72 = $52.10
 Which is exactly the NPV calculated for the project
 Alternatively: without the dividend the equity increased by
the project’s NPV of $52.10 = $562.10 - $510.00. This is
too large an increase in equity, given the increase in debt of
$25.20, if Ralph is to maintain 60% equity.

Implementing a Constant Debt-Equity Ratio

Debt Capacity
 The
amount of debt at a particular date that is
required to maintain the firm’s target debt-to-value
ratio
 The
debt capacity at date t is calculated as:
D t  d  Vt
L
d is the firm’s target debt-to-value ratio and VLt is
the project’s levered continuation value on date t.
 Where
Implementing a Constant Debt-Equity Ratio

Debt Capacity
 VLt
Vt
L
calculated as:

F C Ft
 1
V alue of F C F in year t  2 and beyond

V
1  rw acc
L
t  1
Debt Capacity


In order to maintain the target financing, the amount
of new debt must fall over the life of the project.
This is true because the value of the project
depends upon the future cash flow at each point in
time. Since the project ends, value decreases. Since
value decreases, debt must also decrease.
year
Free Cash Flow
Levered Value
Debt Capacity d = 40%
0
1
2
3
4
5
$ (25.20) $ 12.45 $16.35 $20.25 $24.15 $ 28.05
$ 77.30 $ 71.42 $61.14 $46.09 $25.85 $ $ 30.92 $ 28.57 $24.46 $18.43 $10.34 $ -
The Adjusted Present Value Method

Adjusted Present Value (APV)
A
valuation method to determine the levered value
of an investment by first calculating its unlevered
value and then adding the value of the interest tax
shield and deducting any costs that arise from other
market imperfections
V
L
 APV
 V
U
 PV (Interest T ax Shield)
 PV (Financial D istress, Agency, and Issuance C osts)
The Unlevered Value of the Project

The first step in the APV method is to calculate the
value of the free cash flows using the project’s cost
of capital if it were financed without leverage.
The Unlevered Value of the Project

Unlevered Cost of Capital
 The
cost of capital of a firm, were it unlevered:
for a firm that maintains a target leverage ratio, it
can be estimated (recall the picture) as the weighted
average cost of capital computed without taking into
account taxes (pre-tax WACC).
rU

E
E  D
 This
rE 
D
E  D
rD  P retax W A C C
is, strictly speaking, only true for firms that adjust their
debt to maintain a target leverage ratio.
The Unlevered Value of the Project

For Ralph, the unlevered cost of capital is calculated
as:
 0.60  12.0%  0.40  5.0%
rU
 9.2%

The project’s value without leverage is then
calculated as:
V
U

12.45
1.0 92

16.35
1.0 92
 $75.71 m illion
2

20.25
1.0 92
3

24.15
1.0 92
4
+
28.05
1.092
5
Valuing the Interest Tax Shield

The value of $75.71 million is the value of the
unlevered project and does not include the value of
the tax shield provided by the interest payments on
debt.
Interest paid in year t  rD  D t
 The
 1
interest tax shield is equal to the interest paid multiplied
by the corporate tax rate.
Interest Tax Shield

From the debt capacity calculation we can find the
interest associated with the project if the financing is
kept at the target.
year
Free Cash Flow
Levered Value
Debt Capacity d = 40%
Interest
Interest Tax Shield
0
$ (25.20)
$ 77.30
$ 30.92
$ $ -
1
$ 12.45
$ 71.42
$ 28.57
$ 1.55
$ 0.54
2
$16.35
$61.14
$24.46
$ 1.43
$ 0.50
3
$20.25
$46.09
$18.43
$ 1.22
$ 0.43
4
$24.15
$25.85
$10.34
$ 0.92
$ 0.32
5
$ 28.05
$ $ $ 0.52
$ 0.18
Valuing the Interest Tax Shield

The next step is to find the present value of the
interest tax shield.
 When
the firm maintains a target leverage ratio, its
future interest tax shields have similar risk to the project’s
cash flows, so they should be discounted at the project’s
unlevered cost of capital.
P V (interest tax shield) 
0. 54
1.0 92

0.5 0
1.0 92
 $1.59 m illion
2

0. 43
1.0 92
3

0. 32
1.0 92
4
+
0.18
1.092
5
Valuing the Project with Leverage

The total value of the project with leverage is the
sum of the value of the interest tax shield and the
value of the unlevered project.
V
L
 V
U
 P V (interest tax shield)
 75.71  1.59  $77.30 m illion
 The
NPV of the project is $52.10 million
 $77.30

million – $25.20 million = $52.10 million
This is exactly the same value found using the WACC approach.
Summary of the APV Method
1.
2.
Determine the investment’s value
without leverage.
Determine the present value of the interest
tax shield.
a.
b.
3.
Determine the expected interest tax shield.
Discount the interest tax shield.
Add the unlevered value to the present value of
the interest tax shield to determine the value of
the investment with leverage.
Summary of the APV Method

The APV method has some advantages.
 It
can be easier to apply than the WACC method when
the firm does not maintain a constant debt-equity ratio.
 The
APV approach also explicitly values market
imperfections and therefore allows managers to
measure their contribution to value.
The Flow-to-Equity Method

Flow-to-Equity
A
valuation method that calculates the free cash flow
available to equity holders taking into account all
payments to and from debt holders.
 Free
Cash Flow to Equity (FCFE), the free cash flow that
remains after adjusting for interest payments, debt issuance
and debt repayments
 The
cash flows to equity holders are then discounted
using the equity cost of capital.
Free Cash Flow to Equity
Free Cash Flow to Equity
Year
Unlevered NI
Less After Tax Interest
Plus Depr
Less Net Cap Ex
Less Change in NWC
Plus Net Borrowing
Free Cash Flow to Equity
$
$
$
$
$
$
$
0
(5.20)
20.00
30.92
5.72
$
$
$
$
$
$
$
1
8.45
1.00
4.00
(2.35)
9.09
$
$
$
$
$
$
$
2
12.35
0.93
4.00
(4.11)
11.31
$
$
$
$
$
$
$
3
16.25
0.79
4.00
(6.02)
13.43
$
$
$
$
$
$
$
4
20.15
0.60
4.00
(8.09)
15.46
5
$ 24.05
$ 0.34
$ 4.00
$ $ $ (10.34)
$ 17.37
Valuing the Equity Cash Flows

Because the FCFE represent payments to equity holders,
they should be discounted at the project’s equity cost of
capital.

Given that the risk and leverage of the project are the same
as for Ralph Inc. overall, we can use Ralph’s equity cost of
capital of 12.0% to discount the project’s FCFE.
N P V ( F C F E )  5.72 
9.09
1.1 2

11.31
1.1 2
2

13.43
1.1 2
3

15.46
1.1 2
4
+
17.37
1.12
5
 $52.10 m illion

The value of the project’s FCFE represents the gain to shareholders
from the project and it is identical to the NPV computed using the
WACC and APV methods. (The debt is sold at a fair price.)
Project-Based Costs of Capital


In the real world, a specific project may have
different market risk than the average project for
the firm.
In addition, different projects will may also vary in
the amount of leverage they will support.
Estimating the Unlevered Cost of Capital

Suppose the project Ralph launches faces different
market risks than its main business.
 The
unlevered cost of capital for the new project can
be estimated by looking at publicly traded, pure play
firms that have similar business risks.
Estimating the Unlevered Cost of Capital

Assume two firms are comparable to the chew toy
project in terms of basic business risk and have the
following observable characteristics:
Firm
Equity Beta
Debt Beta
Debt-to-Value
Ratio
Firm A
1.7
0.05
40%
Firm B
1.9
0.10
50%
Estimating the Unlevered Cost
of Capital using Betas

We now find their unlevered or asset betas:




A
U
B
U
E

E
A
D
E

E
B
A
A

A
E
D

E
A
B
D
B

B
E
E
B
A
D 
B
D 
A
D
D

A
B
D
B
0.6
0.6  0.4
0.5
0.5  0.5
1.7 
1.9 
0.4
0.6  0.4
0.5
0.5  0.5
0.05  1.04
0.1  1.0
An average of these unlevered betas is 1.02.
Note, an unlevered beta of 1.02 gives an unlevered
cost of equity capital of:
rU  r f   U ( R P )  4%  1.02(6% )  10.12%
Project Leverage
and the Equity Cost of Capital


Now assume that Ralph plans to maintain a 20% debt
to value ratio for its chew toy project, and it expects its
borrowing cost to be 4%.
We now “relever” the unlevered beta estimate of 1.02
and using the SML we find the cost of levered equity:
 E  U 
D
E
(  U   D )  1.02 
0.2
(1.02  0.0)  1.275
0.8
rE  r f   E ( R P )  4%  1.275(6% )  11.65%

A cost of debt capital of 4% is consistent with the low
leverage chosen and a debt beta of 0.
Project Leverage and the
Weighted Average Cost of Capital

With a 20% debt to value ratio, a cost of equity
capital of 11.65%, and a cost of debt capital of
4% we can now estimate the WACC for the project.
rW A C C 
0.8
0.8  0.2
11.65% 
0.2
0.8  0.2
4% (1  0.35)  9.84
An Alternate Approach


From the observable (or measurable) data we can
get estimates of the cost of equity capital and the
cost of debt capital:
Firm A:
rE  4%  1.7  6%  14.2%
rD  4%  0.05  6%  4.3%

Firm B:
rE  4%  1.9  6%  15.4%
rD  4%  0.1  6%  4.6%
An Alternate Approach

Recall the relation between the levered cost of equity
capital and the unlevered cost of equity capital:
rE

( rU  rD )
E
Rearranging this we find:
rU 

 rU 
D
E
ED
rE 
D
ED
rD  pre-tax W A C C
In other words, the unlevered cost of equity capital
equals the pre-tax WACC
Estimating the Unlevered Cost of Capital

Assuming that both firms maintain a target leverage
ratio, the unlevered cost of capital for each
competitor can be estimated by calculating their
pretax WACC.
Firm A: rU
 0.60  14.2%  0.40  4.3%  10.24 %
Firm B: rU
 0.50  15.4%  0.50  4.6%  10.0%

Based on these comparable firms, we estimate an
unlevered cost of capital for the project that is
approximately 10.12%.
Project Leverage
and the Equity Cost of Capital

Ralph plans to maintain a 20% debt to value ratio
for its chew toy project, and it expects its borrowing
cost to be 4%.
 Given
the unlevered cost of capital estimate of
10.12%, the chew toy division’s equity cost of capital is
estimated to be:
rE
 10.12% 
0.20
0.80
 11.65%
(10.12%  4% )
Project Leverage and the
Weighted Average Cost of Capital

The division’s WACC can now be estimated to be:
rW A C C
 0.80  11.65%  0.20  4.0%  (1  0.35)
 9.84%

An alternative method for calculating the chew toy
division’s WACC is:
rW A C C
 rU  d  c rD
 10.12%  0.20  0.35  4%
 9.84%