Transcript Finance I - Universidade Nova de Lisboa

Corporate Finance
Lecture 10
Topics covered

Capital budgeting with debt
– APV
– FTE
– WACC

Beta and leverage
Capital budgeting with
debt

Adjusted Present Value Approach

Flows to Equity Approach

Weighted Average Cost of Capital
Method
Adjusted Present Value
APV = NPV + NPVF


The value of a project to the firm can be
thought of as the value of the project to an
unlevered firm (NPV) plus the present value
of the financing side effects (NPVF):
There are four side effects of financing:
–
–
–
–
The Tax Subsidy to Debt
The Costs of Issuing New Securities
The Costs of Financial Distress
Subsidies to Debt Financing
APV Example
Consider a project of the Pearson Company, the timing and size of
the incremental after-tax cash flows for an all-equity firm are:
–$1,000
0
$125
$250
$375
$500
1
2
3
4
The unlevered cost of equity is r0 = 10%:
NPV10%
NPV10%
$125
$250
$375
$500
 $1,000 



2
3
(1.10) (1.10) (1.10) (1.10) 4
 $56.50
The project would be rejected by an all-equity firm: NPV < 0.
APV Example (continued)
Now, imagine that the firm finances the project with
$600 of debt at rB = 8%.
 Pearson’s tax rate is 40%, so they have an interest
tax shield worth TCBrB = .40×$600×.08 = $19.20
each year.
The net present value of the project under leverage is:

APV = NPV + NPV debt tax shield
4
$19.20
APV  $56.50  
t
(
1
.
08
)
t 1
APV  $56.50  63.59  $7.09
So, Pearson should accept the project with debt.
APV Example (continued)


Another way to calculate the NPV of the loan.
Previously, we calculated the PV of the interest tax
shields. Now, let’s calculate the actual NPV of the loan:
$600  .08  (1  .4) $600
NPVloan  $600  

t
4
(1.08)
(1.08)
t 1
NPVloan  $63.59
APV = NPV + NPVF
APV  $56.50  63.59  $7.09
4
Which is the same answer as before.
Flows to Equity


Discount the cash flow from the project to the
equity holders of the levered firm at the cost
of levered equity capital, rS.
There are three steps in the FTE Approach:
– Step One: Calculate the levered cash flows
– Step Two: Calculate rS.
– Step Three: Valuation of the levered cash
flows at rS.
Step One: Levered Cash Flows
Since the firm is using $600 of debt, the equity holders only
have to come up with $400 of the initial $1,000.
 Thus, CF0 = –$400
 Each period, the equity holders must pay interest expense.
The after-tax cost of the interest is B×rB×(1 – TC) =
$600×.08×(1 – .40) = $28.80
CF3 = $375 – 28.80 CF4 = $500 – 28.80 – 600
CF2 = $250 – 28.80
CF1 = $125 – 28.80

–$400
0
$96.20
1
$221.20
$346.20
–$128.80
2
3
4
Step Two: Calculate rS
B
rS  r0  (1  TC )( r0  rB )
S
B
B
To calculate the debt to equity ratio, , start with
S
V
4
$125
$250
$375
$500
19.20
PV 




2
3
4
t
(1.10) (1.10) (1.10) (1.10)
(
1
.
08
)
t 1
P V = $943.50 + $63.59 = $1,007.09
B = $600 when V = $1,007.09 so S = $407.09.
$600
rS  .10 
(1  .40)(.10  .08)  11.77%
$407.09
Step Three: Valuation

Discount the cash flows to equity holders at
rS = 11.77%
–$400
$96.20
$221.20
$346.20
–$128.80
0
1
2
3
4
$96.20
$221.20
$346.20
$128.80
PV  $400 



2
3
(1.1177) (1.1177) (1.1177) (1.1177) 4
PV  $28.56
WACC Method for Pearson
S
B
rW ACC 
rS 
rB (1  TC )
SB
SB


To find the value of the project, discount the unlevered
cash flows at the weighted average cost of capital.
Suppose Pearson’s target debt to equity ratio is 1.50
B
1.5S  B
1.50 
S
S
B
1.5S
1.5
 1  0.60  0.40


 0.60
SB
S  B S  1.5S 2.5
rW ACC  (0.40)  (11.77%)  (0.60)  (8%)  (1  .40)
rW ACC  7.58%
Valuation for Pearson using
WACC

To find the value of the project, discount the
unlevered cash flows at the weighted
average cost of capital
NPV  $1,000 
$125
$250
$375
$500



(1.0758) (1.0758) 2 (1.0758)3 (1.0758) 4
NPV7.58% = $6.68
A Comparison of the APV,
FTE and WACC



All three approaches attempt the same task:valuation
in the presence of debt financing.
Guidelines:
– Use WACC or FTE if the firm’s target debt-to-value
ratio applies to the project over the life of the
project.
– Use the APV if the project’s level of debt is known
over the life of the project.
In the real world, the WACC is the most widely used
by far.
Summary: APV, FTE, and
WACC
APV
Initial Investment
All
Cash Flows
UCF
Discount Rates
r0
PV of financing effectsYes
WACC
FTE
All
Equity Portion
UCF
rWACC
LCF
rS
No
No
Which approach is best?
Use APV when the level of debt is constant
Use WACC and FTE when the debt ratio is constant
– WACC is by far the most common
– FTE is a reasonable choice for a highly levered firm
Estimating the discount
rate






Firm A wants to finance a new project with a B/S
ratio of 1/3. Its borrowing rate is 10%.
Firm B in the same industry has a B/S ratio of 2/3.
The beta of its equity is 1.5. Firm B’s borrowing rate
is 12%.
Corporate tax rate = 40%.
Market risk premium = 8.5%
Rf = 8%
What is the discount rate for Firm A’s new project?
Estimating the discount
rate

Firm B’s cost of equity

Firm B’s cost of capital if unlevered
rs  R f   * RM  R f 
20.75%  8%  1.5 * 8.5%
B
rs  r0  (1  Tc )( r0  rB )
S
2
20.75%  r0  (1  0.4)( r0  0.12)
3
r0  0.1825
Estimating the discount
rate
APV
FTE
r0  0.1825
rs  r0 
B
(1  Tc )( r0  rB )
S
1
0.1825  (1  0.4)( 0.1825  0.10)  0.199
3
WACC
S
B
rW ACC 
rS 
rB (1  TC )
SB
SB
3
1
* 0.199  * 0.1* (1  0.4)  0.16425
4
4
Beta and Leverage
Riskless debt
Without
corp tax
With
corp tax
Risky debt
Debt
 β Debt
Asset
Equity

 β Equity
Asset
β Asset 
Beta and Leverage
Riskless debt
Without
corp tax
With
corp tax
Equity
β Asset 
 β Equity
Asset
Risky debt
Debt
 β Debt
Asset
Equity

 β Equity
Asset
β Asset 
Beta and Leverage
Riskless debt
Risky debt
Without
corp tax

Debt
β Equity  1 
 Equity
With
corp tax

β Asset

Debt
 β Debt
Asset
Equity

 β Equity
Asset
β Asset 
Beta and Leverage
Riskless debt
Risky debt
Without
corp tax

Debt

β Equity  1 
 Equity
With
corp tax

β Asset

β Equity  β Unleveredfirm 
B
(1  TC )β Unleveredfirm 
SL
Debt
 β Debt
Asset
Equity

 β Equity
Asset
β Asset 
Beta and Leverage: with Corp.
Taxes

In a world with corporate taxes, and riskless
debt


Debt
β Equity  1 
 (1  TC ) β Unleveredfirm
 Equity

>1 for a levered firm
β Equity  β Unleveredfirm
Beta and Leverage
Riskless debt
Risky debt
Without
corp tax

Debt
β Equity  1 
 Equity
With
corp tax β Equity  β Unleveredfirm 
(1  TC )β Unleveredfirm 
B
SL

β Asset

Debt
 β Debt
Asset
Equity

 β Equity
Asset
β Asset 
β Equity  β Unlevered firm 
(1  TC )(β Unlevered firm
B
 β Debt ) 
SL
Beta and leverage:
Example







A firm considers to invest $1 million in a new
project.
The projct is expected to bring a perpetual
unlevered after-tax cash flow of $300,000 a year.
The target debt to equity ratio for this project is 1.
The three competitors in the same industry have
unlevered betas of 1.2, 1.3, 1.4.
The risk free rate is 5%. The market premium is
9%.
The corporate tax rate is 34%.
What is the NPV of the project?
Beta and leverage:
Example
1. Average unlevered beta:
(1.2+1.3+1.4)/3=1.3
2. Levered beta:


Debt
β Equity  1 
 (1  TC ) β Unleveredfirm
 Equity

(1+1/1*(1-0.34))*1.3=2.16
3. Cost of levered equity Rs
0.05+2.16*0.09=0.244
Beta and leverage:
Example
4. Rwacc
rwacc
B
S
  rb  (1  Tc )   rs
V
V
½*0.05*0.66+1/2*0.244=0.139
5. NPV
-1,000,000+300,000/0.139=1,158,273