NPV
1
NPV
• There are three ways to apply the NPV
principle
• Weighted Average Cost of Capital (WACC)
• Adjusted Present Value (APV)
• Flow to Equity (FTE)
2
NPV
WACC
• Work out the WACC using the after tax cost of
debt
• Rwacc = E re + D rd (1-Tc)
E+D
E+D
E = market value of equity
D = market value of debt
Tc = marginal corporate tax rate
re = equity cost of capital
rd = debt cost of capital
3
NPV
WACC
rwacc
E
D

rE 
rD (1   c )
E  D
E  D
– Because the WACC incorporates the tax
savings from debt, we can compute the levered
value of an investment, by discounting its future
free cash flow using the WACC.
L
0
V
FCF3
FCF1
FCF2




2
3
1  rwacc
(1  rwacc )
(1  rwacc )
4
NPV
WACC
Assume Avco is considering introducing a new line of packaging, the RFX
Series.
Avco expects the technology used in these products to become
obsolete after four years. However, the marketing group expects annual
sales of $60 million per year over the next four years for this product
line.
Manufacturing costs and operating expenses are expected to be $25
million and $9 million, respectively, per year.
5
NPV
WACC
– Developing the product will require upfront
R&D and marketing expenses of $6.67
million, together with a $24 million investment
in equipment.
• The equipment will be obsolete in four years and
will be depreciated via the straight-line method
over that period.
– Avco expects no net working capital
requirements for the project.
– Avco pays a corporate tax rate of 40%.
6
NPV
WACC
7
NPV
WACC
NB Net debt used i.e. less cash
8
NPV
WACC
• Avco intends to maintain a similar (net)
debt-equity ratio for the foreseeable future,
including any financing related to the RFX
project. Thus, Avco’s WACC is
rwacc
E
D
300
300

rE 
rD (1   c ) 
(10%) 
(6%)(1  0.40)
E D
E D
600
600
 6.8%
9
NPV
WACC
• The value of the project, including the tax
shield from debt, is calculated as the
present value of its future free cash flows.
V0L 
18
18
18
18



 $61.25 million
2
3
1.068
1.068
1.068
1.0684
• The NPV of the project is $33.25 million
$61.25 million – $28 million = $33.25 million
10
NPV
WACC
Implementing a Constant Debt-Equity Ratio
• By undertaking the RFX project, Avco
adds
new assets to the firm with initial market
value $61.25 million.
– Therefore, to maintain its debt-to-value ratio,
Avco must add $30.625 million in new debt.
• 50% × 61.25 = $30.625
11
NPV
WACC
• Avco can add this debt either by reducing cash
and/or by borrowing and increasing debt.
– Assume Avco decides to spend its $20 million in cash
and borrow an additional $10.625 million.
• Because only $28 million is required to fund the project, Avco
will pay the remaining $2.625 million to shareholders through
a dividend (or share repurchase).
– $30.625 million − $28 million = $2.625 million
12
NPV
WACC
13
• The market value of Avco’s equity
increases by $30.625 million.
$330.625 − $300 = $30.625
• Adding the dividend of $2.625 million, the
shareholders’ total gain is $33.25 million.
$30.625 + 2.625 = $33.25
– Which is exactly the NPV calculated for the
RFX project
14
NPV
WACC
• 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:
Dt  d  Vt L
• Where d is the firm’s target debt-to-value ratio and VLt is
the levered continuation value on date t.
15
NPV
WACC
•
Implementing a Constant
Debt-Equity Ratio (cont'd)
• Debt Capacity
– VLt calculated as:
Value of FCF in year t  2 and beyond
Vt
L

FCFt  1 
L
t 1
V
1  rwacc
16
NPV
WACC
• Table 18.4
e.g. 47.41 = 18/1.068 + 18/1.1406 +18/1.218
17
NPV
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 Tax Shield)
 PV (Financial Distress, Agency, and Issuance Costs)
18
NPV
APV
• We first need to calculate the unlevered
value
• Then add the value of the tax shield plus
any other costs
• To calculate unlevered value need the
unlevered cost of equity
• The unlevered cost of equity will equal the
pre tax WACC
19
NPV
APV
rU  0.50  10.0%  0.50  6.0%  8.0%
rU

VU 
E
rE 
E  D
D
rD  Pretax WACC
E  D
18
18
18
18



 $59.62 million
2
3
4
1.08
1.08
1.08
1.08
20
NPV
APV
• The value of $59.62 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.
• The interest tax shield is equal to the interest paid
multiplied by the corporate tax rate.
21
NPV
APV
• Now value the tax shield
We know from slide 17 what the debt capacity is
1.84 = 30.62 x .06 and 1.84 x .4 = .73
22
• 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.
0.73
0.57
0.39
0.20
PV (interest tax shield) 



 $1.63 million
2
3
4
1.08 1.08
1.08
1.08
23
NPV
APV
• 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  PV (interest tax shield)  59.62  1.63  $61.25 million
– The NPV of the project is $33.25 million
• $61.25 million – $28 million = $33.25 million
– This is exactly the same value found using the WACC
approach.
24
NPV
APV
1. Determine the investment’s value
without leverage.
2. Determine the present value of the interest
tax shield.
a. Determine the expected interest tax shield.
b. Discount the interest tax shield.
3. Add the unlevered value to the present value
of the interest tax shield to determine the value
of the investment with leverage.
25
NPV
APV
• More complex to use as have to:
- compute unlevered cost of equity
- compute value of tax shield
• So when would you use it?
- easier to apply when a constant debt
equity ratio not going to be used
- explicitly includes earnings and costs due
to debt
26
NPV
FTE
• 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
– The cash flows to equity holders are then
discounted using the equity cost of capital.
27
NPV
FTE
• Free Cash Flow to Equity (FCFE)
– The free cash flow that remains after
adjusting for interest payments, debt issuance
and debt repayments
• The first step in the FTE method is to
determine the project’s free cash flow to
equity.
• Then discount them using the cost of
equity
28
NPV
FTE
29
NPV
FTE
• 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 RFX project are the
same as for Avco overall, we can use Avco’s equity cost of
capital of 10.0% to discount the project’s FCFE.
9.98
9.76
9.52
9.27
NPV (FCFE )  2.62 



 $33.25 million
2
3
4
1.10 1.10
1.10
1.10
30
NPV
FTE
1. Determine the free cash flow to equity of
the investment.
2. Determine the equity cost of capital.
3. Compute the equity value by discounting
the free cash flow to equity using the
equity cost
of capital.
31
NPV
FTE
• The FTE method offers some advantages.
– It may be simpler to use when calculating the value of
equity for the entire firm, if the firm’s capital structure
is complex and the market values of other securities
in the firm’s capital structure are not known.
– It may be viewed as a more transparent method for
discussing a project’s benefit to shareholders by
emphasizing a project’s implication for equity.
• The FTE method has a disadvantage.
– One must compute the project’s debt capacity to
determine the interest and net borrowing before
capital budgeting decisions can be made.
32