McGraw-Hill/Irwin
Principles of
Corporate Finance
Tenth Edition
Slides by
Matthew Will
Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved.

Topics Covered

After Tax WACC

Valuing Businesses

Using WACC in Practice

Adjusted Present Value

Your Questions Answered
19-2

Capital Project Adjustments
1. Adjust the Discount Rate

Modify the discount rate to reflect capital structure, bankruptcy risk, and other factors.
2. Adjust the Present Value

Assume an all equity financed firm and then make adjustments to value based on financing.
19-3

After Tax WACC
Tax Adjusted Formula
19-4
WACC
 r
D


Tc

D
V
 r
E
E
V

After Tax WACC
Example - Sangria Corporation
The firm has a marginal tax rate of 35%. The cost of equity is 12.4% and the pretax cost of debt is 6%.
Given the book and market value balance sheets, what is the tax adjusted WACC?
19-5

After Tax WACC
Example - Sangria Corporation - continued
19-6
Balance Sheet (Book Value, millions)
Assets 1,000 500 Debt
Total assets 1,000
500 Equity
1,000 Total liabilities

After Tax WACC
Example - Sangria Corporation - continued
19-7
Balance Sheet (Market Value, millions)
Assets 1,250 500 Debt
750 Equity
Total assets 1,250 1,250 Total liabilities

After Tax WACC
Example - Sangria
Corporation - continued
Debt ratio = (D/V) = 500/1,250 = .4 or 40%
Equity ratio = (E/V) = 750/1,250 = .6 or 60%
WACC
 r
D

( 1

Tc )

D
V
 r
E
E
V
19-8

After Tax WACC
Example - Sangria Corporation - continued
WACC
 r
D

( 1

Tc )

D
V
 r
E
E
V
WACC

.
06

( 1

.
35 ) .
 

.
124
 

.
090

9 .
0 %
19-9

After Tax WACC
Example - Sangria Corporation - continued
The company would like to invest in a perpetual crushing machine with cash flows of $1.731 million per year pre-tax.
Given an initial investment of $12.5 million, what is the value of the machine?
19-10

After Tax WACC
Example - Sangria Corporation - continued
The company would like to invest in a perpetual crushing machine with cash flows of $1.731 million per year pre-tax. Given an initial investment of $12.5 million, what is the value of the machine?
19-11
Cash Flows
Pretax cash flow
Tax @ 35%
After-tax cash flow
1.731
0.606
$1.125 million

After Tax WACC
Example - Sangria Corporation - continued
The company would like to invest in a perpetual crushing machine with cash flows of $1.731 million per year pre-tax. Given an initial investment of $12.5 million, what is the value of the machine?
NPV

C
0
 r
C

1 g
 
12 .
5

1 .
125
.
09

0
19-12

After Tax WACC
Example - Sangria Corporation – continued
Perpetual Crusher project
19-13
Balance Sheet - Perpetual Crusher (Market Value, millions)
Assets 12.5
5.0
Debt
Total assets 12.5
7.5
Equity
12.5
Total liabilities

After Tax WACC
Example - Sangria Corporation – continued
Perpetual Crusher project
After tax interest
 r
D
( 1

T
C
) D

.
06

( 1

.
35 )

5

.
195
Expected equity income

C
 r
D
( 1

T
C
) D

1 .
125

.
195

0 .
93
19-14

After Tax WACC
Example - Sangria Corporation – continued
Perpetual Crusher project
Expected equity return
 r
E
 expected equity income equity val ue

0 .
93

.
124 or 12.4%
7 .
5
19-15

Capital Budgeting
Valuing a Business or Project

The value of a business or Project is usually computed as the discounted value of FCF out to a valuation horizon (H).

The valuation horizon is sometimes called the terminal value.
19-16

Capital Budgeting

Valuing a Business or Project
PV

(
FCF
1
1
 r )
1

(
FCF
2
1
 r )
2

...

(
FCF
H
1
 r )
H

( 1
PV
H
 r )
H
19-17
PV (free cash flows)
PV (horizon value)

19-18
Valuing a Business
Example: Rio Corporation
1 Sales
2 Cost of goods sold
3 EBITDA (1-2)
4 Depreciation
5 Profit before tax (EBIT) (3-4)
6 Tax
7 Profit after tax (5-6)
8 Investment in fixed assets
9 Investment in working capital
10 Free cash flow (7+4-8-9)
PV Free cash flow, years 1-6
PV Horizon value
PV of company
Latest year
0
83.6
63.1
20.5
3.3
17.2
6
11.2
11
1
2.5
20.3
67.6
87.9
1
89.5
66.2
23.3
9.9
13.4
4.7
8.7
14.6
0.5
3.5
2
95.8
71.3
24.4
10.6
13.8
4.8
9
15.5
0.8
3.2
Forecast
3
102.5
76.3
26.1
11.3
14.8
5.2
9.6
16.6
0.9
3.4
4
106.6
79.9
26.6
11.8
14.9
5.2
9.7
15
0.5
5.9
5
110.8
83.1
27.7
12.3
15.4
5.4
10
15.6
0.6
6.1
6
115.2
87
28.2
12.7
15.5
5.4
10.1
16.2
0.6
6
113.4 (Horizon value in year 6)
7
118.7
90.2
28.5
13.1
15.4
5.4
10
15.9
0.4
6.8

Valuing a Business
Example: Rio Corporation – continued - assumptions
Assumptions
Sales growth (percent)
Tax rate, percent
WACC
Long term growth forecast
6.7
75.5
13.3
79.2
5
35%
9%
3%
7
74
13
79
14
7
74.5
13
79
14
7
74.5
13
79
14
4
75
13
79
14
4
75
13
79
14
4
75.5
13
79
14
3
76
13
79
14
Fixed assets and working capital
Gross fixed assets
Less accumulated depreciation
Net fixed assets
Depreciation
Working capital
95
29
66
3.3
11.1
109.6
38.9
70.7
9.9
11.6
125.1
49.5
75.6
10.6
12.4
141.8
60.8
80.9
11.3
13.3
156.8
72.6
84.2
11.8
13.9
172.4
84.9
87.5
12.3
14.4
188.6
97.6
91
12.7
15
204.5
110.7
93.8
13.1
15.4
19-19

Valuing a Business
Example: Rio Corporation – continued
FCF = Profit after tax + depreciation + investment in fixed assets
+ investment in working capital
FCF = 8.7 + 9.9 – (109.6 - 95.0) – (11.6 - 11.1) = $3.5 million
19-20

19-21
Valuing a Business
Example: Rio Corporation – continued
PV(FCF)

3.5
1.09


3 .
2
1.09
 
3 .
4
1.09
 
5 .
9
1.09
 
6 .
1
1.09
 
6 .
0
1.09

6

20 .
3

Valuing a Business
Example: Rio Corporation – continued
Horizon Value

PV
H

FCF
H wacc


1 g

6 .
8
.
09

.
03
PV(horizon value)

1

1.09

6

113 .
4

$ 67 .
6

113 .
4
19-22

Valuing a Business
Example: Rio Corporation – continued
PV(busines s)

PV(FCF)

PV(horizon

2 0 .
3

67 .
6

$87.9
million
value)
19-23

WACC vs. Flow to Equity
– If you discount at WACC, cash flows have to be projected just as you would for a capital investment project. Do not deduct interest.
Calculate taxes as if the company were allequity financed. The value of interest tax shields is picked up in the WACC formula.
19-24

WACC vs. Flow to Equity
– The company's cash flows will probably not be forecasted to infinity. Financial managers usually forecast to a medium-term horizon -- ten years, say -- and add a terminal value to the cash flows in the horizon year. The terminal value is the present value at the horizon of posthorizon flows. Estimating the terminal value requires careful attention, because it often accounts for the majority of the value of the company.
19-25

WACC vs. Flow to Equity
– Discounting at WACC values the assets and operations of the company. If the object is to value the company's equity, that is, its common stock, don't forget to subtract the value of the company's outstanding debt.
19-26

Tricks of the Trade

What should be included with debt?
– Long-term debt?
– Short-term debt?
– Cash (netted off?)
– Receivables?
– Deferred tax?
19-27

After Tax WACC

Preferred stock and other forms of financing must be included in the formula
19-28
WACC

( 1

Tc )
D
 r
D
V

P
V r
P

E
V r
E

After Tax WACC
Example - Sangria Corporation - continued
Calculate WACC given preferred stock is $25 mil of total equity and yields 10%.
Balance Sheet (Market Value, millions)
Assets 125 50 Debt
Total assets 125
25 Preferred Equity
50 Common Equity
125 Total liabilities
WACC

( 1

.
35 )
50
125

.
08

.
1104

11 .
04 %

25
125

.
10

50
125

.
146
19-29

Tricks of the Trade

How are costs of financing determined?
–
Return on equity can be derived from market data
–
Cost of debt is set by the market given the specific rating of a firm’s debt
–
Preferred stock often has a preset dividend rate
19-30

WACC & Debt Ratios
Example continued : Sangria and the Perpetual Crusher project at 20% D/V
19-31
Step 1 – r at current debt of 40% r

.
06 (.
4 )

.
124 (.
6 )

.
0984
Step 2 – D/V changes to 20% r
E

.
0984

(.
0984

.
06 )(.
25 )

.
108
Step 3 – New WACC
WACC

.
06 ( 1

.
35 )(.
2 )

.
108 (.
8 )

.
0942

After Tax WACC
Example - Sangria Corporation - continued
19-32

Investment & Financing Interaction
19-33

Investment & Financing Interaction
Adjusted Cost of Capital
(alternative to WACC)
M&M Formula --> ADR = r (1 - Tc L )
L = Debt / Value r = Cost of equity @ all equity
Tc = Corp Tax Rate alternative to WACC (almost same results)
19-34

Investment & Financing Interaction
Adjusted Cost of Capital
(alternative to WACC)
19-35
WACC
 r

Lr
D
T c


1
 r
1
 r
D
A



Capital Project Adjustments
1. WACC
2. Adjust the Discount Rate

Modify the discount rate to reflect capital structure, bankruptcy risk, and other factors.
19-36
3. Adjust the Present Value

Assume an all equity financed firm and then make adjustments to value based on financing.

Adjusted Present Value
APV = Base Case NPV
+ PV Impact

Base Case = All equity finance firm NPV

PV Impact = all costs/benefits directly resulting from project
19-37

Adjusted Present Value example:
Project A has an NPV of $150,000. In order to finance the project we must issue stock, with a brokerage cost of $200,000.
19-38

Adjusted Present Value example:
Project A has an NPV of $150,000. In order to finance the project we must issue stock, with a brokerage cost of $200,000.
Project NPV = 150,000
Stock issue cost = -200,000
Adjusted NPV - 50,000 don’t do the project
19-39

Adjusted Present Value example:
Project B has a NPV of -$20,000. We can issue debt at 8% to finance the project. The new debt has a PV Tax Shield of $60,000.
Assume that Project B is your only option.
19-40

Adjusted Present Value example:
Project B has a NPV of -$20,000. We can issue debt at 8% to finance the project. The new debt has a PV Tax Shield of $60,000. Assume that
Project B is your only option.
Project NPV = - 20,000
Stock issue cost = 60,000
Adjusted NPV 40,000 do the project
19-41

Adjusted Present Value
Example – Rio Corporation APV
10 Free cash flow (7+4-8-9)
PV Free cash flow, years 1-6
Pv Horizon value
Base-case PV of company
Latest year
0
2.5
19.7
64.6
84.3
Debt 51
1
3.5
50
3.06
1.07
2
3.2
49
3
1.05
PV Interest tax shields
APV
Tax rate, percent
Opportunity cost of capital
WACC (To discount horizon value to year 6)
Lomg term growth forecast
Interest rate (years 1-6)
After tax debt service
5
89.3
35%
9.84%
9%
3%
6%
2.99
2.95
Forecast
3
3.4
4
5.9
48
2.94
1.03
2.91
47
2.88
1.01
2.87
5
6.1
46
2.82
0.99
45
2.76
0.97
6
6
2.83
2.79
7
6.8
19-42

Adjusted Present Value
Example – Rio Corporation APV - continued
APV

Base case NPV

PV(Intere st tax shields)

84 .
3

5 .
0

$ 89 .
3 million
19-43