(1.09)6 1 + g  Where: FCFH+1 = Forecast FCF in year 7 = $6.8 million g = Long-term growth rate = 3% PVH = $67.6 million Total value = PV(FCF) + PVH = $20.3 million + $67.6 million = $87.9 million Therefore, the value of Rio Corporation is $87.9 million.

1. Principles of
Chapter 19 Corporate Finance
Tenth Edition
Financing and
Valuation
Slides by
Matthew Will
McGraw-Hill/Irwin Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved.

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

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

4. 19-4
After Tax WACC
Tax Adjusted Formula
D  E
WACC = rD × (1 − Tc) ×   +  rE × 
V   V

5. 19-5
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?

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

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

8. 19-8
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%
D  E
WACC = rD × (1 − Tc) ×   +  rE × 
V   V

9. 19-9
After Tax WACC
Example - Sangria Corporation - continued
D  E
WACC = rD × (1 − Tc) ×   +  rE × 
V   V
WACC = .06 × (1 − .35)( .40) + .124( .60)
= .090
= 9 .0 %

10. 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?

11. 19-11
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?
Cash Flows
Pretax cash flow 1.731
Tax @ 35% 0.606
After-tax cash flow $1.125 million

12. 19-12
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?
C1
NPV = C0 +
r−g
1.125
= −12.5 +
.09
=0

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

14. 19-14
After Tax WACC
Example - Sangria Corporation – continued
Perpetual Crusher project
After tax interest = rD (1 − TC ) D = .06 × (1 − .35) × 5 = .195
Expected equity income = C − rD (1 − TC ) D = 1.125 − .195 = 0.93

15. 19-15
After Tax WACC
Example - Sangria Corporation – continued
Perpetual Crusher project
expected equity income
Expected equity return = rE =
equity value
0.93
= = .124 or 12.4%
7.5

16. 19-16
Capital Budgeting
V

17. 19-17
Capital Budgeting
Valuing a Business or Project
FCF1 FCF2 FCFH PVH
PV = + + ... + +
(1 + r ) (1 + r )
1 2
(1 + r ) H
(1 + r ) H
PV (free cash flows) PV (horizon value)
In this case rr = wacc
In this case = wacc

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

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

20. 19-20
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

21. 19-21
Valuing a Business
Example: Rio Corporation – continued
3.5 3.2 3.4 5 .9 6.1 6.0
PV(FCF) = + + + + +
1.09 (1.09 ) 2
(1.09) (1.09) (1.09) (1.09)
3 4 5 6
= 20.3

22. 19-22
Valuing a Business
Example: Rio Corporation – continued
FCFH +1  6.8 
Horizon Value = PVH = =  = 113.4
wacc − g  .09 − .03 
1
PV(horizon value) = ×113.4 = $67.6
(1.09) 6

23. 19-23
Valuing a Business
Example: Rio Corporation – continued
PV(business) = PV(FCF) + PV(horizon value)
= 20.3 + 67.6
= $87.9 million

24. 19-24
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 all-
equity financed. The value of interest tax
shields is picked up in the WACC formula.

25. 19-25
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 post-
horizon flows. Estimating the terminal value requires
careful attention, because it often accounts for the
majority of the value of the company.

26. 19-26
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.

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

28. 19-28
After Tax WACC
 Preferred stock and other forms of financing
must be included in the formula
D  P  E 
WACC = (1 − Tc) × rD  +  × rP  +  × rE 
V  V  V 

29. 19-29
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
25 Preferred Equity
50 Common Equity
Total assets 125 125 Total liabilities
 50   25   50 
WACC = (1 − .35) × .08  +  × .10  +  × .146 
 125   125   125 
= .1104
= 11.04%

30. 19-30
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

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

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

33. 19-33
Investment & Financing Interaction
Adjusted Present Value
vs.
Adjusted Discount Rate

34. 19-34
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)

35. 19-35
Investment & Financing Interaction
Adjusted Cost of Capital
(alternative to WACC)
Miles and Ezzell
 1 +r A 
WACC = r − LrDTc 
1+ r  
 D 

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

37. 19-37
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

38. 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.

39. 19-39
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

40. 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.

41. 19-41
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

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

43. 19-43
Adjusted Present Value
Example – Rio Corporation APV - continued
APV = Base case NPV + PV(Intere st tax shields)
= 84.3 + 5.0 = $89.3million